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# Area Of A Rectangle With A Semi Circle Cut Out

If you specify a Point, the text will start with its top left corner at that Point and simply stretch out to the right. What is the 2D cross section of this image when cut horizontally? 2D cross sections of 3D shapes Semi-Circle. Find the area of the circles. What is the area of this. The two small circles have their centers on AC and just touch at O, the center of the large circle. An interesting aspect of the golden rectangle is that when the square section is removed, the remainder is another golden rectangle. This is also the equation for a circle centered on the origin on the coordinate plane. I enlarged it using Microsoft Word to make it the size of the page basically. You can draw a Pie shape and drag its modifier to create a semi-circle. ) Blue rectangle with yellow oval inside (ikea) Blue half rectangle cut diagonal with white P (sap) Red shapes outlining a blank A (adobe) Red rectangle with white ‘s (campbells) Colourful fan shape, sort of like a peacock shape (nbc) Circle with red white and blue (pepsi) Red modified ‘S’ (suzuki). Area of an arch given angle. As i have finished up college i have no lecturers to ask how you would. If the width of the rectangle is the diameter of the circle, then r is half of that. The largest possible triangle that can be inscribed inside a semicircle is the right angled triangle whose hypotenuse is the diameter of the semicircle, and whose other two sides are equal. com is an awesome resoource for pre-school through Kindergarten aged kiddos. ) Measure the height of your PVC fittings and the width of THE TOP PIECE of plywood/particle board. If the graph is that of a semi-circle of radius : from to , the area is. I have a feeling that I have erred in the differentiation. The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common. This formula is also valid for cylinders. To find area of inscribed circle in a triangle, we use formula S x r = Area of triangle, where s is semi-perimeter of triangle and r is the radius of inscribed circle. This restaurant stands out like a beacon on your approach. Start studying Circles/ Perimeter and Area of Composite Figures. Area and Perimeter of Composite Figures. So let me write that, so diameter, the diameter here is 16 millimeters and they want us to figure out the area, the area of the surface of this candy. Radius of circle = 8 cm − 4 cm = 4 cm. Because the ring is hollow, all of its mass has to sit at a distance R from the center; hence, you have =R 2 and I = MR 2. Checkpoint 4 4-71: Math 8 Name _____ Period ____ Area and Perimeter of Circles and Complex Figures checkpoint 4 area and perimeter page 3 11. A = πr×r; A = πr 2; Using Areas of Triangles. The rectangle has a length of m and a width of m. If the text doesn't fit in to bounds of the rectangle, then it'll be cut off, as you see from the screenshot. (You might even want to find a tile floor, and at least pretend the tiles are 1 foot square. so the area of a semi-circle is just half of the value of the above formula. -Verify that the maximum value for A (x) on [0, r] is 2 r 2. Spread a thin layer of flour evenly over the surface of your kitchen table or other large flat surface, and cover the rolling pin in flour as well. Working out the Area of the Rectangle involves using the Circumference of the circle which the Rectangle is wrapped around. Find the area of the object, in square feet. Members-Only Access. How does one compute the area of intersection between a triangle (specified as three (X,Y) pairs) and a circle (X,Y,R)? I've done some searching to no avail. If the dimensions. One using geometry, and the other using calculus. 7 In the given figure, the area of the shaded region between two concentric circles is 286. Calculate the measure of the length of the circumference and area of a circle. The formula for finding the area of a full circle is πr 2, where "r" represents the radius of the circle. mrmaisonet 133,764 views. The area is 48 inches times 36 inches, so the area is (48 inches times 36 inches is) 1,728 inches squared. For centroid, moments of inertia, polar moments of inertia, and radius of gyration, click on one of the following shapes:. It is an online Geometry tool requires radius length of a circle. Cut out and attach the fins Cut out the two fin units. a half of a circle; an object or arrangement of objects in the form of a half circle…. To calculate the area of a triangle, find the width and height, multiply them together and divide by 2. Given that the perimeter of the figure is 58 cm, calculate : (i) the dimensions of the rectangle. To do this, you will need to find the area of the rectangle, then find the area of the half circle, and add them together. Find the area of the circle. Discovering the Area Formula for Circles. Area of semi-circle formula is derived from the formula of a circle. Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm x 7 cm. Find missing dimensions of the rectangle. So, split it into four shapes for obtaining the total area of the running track. Area of a rectangle with a semi circle cut out. Then play a game. Find the area of the circles. The trick is to make lines go considerably out of the circle like this: For some reason it doesn't work if they cross just a little. The area of the figure will be the sum of the areas of the rectangle and the semicircles. I'm going to create circular hole in rectangle box which dimensions and image are give below. Central angle A central angle has its vertex at the …. For centroid, moments of inertia, polar moments of inertia, and radius of gyration, click on one of the following shapes:. Using this formula, we can find radius of inscribed circle which hence can be used to find area of inscribed circle. Area of a Semi-Circle: A semi-circle is half of a circle. There is a rather significant issue with using SVG-defined clip paths though: they are pinned to the upper left of the document. I cannot use a black rectangle with a white circle on top of it because the half circle has to be transparent and let the background show through. Now you have all the necessary tools for finding moments of inertia of composite areas. If the number of sectors cut from the circle is increased, the parallelogram will eventually look like a rectangle with length equal to πr and breadth equal to r. Semi-circles are drawn on the lengths as shown. You can use the area of a rectangle in order to help you calculate the area right-angled triangle. find the area of the circle with radius 3 cm below. Find missing dimensions of the rectangle. How might I go about measuring the area of the smaller part of the circle cut off by the line? Area of circle cut by line Intersection between a rectangle and. Edit a shape. Semi-circles are drawn on the lengths as shown. Area of semi-circle = 3. the line is the diameter of the semi-circular end. Area of a Semi-Circle: A semi-circle is half of a circle. An easy to use, free area calculator you can use to calculate the area of shapes like square, rectangle, triangle, circle, parallelogram, trapezoid, ellipse, and sector of a circle. (Use π = 22/7) [CBSE 2013]. To find area of inscribed circle in a triangle, we use formula S x r = Area of triangle, where s is semi-perimeter of triangle and r is the radius of inscribed circle. Using Smart dimension tool, apply the given length (100 mm) and breadth (60 mm). Can be solved with calculus to get the width of the window = 1. I have a feeling that I have erred in the differentiation. The diameter of the semi-circle is 13 cm. If it is an irregular reservoir, segment it into the surface shape of a rectangle and up to four triangles. How to find the area of a rectangle: The area of a rectangle can be found by multiplying the base times the height. Side of polygon given area. A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. ABC is an isosceles triangle with AB = AC. A circle is fomed on a piece of papv by a he that is the same distance from a spccifrc point called the center of the circle. square meter). Area and Perimeter of Composite Figures. The perimeter of a plane 2-D figure is the length of the outer periphery of the figure. Circle Facts. )] This Pythagorean equation of a circle ends up being an immensely useful tool to use on the GMAT. 6 square feet. Semi-circle on a rectangle 18. A circle of radius 0. The program will prompt user to enter the radius and based on the input it would calculate the values. It is an online Geometry tool requires two length sides of a rectangle. If one was to choose random numbers from a uniform distribution within the bounding rectangle then the ratio of those falling within the circle to the total number will be the ratio of the area of the circle to the rectangle. We are to determine the largest rectangle that can be inscribed in a circle—meaning the value of its area is larger than the area of other rectangles that could be inscribed in the circle. Compute the arc angle by inserting the values of the arc length and radius. The centroid of the rectangle is the point at which its diagonals intersect. As shown in the figure below: Centroid of Semi-circle Formula: $$\bar{Y}= \frac{4R}{3π }$$ Example. What STATE/NATIONAL STANDARD(s) am I addressing in this lesson?. Remember to include units. Area of remaining cardboard = Area of rectangle – Area of two semicircle. The dimensions are m = 80. The word circle is derived from the Greek word kirkos, meaning hoop or ring. The area of a square that has a side-length of 1 cm is 1 square centimetre (or 1 cm 2 ). … I’m probably just missing something, but I’m not finding an obvious way to get the path to move along with the element it’s applied to, like the way clip-path works if you use a basic element right in the CSS. As i have finished up college i have no lecturers to ask how you would. 5 cm squared) from the area of the square (100 cm squared) to determine the area outside the circle, but still within the square. The unit of dimension of the second moment of area is length to fourth power, L 4, and should not be confused with the mass moment of inertia. Sudden infant death syndrome c. Area is measured in square units such as square inches, square feet or square meters. I guess [email protected] mentioned, there is techinically edge so I couldn't project the on YZ plane. Step 2: Divide the circumference in half. The picture below illustrates how the formula for the area of a cylinder is simply the sum of the areas of the top and bottom circles plus the area of a rectangle. Tracing paper may be used. The calculation for the perimiter of a circle = Pi X diameter, which for a whole circle with radius 2" would be 4 X Pi = 12. To find the perimiter, you need the circumference of the circle + the 2 sides of the rectangle that are exposed (each. What is the perimeter of the rectangle? Imagine cutting out a circle which is just contained inside a semicircle. The links will open a new browser window. 14 ft 2; Area of semi-circle = 3. Again, there are several ways to work out the area of the path in this example. Subtract the area of the circle (78. 5 mm 2, 4 mm 2, 6 mm 2, 10 mm 2, 16 mm 2. From the formula A = πr 2, we see that we can find the radius of a circle by dividing its area by π and then get the positive square-root. Area of a Semi-Circle: A semi-circle is half of a circle. The length of the rectangle is 17 cm. I will encourage students to extend their understanding of where the formula for finding the area of a circle comes from by using other circles. Which is the leading cause of death in infants younger than 1 year in the United States? a. the area of this rectangle would be If I find the mass of the paper cut out circle, the area of the circle will be:. We are asked to consider a fixed circle and all rectangles which can be inscribed in the circle. You add the area of the square with the area of the semi. How to Find the Area of a Shaded Region. Round Corner Calculator. A common problem in geometry class is to have you calculate the area of a circle based on provided information. Area and Perimeter of Circle and Semi-Circle Perimeter. The perimeter and area of triangles, quadrilaterals (rectangle, parallelogram, rhombus, kite and square), circles, arcs, sectors and composite shapes can all be calculated using relevant formulae. Students might forget to divide the area of the circle by 2 to find the area of the half-circle. Area and Perimeter of a circle. Sketch the curve y2 = x(x − 4)2 and ﬁnd the volume of the solid of revolution formed when the closed loop of the curve is rotated. The circumference of a circle is 2 x pi x r, pi being 3. If BO = OC, find the area of the shaded region. The area cut oﬀ by the x-axis and the curve y = x2 − 3x is rotated about the x-axis. This is one of those cases where sexual. The segment smaller than the semi-circle is called the minor segment and the segment larger than the semi-circle is called the major segment. the line is the diameter of the semi-circular end. A graph of a circle is formed when an arc is drawn from a fixed point (called the centre of the circle) in such a way that any point on the curve is the same distance from the centre. first we need to draw a huge circle on a chart paper with unknown radius. Name two ways that can be used to find the area of the rectangle. with squares cut out of the corners of the sides, as shown. Working out the Area of the Rectangle involves using the Circumference of the circle which the Rectangle is wrapped around. Extend the rectangle until it snaps to the guide (the rectangle should now cover half the circles). Hence, the width w and height h of the rectangle is 2x and 2y and its area is To eliminate y in eq. Press "CTRL+X" at once to cut the section from the pdf or right click the selected area and click "Cut" from the drop down menu. Area of a rectangle = Length x Width x Height (same for parallelogram) Area of a triangle = 1/2 Base x Height or S^2 times root four. Area of Part of a Circle Given a circle of radius a, cut out a tab of height b. I enlarged it using Microsoft Word to make it the size of the page basically. Visit https://maisonetmath. 5 (explain how you do it please! Thanks!) asked by Matt on May 10, 2011; calculus- optimization. Calculate the area of each part, giving your answer correct to 2 decimal places. The smaller side of the rectangle is (a) 30 cm. To calculate the area of a circle, find the diameter, divide it by 2, square that and multiply by pi (3. 14 b) Work out the circumference of the base of the table. Enter one value and choose the number of decimal places. 10 per square meter How much does Sam earn cutting this area: Let's break the area into two parts: Part A is a square:. The diameter of the circle is 4 ft. 571 = 200 - 157. Discovering the Area Formula for Circles. Determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass. Volume of Cubes and Rectangular Prisms. Area of a Circle Segment Given the Central Angle Definition: The number of square units it takes to fill a segment of a circle Try this Drag one of the orange dots that define the endpoints of the segment. Centroids of Plane Areas - Square, rectangle, cirle. Find the area of the object, in square feet. Area of a sector. To find the segment area, you need the area of triangle IDK so you can subtract it from the area of sector IDK. Although the majority of people in the West live in stable monogamous partnerships, it is a recent phenomenon as far as the human race is concerned. It’s easy to work out the perimeter of a shape with straight edges, such as a square, because you simply add the lengths of each edge together. Area of a Semicircle Calculator A semicircle is nothing but half of the circle. After a lot of research,  I learned that unemployment is really created and not genuine. Switching the input values above changes the layout and gives. I cannot use a black rectangle with a white circle on top of it because the half circle has to be transparent and let the background show through. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. Favorite Answer. We look at a number of examples of circle and semi-circle functions, sketch their graphs, work out their domains and ranges, determine the centre and radius of a circle given its function, etc. If you know the diameter of your circle, you can use a standard formula to figure out the width of the fabric cut needed to make a tube. The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common. Christmas Cut-out Age 11 to 14 Short Challenge Level: Weekly Problem 52 - 2017 A rectangle with area $125\text{cm}^2$ has sides in the ratio $4:5$. The area of a circle is 3. Then the sum of the areas of the two semicircles is half the area of (O). The attribute clip-path references a element with a single rect element. The area of a triangle can be defined as 1/2 * base * height or just 1/2 bh. Jump to Hero Section Vinter-eventyr På Glow er der er altid nye vidunderlige eventyr at opleve i det 6000 kvadratmeter smukke lysunivers. I've got a plane spaced out in front of my face with a circle on it, and I am going to use the Lofted Boss / Bass from my rectangle face to the circle giving the face a curved surface up to the circle. Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser 11. 7, there are not many differences for users of PS 8 or earlier versions. Rectangle Area Definition. 57% of the original square. We start out with a unit semi-circle: Q: What is the area of the red shaded region below bounded by: I could think of two alternative ways of solving. Nearby Single Family homes range from $269K to$1M list price, with average value of \$184/Sqft and average size of 2,594 Sqft. So radius of the semicircle = We have to find the perimeter of the shaded region. Find the radii of the circles. Stewart did not invent the phrase -- search books. Two semi-circles cap a square at one end as in the diagram below. Perimeter of an isosceles trapezoid Let a and b be the lengths of the parallel sides. You can use the area of a rectangle in order to help you calculate the area right-angled triangle. Once you have reached the bottom, adhere the top end to it to secure the circular frame. There are two ways in which you can create a semi-circle: You can draw a Circle and intersect it with a Rectangle to create a semi-circle. Start studying Circles/ Perimeter and Area of Composite Figures. Now you can cut/cover the circle at any point to make. the semicircle is 4cm and squere is 4cm. Given that the perimeter of the figure is 58 cm, calculate : (i) the dimensions of the rectangle. Give an example: “This is a circle. The circle cutout will be used as a table top. I only want the sides of the circle. A circle of radius 8 cm is cut into 6 parts of equal size, as shown in the diagram. Area of a triangle calculation using all different rules, side and height, SSS, ASA, SAS, SSA, etc. There is a rather significant issue with using SVG-defined clip paths though: they are pinned to the upper left of the document. Or essentially the area of this circle. This is a good place for a break. What is the perimeter of a semi-circle with a diameter of 8cm? Step 1: Find the circumference of the full circle. Area of a rectangle with a semi circle cut out. You cut out a shape within an existing shape so that the layers underneath show through. For any other polygon, if you simply add the dimensions of each side, you can calculate the perimeter. The value of the area A at x = 100 is equal to 10000 mm 2 and it is the largest (maximum). Required area is equivalent to finding the area of largest possible triangle that can be inscribed in the semi circle. Hence the area of a semi-circle is just the half of the area of a circle. 18400 + π × 20 2 = 18400 + 1256. What is the formula for finding area of a rectangle? Q. Now we all know that the area of a rectangle is its length multiplied by its height. To find the surface area of a prism (or any other geometric solid) we open the solid like a carton box and flatten it out to find all included geometric forms. Question: A piece of plexiglass is in the shape of a semi-circle with a radius 2 m. Create a new master shape. !Shown below is a compound shape made from a rectangle and semi-circle. Give your answer correct to 3 significant figures. 0 mm and n = 40. Area of a parallelogram given sides and angle. Just enter the value of radius in the area of a semicircle calculator to compute the semicircle area within a blink of an eye. Find the area of the largest rectangle that can be inscribed inside a semi circle with a radius of 10 units. The areas between the semi-circles and the circles form crescents. 6 square inches. The area is 48 inches times 36 inches, so the area is (48 inches times 36 inches is) 1,728 inches squared. Subtract area of circles from rectangle. Semicircle definition is - a half of a circle. [The more general equation for a circle with a center (a,b) is (x-a)^2 + (y-b)^2 = r^2. PDFill PDF Drawing: Rectangle, Circle and Basic Shape Tool (See Example PDF and Example PDFill Project File ) You can use this tool to draw rectangle, square, round corner, circle, ellipse, arc and pie, and more basic shapes into PDF document. total area is to be 9,000 square feet? 14. If the ring were cut out better, the inside pieces would not be disturbed. " Such polygons have four sides, and you can determine the area by multiplying the length by the width. A diagram is shown with a circle, centred on a rectangle with given dimensions. Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm x 7 cm. Find the area of the shaded portion. Concrete Paver Circle Pattern Packages provide the ability to add complete circles, half circles, or fan. meter), the area has this unit squared (e. This calculator will calculate the area of a circle given its radius, using the famous formula area = pi times r squared. If you want to create a more advanced diagram like overlapping circles, an organizational chart, or a flowchart, you can create a SmartArt graphic instead of drawing each shape manually. A semi-circular portion with BC as diameter is cut off. So here, instead of area, we're asked to find the arc length of the partial circle, and that's we have here in this bluish color right over here, find this arc length. The links will open a new browser window. A rectangular paperboard 31in long and 22 wide has a semicircle cut out of it, as shown below. A doorway is decorated as shown in the figure. The diameter of the semi-circle is 13 cm. Find the perimeter of a square with side length 5 in. As i have finished up college i have no lecturers to ask how you would. A homemade texture game: a square cut out of sandpaper, a circle made with yarn, a triangle cut out of fake fur, etc. πR2 = Area I'm going to use inches here: Radius is 84" = surface area of 22,156" squared. The circumference of a circle is 2 x pi x r, pi being 3. Stewart did not invent the phrase -- search books. You could view the path as four separate rectangles, calculate their dimensions and then their area and finally add the areas together to give a total. Let's say the radius of the semi-circle is 5 centimeter (2. Therefore, we need to use another method for determining the area. We are asked to find this area, but we may also have to identify the rectangle which achieves this area along the way. Area of Intersecting Circles - Calculate area of intersecting circles; Area Survey App - Online calculator app to make an exact plot of a surveyed area - like a room, a property or any 2D shape; Area Units Converter - Convert between area units; Centroids of Plane Areas - Square, rectangle, cirle. Find the area enclosed by the track. The program will prompt user to enter the radius and based on the input it would calculate the values. Give your answer correct to 3 significant figures. = Area of rectangle - Area of semi-circle #20 14 72 2277 # = - ## =280 77- ] Hence, area of remaining part =203 cm 3. !The diagram shows a rectangle with a circle cut out. On the Home tab, in the Tools group, click the arrow next to Rectangle, and then do one of the following: To draw a rectangle, select the Rectangle tool. Semicircle Calculator. The diameters of the two circles are in the ratio 3 : 4 and the sum of the areas of the circles is equal to the area of a circle whose diameter is 36 cm. If the difference of the radii of the two circles is 7 cm, find the sum of their radii. 5 cm squared) from the area of the square (100 cm squared) to determine the area outside the circle, but still within the square. There is one face and sides. Formulas, explanations, and graphs for each calculation. Each calculator is associated with web pageor on-page equations for calculating the sectional properties. Review basic shapes with the group: circle, triangle, square, rectangle, oval, semi-circle. This is also the equation for a circle centered on the origin on the coordinate plane. 5 mm 2, 4 mm 2, 6 mm 2, 10 mm 2, 16 mm 2. first we need to draw a huge circle on a chart paper with unknown radius. The following links are to calculators which will calculate the Section Area Moment of Inertia Properties of common shapes. The extrude needs to follow the curve of the surface and will not go thru the wall. Maximizing Window Area Date: 02/24/97 at 20:37:16 From: pierre Subject: Related rates The business office wants to put in Norman windows, which are windows in the shape of rectangles capped by a semicircle. Take the other cake and cut a smaller circle for the middle part. 14(1 ft (1 ft); Area of Circle = 3. Not a member? Join Now. A circle does not have a base and height like a triangle or rectangle. What is the ESSENTIAL QUESTION that I want my students to be able to answer? Why are circles important in our lives? What are some applications of circles in our world today? 2. What STATE/NATIONAL STANDARD(s) am I addressing in this lesson?. A rectangular piece of dimensions 3 cm × 2cm was cut from a rectangular sheet of paper of dimensions 6 cm × 5cm (Fig. If you have a hemispherical object then it has a base which is a circle of radius r. Much like the top of a water bottle. If the area of the rectangle is 168 cm 2 and ratio of radius of the circle and breadth of the rectangle is 19 : 2. Area of a rectangle is length times width, and our length and width are 3 feet and 4 feet, or 36 inches and 48 inches. So let me write that, so diameter, the diameter here is 16 millimeters and they want us to figure out the area, the area of the surface of this candy. Thus, we know that the white area is four times the area of one of the white circles. Go to sketch and select rectangle button from command manager. The circumference of a circle is 2 x pi x r, pi being 3. Let's say the radius of the semi-circle is 5 centimeter (2. Area of a rectangle with a semi circle cut out. The links will open a new browser window. a) Work out the circumference of the top of the table. Be sure to include the correct unit in your answer. This is a good place for a break. If you specify a Point, the text will start with its top left corner at that Point and simply stretch out to the right. What is the formula for finding area of a rectangle? Q. The length of the rectangle is 17 cm. Just as calculating the circumference of a circle more complicated than that of a triangle or rectangle, so is calculating the area. Subtract area of circles from rectangle. Cut out and shape the rocket body Cut out the rectangle. Usually, all you have to do is subtract the white area from the area of the whole figure are to get the gray. Find out what the radius, diameter and circumference are, how to measure the area of a circle, what a circle chord, sector and segment are and much more. 14 (constant) in the program. Area (Polygon, Triangle, Circle, Square) Area is the amount of space inside a two-dimensional shape. The running track displays two rectangles and two semi circles. Area of an ellipse. Think of a 24" circle with the outer 2" cut out - this is the ring. His section is half circle , upper and higher section of half cylinder. I have a feeling that I have erred in the differentiation. So, split it into four shapes for obtaining the total area of the running track. My fifth result was to a book from 1845 on sacred architecture. The largest possible triangle that can be inscribed inside a semicircle is the right angled triangle whose hypotenuse is the diameter of the semicircle, and whose other two sides are equal. Arc Length and Area of a Sector Reporting Category Polygons and Circles. Free GK Alerts- JOIN OnlineGK to 9870807070 24. The length of the rectangle is 15 cm. Thanks for the help + time. )] This Pythagorean equation of a circle ends up being an immensely useful tool to use on the GMAT. We know the formula to calculate area of a circle is πr^2, by dividing this by 2 we will get the area of a semicircle. An easy to use, free area calculator you can use to calculate the area of shapes like square, rectangle, triangle, circle, parallelogram, trapezoid, ellipse, and sector of a circle. Don't forget to multiply by 2 Total Dark Red Area = 128 -100. To make a mathematical model we draw a diagram and label its parts. The area of a n equilateral triangle is 49 cm 2. Numbers Skateboard Complete Mariano Edition 6 Series 1 8. Sudden infant death syndrome c. A little puzzle to round the month out. Sol: The base of the cone will be circle inscribed in a face of the cube and its height will be equal to an edge of the cube. A common beginning geometry problem is calculating the area of standard shapes such as squares and circles. Area of a rectangle with a semi circle cut out. Rectangle = x+18 Square = x-9 Since we know that the area is equivlent we muplitply them together (x+18)(x-9) Use Quadrtic Formula: in A=1, b=9, c=-162---> take out the subbtraction--> Simplify x = 9 Hence the length of the retangle is 18+(9)=27cm and the width is 9cm. Just enter the value of radius in the area of a semicircle calculator to compute the semicircle area within a blink of an eye. Sum of the angles of a triangle is 180 degrees. A semi-circular portion with BC as diameter is cut off. So let's see. Although the screenshots for this beginners' tutorial were done with Photoshop v. A circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5. The chord AB of a circle is 90 cm and the distance from the center is 40 cm. Area and circumference of a circle often gives our students their first taste of geometry during the year. What is the area of the rug? d = 2 ft; r = 1 ft; Area of circle = 3. A faster way would be to work out the area of the whole shape and the area of the internal rectangle. 5 cm 2, equaling 21. Then draw a rectangle in the graphics area. Formulas, explanations, and graphs for each calculation. circum = 2pi r = 2 pi (15) = 30 pi = 94. The area of the shaded L-shaped region is A) 7 B) 10 C) 12. Area of Two Rectangles. An intermediate step in this learning process is combining the two shapes. My goal was to add a m. Cut out and attach the fins Cut out the two fin units. calculate surface area by using double integral. A half cylinder of radius R and height h.   Right from the origin of man people were engaged in different types of jobs. !Work out the shaded area. In this tutorial, we'll learn the essentials of working with shapes and Shape layers in Photoshop! We'll start by learning how to use the five geometric shape tools - the Rectangle Tool, the Rounded Rectangle Tool, the Ellipse Tool, the Polygon Tool, and the Line Tool. This will be the body tube of the rocket. A diagram is shown with a circle, centred on a rectangle with given dimensions. Find the area of the largest rectangle that can be inscribed inside a semi circle with a radius of 10 units. Find the area of a circle or simple fraction of a circle, e. Cutting a semi-circle. If you are advanced SolidWorks user please avoid it. (Take π = 22/7). We are to determine the largest rectangle that can be inscribed in a circle—meaning the value of its area is larger than the area of other rectangles that could be inscribed in the circle. One diagonal cuts the square into two 45-45-90 special triangles. Fill the circle with radius r with concentric circles. One way to compute the area would be split the area into vertical strips and integrate with respect to x: Area = y dx. Therefore, the area of a circle of radius r, which is twice the area of the semi-circle, is equal to ⋅ =. There are different ways of. [SOLVED] Cut half of a circle? By littlebigman, October 20, Use the Rectangle Select tool to select the region you don't want. For the head I printed out this image. So let me write that, so diameter, the diameter here is 16 millimeters and they want us to figure out the area, the area of the surface of this candy. What is the perimeter of the rectangle? Imagine cutting out a circle which is just contained inside a semicircle. com is an awesome resoource for pre-school through Kindergarten aged kiddos. Area and Perimeter of Composite Figures. We can use a few short-cut formulas for the perimeter of a square and rectangle. Find the area of the largest rectangle that can be inscribed inside a semi circle with a radius of 10 units. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. It is an online Geometry tool requires radius length of a circle. The area of the whole circle is. The area of a circle = 3. the semicircle is 4cm and squere is 4cm. Cut out and attach the fins Cut out the two fin units. Draw a custom shape. Area of a Circle Formula A = b⋅h • Start with the formula 1 for the area of a A = ⋅ 2π r ⋅ h rectangle. If BO = OC, find the area of the shaded region. Thus, we know that the white area is four times the area of one of the white circles. triangle = a + b + c. A graph of a circle is formed when an arc is drawn from a fixed point (called the centre of the circle) in such a way that any point on the curve is the same distance from the centre. Several laminated shapes which can be used to create various combinations (two squares=a rectangle, two triangles=a diamond, etc. In an equilateral triangle of side 24 cm, a circle is. If you want to create a more advanced diagram like overlapping circles, an organizational chart, or a flowchart, you can create a SmartArt graphic instead of drawing each shape manually. same day printing, same day printing johannesburg, same day printing pretoria, same day printing sandton, same day printing randburg, same day printing parktown…. Create two shapes and position them so they overlap each other. Here the Greek letter π represents a constant, approximately equal to 3. A graph of a circle is formed when an arc is drawn from a fixed point (called the centre of the circle) in such a way that any point on the curve is the same distance from the centre. So, split it into four shapes for obtaining the total area of the running track. We know that the area of a circle is equal to pi times our radius squared. Since you're finding the area of a semi-circle, you'll be looking for half of the area of a circle, which means you have to use the formula for finding the area of a semi-circle and then divide it by two. com Area of a rectangle Area of a right-angled triangle Area of a circle Area of composite shapes Created by Mr Lafferty S3 S5 Int 1 - A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. A high school track is shaped like a rectangle with a semi-circle (half a circle) on each end. Step 2: Divide the circumference in half. The ballerina bodice: using the small triangle you snipped off the top as a guide, cut out a purple rectangle bodice. A circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5. Radius, diameter, arc length and perimeter have the same unit (e. Cut out and attach the fins Cut out the two fin units. So to work out the area of a quadrant, first work out the area of the whole circle (use the formula A = π ×r²) and then divide the answer by 4. Area of a Semicircle Calculator A semicircle is nothing but half of the circle. Area of Circles, Sector and Segment Class – X Area of 4 semi. A curved edge or circle is usually accomplished by spacing the pavers close together near the center and gapped slightly more at the farthest point from the center of the circle. Draw a custom shape. So radius of the semicircle = We have to find the perimeter of the shaded region. Length of diameter of a semicircle = 150 m. Area of an arch given height and radius. How does this rectangle calculator work? Depending on the dimension to be determined, this rectangle calculator uses the formulas explained here: In case you select to solve for area (A) you have to provide the length (l) and the width (w) then: If you want to calculate the perimeter (P) you have to input the length (l) and the width (w):. circle = 2pi r. Take the other cake and cut a smaller circle for the middle part. The Triangle. Designing a patio can be quite exciting when you realize how much freedom you have. This website and its content is subject to our Terms and Conditions. 5 cm squared) from the area of the square (100 cm squared) to determine the area outside the circle, but still within the square. Let us first find the area of rectangle. This is one of those cases where sexual. Area of a circular sector. Use the value 3. I cannot use a black rectangle with a white circle on top of it because the half circle has to be transparent and let the background show through. The diameter is then twice the radius. Assume, in addition, that the semicircles formed on the chords as diameters touch each other in point P on MN. 6 square feet. This is the perimeter of the semi-circle!. Rectangle and a semi-circle 12. Use a single window for an accent – or make a bold statement with a wall of windows. 5 cm squared. Hence, the width w and height h of the rectangle is 2x and 2y and its area is To eliminate y in eq. And you can see this is going three fourths of the way around the circle, so this arc length is going to be three fourths of the circumference. The circumference of a circle is the distance around the outside of the circle. Circle Area Definition. The Triangle. The area of the figure will be the sum of the areas of the rectangle and the semicircles. I will encourage students to extend their understanding of where the formula for finding the area of a circle comes from by using other circles. Pella makes it easy and affordable to create a custom look. It can be determined easily using a formula, A = πr 2, where r is the radius of the circle. If you enter the diameter of the pizza in B2, the radius is =B2/2. When the ring is rotated, the inside jagged edges accidentally move the other inside parts. We like to celebrate with rainbow snack and colorful doable artwork. Are you looking to buy a car but can't decide between a MG HS or Mercedes-Benz CLS53? Use our side by side comparison to help you make a decision. This is the perimeter of the semi-circle!. Semi Circle Shape. This video shows how to find the radius or diameter of a circle when given the area. Just enter the value of radius in the area of a semicircle calculator to compute the semicircle area within a blink of an eye. Adhere the tape's exterior to the interior by twisting it from top to bottom with both hands. A quadrant is a quarter of a circle. 18400 + π × 20 2 = 18400 + 1256. Area and circumference of circle calculator uses radius length of a circle, and calculates the perimeter and area of the circle. Now you have all the necessary tools for finding moments of inertia of composite areas. Taking each angular point as centre, circles are drawn with radius equal to half length of the side of the triangle. ) Mosaic games; Cardboard shapes for lacing. If the ring were cut out better, the inside pieces would not be disturbed. We will discuss how all of the area formulas they have learned so far are all based on finding the area of a rectangle. Let x be the side length of one side of the square. 14(1 ft (1 ft); Area of Circle = 3. This will be the body tube of the rocket. Find the area of the largest rectangle that can be inscribed inside a semi circle with a radius of 10 units. 14 for pie , and do not round your answer. Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser 11. 57 ft 2: 10: A spinner has 6 sectors, half of which are red and half of which are black. Finding the area of a shaded region is a common GMAT geometry question type, and one that students tend to struggle with for whatever reason. Problem 722 Locate the centroid of the shaded area in Fig. To find the volume of a prism (it doesn't matter if it is rectangular or triangular) we multiply the area of the base, called the base area B, by the height h. 2) Press the Delete key. 14 as an approximation for. Area of a Circle Segment Given the Central Angle. Now you can cut/cover the circle at any point to make. What is the area of the left over aluminum sheet?. Since the area of the rotated circle is π r 2, Pappus’ theorem tells us that the volume of the torus is 2 π R π r 2 = 2 π 2 r 2 R. So the area of a semicircle is when you cut a full circle into half you get the area of a semicircle. Area of a rectangle with a semi circle cut out. 5 m, find the area of the playground. The diagram shows a circle split into two regions: A and B. We look at a number of examples of circle and semi-circle functions, sketch their graphs, work out their domains and ranges, determine the centre and radius of a circle given its function, etc. Representing Water on Tinkercad: When I first came to Tinkercad a year ago, I saw water represented as un-textured, extended blue rectangles. Because the ring is hollow, all of its mass has to sit at a distance R from the center; hence, you have =R 2 and I = MR 2. Math Open Reference. [SOLVED] Cut half of a circle? By littlebigman, October 20, Use the Rectangle Select tool to select the region you don't want. The straightaway is twice the width of the field I need to find the area enclosed by the track to the nearest sq foot. Check out our circle facts for kids and learn some interesting information about this two dimensional polygon. Semi-circle on a rectangle 18. The area of the rectangle is 12 x 12 = 324. I have had a good deal of success with all questions bar one. Find the area of the circles. Then click Calculate. Find the area of the shaded region. And so when we think about area, we know that the area of a circle, the area of a circle is equal to pi times the radius of the circle squared. A rectangle is a four-sided polygon having the length of the opposite sides to be equal. PEDS FINAL QUESTIONS TEST BANK CHAPTER 1: 2. Sudden infant death syndrome c. Be sure to include the correct unit in your answer. The attribute clip-path references a element with a single rect element. Strategy 2: Fill in and Cut out. In this course we will leave all answers in their exact form (i. Remember to include units. Take the other cake and cut a smaller circle for the middle part. Representing Water on Tinkercad: When I first came to Tinkercad a year ago, I saw water represented as un-textured, extended blue rectangles. Stick that onto the skin tone paper and cut out another rectangle but this time include a longish neck (long, so there is space to glue the head). This calculator will calculate the area of a circle given its radius, using the famous formula area = pi times r squared. Cut out and shape the rocket body Cut out the rectangle. The task is to calculate the area of the crescents. 56 + 8 = 20. Find the area of the paperboard that remains. What you have is a rectangle and a circle (It's been cut down the middle and the rectangle shoved in it). 6 square feet. For instance, if you draw a square and then draw a circle inside the square so that the circle touches all four sides of the square, you can determine the total. Exercises 1 - Solve the same problem as above but with the perimeter equal to 500 mm. The only tool that I know of that comes close to this is the knife tool but this would be very impractical to cut out with the knife. The rect will not be painted,. First, it should be clear that there is a rectangle with the. Congenital anomalies b. Semicircle Calculator. Take the other cake and cut a smaller circle for the middle part. Its mathematically accurate and useful for Construction projects, wood workers, home owners, students, and real estate. It is an online Geometry tool requires radius length of a circle. Find missing dimensions of the rectangle. The remainder of this unit will be devoted to some pretty complex areas and a handy method for cutting the computations down to size. ABC is an isosceles triangle with AB = AC. Note: Trying to find the area of a rectangle? There's a formula that can help! Check out this tutorial to learn about the formula for the area of a rectangle. Circle area calculator and circumference calculator provide you with a simple way of determining the square footage area for various shapes. Circle Facts. Curved Surface Area of a Cylinder. Find the volume of the solid of revolution formed. To calculate area and circumference we must know the radius of circle. This drawing is composed of a rectangle and a semi-circle. Find the area of the remaining portion of the square. Once this is done, we need to divide our result by 4 in order to get the one-forth that is the one shaded region. Once printed I cut it out and traced it onto a piece of cardboard. Tes Global Ltd is registered in England (Company No 02017289) with its registered office at 26 Red Lion Square London WC1R 4HQ. Radius of circle = 8 cm − 4 cm = 4 cm. Area of Part of a Circle Given a circle of radius a, cut out a tab of height b. Easy to use Material Area Calculator for Asphalt Driveway and How To Estimate. The calculation for the perimiter of a circle = Pi X diameter, which for a whole circle with radius 2" would be 4 X Pi = 12. I am trying to extrude a rectangle shape cut out in a cylinder. This video shows how to find the radius or diameter of a circle when given the area. It is evident that if we make a large number of cuts, the figure formed will approximate a rectangle whose length is equal to one-half of the circumference and whose width is equal to the radius. This is the intersecting set of a square with edge length a and a circle with radius a, where one corner of the square is at the center of the circle. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply. Find the area of the shaded region in the given figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle. Its mathematically accurate and useful for Construction projects, wood workers, home owners, students, and real estate. 5' - 4' in diameter) circle out of a 4x8 sheet of plywood. What is the area of the rug? d = 2 ft; r = 1 ft; Area of circle = 3. !The circle has diameter 8cm. Which is the leading cause of death in infants younger than 1 year in the United States? a. After a lot of research,  I learned that unemployment is really created and not genuine. Find the area of the circles. I used a top from a sauce pan. A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. It is an online Geometry tool requires radius length of a circle. A circle of a diameter of 11.
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# Consider the following statements in the context of governance. I. Encouraging foreign direct investment inflows II. Privatisation of higher educational institutions III. Down-sizing of bureaucracy Which of the above can be used as measures to control the fiscal deficit in India?

 [ A ]    Only III [ B ]    None of the above [ C ]    All of the above [ D ]    Only I [ E ]    Only II
 Answer : Option C Explanation :

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# Linear representation theory of groups of prime-fifth order

This article gives specific information, namely, linear representation theory, about a family of groups, namely: groups of prime-fifth order.
View linear representation theory of group families | View other specific information about groups of prime-fifth order

## Particular cases

Value of prime $p$ Value of $p^5$ Information on groups of order $p^5$ Information on linear representation theory of groups of order $p^5$
2 32 groups of order 32 linear representation theory of groups of order 32
3 243 groups of order 243 linear representation theory of groups of order 243
5 3125 groups of order 3125 linear representation theory of groups of order 3125

## Degrees of irreducible representations

FACTS TO CHECK AGAINST FOR DEGREES OF IRREDUCIBLE REPRESENTATIONS OVER SPLITTING FIELD:
Divisibility facts: degree of irreducible representation divides group order | degree of irreducible representation divides index of abelian normal subgroup
Size bounds: order of inner automorphism group bounds square of degree of irreducible representation| degree of irreducible representation is bounded by index of abelian subgroup| maximum degree of irreducible representation of group is less than or equal to product of maximum degree of irreducible representation of subgroup and index of subgroup
Cumulative facts: sum of squares of degrees of irreducible representations equals order of group | number of irreducible representations equals number of conjugacy classes | number of one-dimensional representations equals order of abelianization

### Grouping by degrees of irreducible representations

Number of irreps of degree 1 Number of irreps of degree $p$ Number of irreps of degree $p^2$ Total number of irreducible representations = number of conjugacy classes Nilpotency class(es) attained by these Description of groups Number of groups case $p = 2$ Number of groups case $p = 3$ Number of groups case $p \ge 5$
$p^5$ 0 0 $p^5$ 1 all abelian groups of order $p^5$ 7 7 7
$p^4$ $p^3 - p^2$ 0 $p^4 + p^3 - p^2$ 2 15 15 15
$p^4$ 0 $p - 1$ $p^4 + p - 1$ 2 the extraspecial groups 2 2 2
$p^3$ $p^3 - p$ 0 $2p^3 - p$ 2, 3 19 24 $p + 21$
$p^2$ $p^3 - 1$ 0 $p^3 + p^2 - 1$ 3 4 10 residue class-dependent
$p^3$ $p^2 - p$ $p - 1$ $p^3 + p^2 - 1$ 3 5 6 6
$p^2$ $p^2 - 1$ $p - 1$ $2p^2 + p - 2$ 4 0 3 6

### Grouping by cumulative sums of squares of degrees

Sum of squares of irreps of degree 1 Sum of squares of irreps of degree at most $p$ Sum of squares of degree at most $p^2$ Total number of irreducible representations = number of conjugacy classes Nilpotency class(es) attained by these Description of groups Number of groups case $p = 2$ Number of groups case $p = 3$ Number of groups case $p \ge 5$
$p^5$ $p^5$ $p^5$ $p^5$ 1 all abelian groups of order $p^5$ 7 7 7
$p^4$ $p^5$ $p^5$ $p^4 + p^3 - p^2$ 2 15 15 15
$p^4$ $p^4$ $p^5$ $p^4 + p - 1$ 2 the extraspecial groups 2 2 2
$p^3$ $p^5$ $p^5$ $2p^3 - p$ 2, 3 19 24 $p + 21$
$p^2$ $p^5$ $p^5$ $p^3 + p^2 - 1$ 3 4 10 residue class-dependent
$p^3$ $p^4$ $p^5$ $p^3 + p^2 - 1$ 3 5 6 6
$p^2$ $p^4$ $p^5$ $2p^2 + p - 2$ 4 0 3 6

Note that it is true in this case that the sum of squares of degrees of irreducible representations of degree dividing any number itself divides the order of the group (in particular, all these numbers are powers of $p$). However, this is not true for all groups and in fact an analogous statement fails for groups of prime-sixth order (see linear representation theory of groups of prime-sixth order). For more, see:

### Correspondence between degrees of irreducible representations and conjugacy class sizes

For groups of order $p^5$, it is true that the list of conjugacy class sizes determines the degrees of irreducible representations. In the case $p = 2$, the converse also holds, i.e., the degrees of irreducible representations determine the conjugacy class sizes.

However, for $p \ge 3$, there is one ambiguous case: the case of $p^2$ degree one and $p^3 - 1$ degree two representations corresponds to two possible lists of conjugacy class sizes: ($p$ of size one, $p^3 - 1$ of size $p$, $p^2 - p$ of size $p^3$), and ($p^2$ of size 1, $p^3 - 1$ of size $p^2$). For $p = 2$, there are no groups fitting the latter case.

Number of conjugacy classes of size 1 Number of conjugacy classes of size $p$ Number of conjugacy classes of size $p^2$ Number of conjugacy classes of size $p^3$ Total number of conjugacy classes = number of irreducible representations Number of degree 1 irreps Number of degree $p$ irreps Number of degree $p^2$ irreps
$p^5$ 0 0 0 $p^5$ $p^5$ 0 0
$p^3$ $p^4 - p^2$ 0 0 $p^4 + p^3 - p^2$ $p^4$ $p^3 - p^2$ 0
$p$ $p^4 - 1$ 0 0 $p^4 + p - 1$ $p^4$ 0 $p - 1$
$p^2$ $p^3 - p$ $p^3 - p^2$ 0 $2p^3 - p$ $p^3$ $p^3 - p$ 0
$p^2$ 0 $p^3 - 1$ 0 $p^3 + p^2 - 1$ $p^2$ $p^3 - 1$ 0
$p$ $p^3 - 1$ 0 $p^2 - p$ $p^3 + p^2 - 1$ $p^2$ $p^3 - 1$ 0
$p$ $p^2 - 1$ $p^3 - p$ 0 $p^3 + p^2 - 1$ $p^3$ $p^2 - p$ $p - 1$
$p$ $p - 1$ $p^2 - 1$ $p^2 - p$ $2p^2 + p - 2$ $p^2$ $p^2 - 1$ $p - 1$


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Home Introduction to foreign exchange investment how to do a good job of money management

# Introduction to foreign exchange investment how to do a good job of money management

Most of the precious metals investors encounter trading losses, summing up its causes will always be attributed to a bad mentality, operating strategies on the stop loss, stop-win, the formulation of the wrong, strict implementation of ineffective, etc., in fact, are not all worth noting cashback forex calculator Online that precious metals investors profit cashbackforexpipcalculator loss is the most critical is how to better use the money cashbackforexprofitcalculator precious metals investment is actually a system engineering investment success In addition to the accuracy of the cashback forex analysis, capital management, risk management, experience, trading skills and luck are all very important factors, especially in the international precious metals market, the trading mechanism is leveraged (i.e. margin trading), investors can trade 50 times or even 100 times their principal amount, which determines that margin trading is a high-risk, high-yield investment if Without perfect capital and risk management, the failure of a single transaction, it is possible for investors to give up or lose everything. Another understanding of the so-called "system engineering" is that investors invest in the precious metals market, the profit and loss of a single transaction does not mean anything, the investor should pursue a stable and sustainable profit, because even if the initial transaction has gained The precious metals market is not a casino, the investor is not a gambler, the investment made can not be equated with gambling the failure of such people is precisely because they do not know these, but also did not learn to survive in this market experience and skills according to the authors experience and understanding of some successful peers, investors who want to get long-term stable profits in the precious metals market, the market Analysis of the right or wrong can only account for up to 30% of the success factors, capital and risk management definitely accounted for more than 50% of the capital management that is how to allocate funds in the investment, the maximum use of funds to obtain the maximum possible profit; and risk management, is to consider the degree of risk of the transaction, the investors ability to bear, in order to minimize the risk of investment risk management is the most important element is how to stop loss. The next is how to stop winning As people usually understand, "revenue and risk are twins", money management and risk management also need to be cleverly combined to maximize returns and minimize the balance of risk Next, the author combined with graphics first introduced several common cashbackforexcalculatorOnlines of money management and use, various methods have their own strengths and weaknesses, the key or In the investor how flexible the use of capital management methods vary from city to city: the first method of capital use is commonly referred to as the pyramid mark-up method assuming that the investor principal has 100,000 U.S. dollars, the investor at a certain point, such as gold (1164.90,-0.90,-0.08%) 1400, buy 30,000 U.S. dollars; to be gold to a certain point, such as gold 1500, the investor believes that gold Will continue to rise, but there has been a period of rise, the back of the upward space may be more limited, and thus again buy when the amount of funds reduced to $20,000; to gold 1550, the investor still think will continue to rise, then add to buy, and because now the rise than the first increase in the position is greater, the upward space may be smaller, so put less money than the first increase in the position, such as$ 10,000 The second method is called the inverted pyramid method, with the above understanding of the pyramid method, our understanding of the inverted pyramid method is much simpler also with the above example, the inverted pyramid method is to buy \$10,000, and then buy 20,000, and then buy 30,000, each time to add more and more money, thus called the inverted pyramid method This method is different from the pyramid method is that the investor Judgment on the market at the point of 10,000 U.S. dollars of gold, the investor is not yet very sure of the gold trend, so small capital intervention; to 20,000 to buy the point of the trend of the market more certain, then increase the amount of money invested; and to 30,000 to buy the point, the investor determined that the trend will continue, more sure, put more money investors to the degree of certainty of the market to determine the size of the funds invested, certainty The greater, the more money invested in this can be seen, this method is more aggressive relative to the pyramid plus code method, the investors degree of certainty of the market as the criterion, relatively subjective judgment of the composition of more, the possible profit space, of course, may suffer losses are also large


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## How to Gain on Power: Novel Conditional Independence Tests Based on Short Expansion of Conditional Mutual Information

Mariusz Kubkowski, Jan Mielniczuk, Paweł Teisseyre; 22(62):1−57, 2021.

### Abstract

Conditional independence tests play a crucial role in many machine learning procedures such as feature selection, causal discovery, and structure learning of dependence networks. They are used in most of the existing algorithms for Markov Blanket discovery such as Grow-Shrink or Incremental Association Markov Blanket. One of the most frequently used tests for categorical variables is based on the conditional mutual information ($CMI$) and its asymptotic distribution. However, it is known that the power of such test dramatically decreases when the size of the conditioning set grows, i.e. the test fails to detect true significant variables, when the set of already selected variables is large. To overcome this drawback for discrete data, we propose to replace the conditional mutual information by Short Expansion of Conditional Mutual Information (called $SECMI$), obtained by truncating the Möbius representation of $CMI$. We prove that the distribution of $SECMI$ converges to either a normal distribution or to a distribution of some quadratic form in normal random variables. This property is crucial for the construction of a novel test of conditional independence which uses one of these distributions, chosen in a data dependent way, as a reference under the null hypothesis. The proposed methods have significantly larger power for discrete data than the standard asymptotic tests of conditional independence based on $CMI$ while retaining control of the probability of type I error.

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 © JMLR 2021. (edit, beta)


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# Article: The Cartoon Picture of Magnets That Has Transformed Science

tags
Ising model, Complex Systems
source
Quanta magazine

The Ising model is an example of very simply defined model that makes complex behavior emerge.

Originally introduced by Wilhelm Lenz and his graduate student Ernst Ising, its purpose was to understand why magnets lose their attractive power when heated past a certain temperature. The model was first tried in 1D, where it fails to show that a magnet stays magnetized, and therefore abandoned.

More than 20 years later, Lars Onsager tried to solve it again for the 2D case. The solution was published in 1944 but still did not attract a lot of interest.

In the 50s, when experimental measurements showed that the Ising model accurately predicted “critical exponents” of various gases, physicists eventually got interested.

At the critical temperature, islands of all sizes coexist, from dots to continents. Here, one arrow can flip another, distant arrow, despite their not being neighbors — an indication that the system’s macroscopic properties have detached from its microscopic details. This detachment is the magic of universality. All systems with the same number of dimensions and the same symmetries go through identical phase transitions, regardless of whether their microscopic parts are iron atoms, water molecules or little arrows.

A striking property of the model is it describes something that looks like a deep universal property of complex systems (composed of many components interacting locally with each other). This has been applied to Physics, Biology, and other fields. It also seems to indicate that complex systems are a relevant framework to analyze natural phenomena and try and reproduce some of its emergent properties.


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# An object, previously at rest, slides 1 m down a ramp, with an incline of pi/3 , and then slides horizontally on the floor for another 3 m. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Jan 26, 2017

The coefficient of kinetic friction will be $\mu = 0.247$

#### Explanation:

This problem is most easily done by conservation of energy.
Two energy forms are involved:

A change in gravitational potential energy: $m g h$

Frictional heating: $\mu {F}_{N} \Delta {d}_{1} + \mu {F}_{N} \Delta {d}_{2}$

where $\Delta {d}_{1}$ is the distance the object slides along the ramp, and $\Delta {d}_{2}$ is the distance is slides along the horizontal surface.

Before we can continue, we need to be aware of a couple of complications

We must express $h$ (the height the object descends) in terms of $\Delta {d}_{1}$ (its displacement along the ramp).

$h = \Delta {d}_{1} \sin \left(\frac{\pi}{3}\right)$

Also, we must note that the normal force on an incline is not equal to mg, but to $m g \cos \theta$, where $\theta = \frac{\pi}{3}$ in this case.

With all that looked after, our equation becomes

$- m g \Delta {d}_{1} \sin \left(\frac{\pi}{3}\right) + \mu m g \cos \left(\frac{\pi}{3}\right) \Delta {d}_{1} + \mu m g \Delta {d}_{2} = 0$

(The first term is negative because the potential energy decreases.)

Notice that we can divide every term by mg, (including the right side of the equation)

So, inserting 1 m for $\Delta {d}_{1}$ and 3m for $\Delta {d}_{2}$ we get:

$- 1 \left(0.866\right) + \left(\mu\right) \left(0.50\right) 1 + \mu \left(3\right) = 0$

$- 0.866 + 0.50 \mu + 3 \mu = 0$

$3.5 \mu = 0.866$

$\mu = 0.247$


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Delta V value

$H_{\psi }=E_{\psi }$

1-D: $E_{TOTAL}\psi (x)=E_{k}\psi (x)+V(x)\psi(x)=-\frac{h^{2}}{8\pi ^{2}m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)$

Victoria Dao 3G
Posts: 65
Joined: Wed Sep 30, 2020 9:50 pm

Delta V value

Hi! I'm still a bit confused as to when we should be doubling and when we are not supposed to double the delta v value. For example, for question 27 from 1B in the textbook (A bowling ball of mass 8.00 kg is rolled down a bowling alley lane at 5.00 ± 5.0 m⋅s-1. What is the minimum uncertainty in its position?), the answer involves NOT doubling the 5ms-1, but why would we not double the delta v value if the value is given as ± 5.0 m⋅s-1?

Selena Quispe 2I
Posts: 91
Joined: Wed Sep 30, 2020 10:01 pm
Been upvoted: 3 times

Re: Delta V value

Hi! So the textbook answer is wrong and Lavelle clarifies this through his Solution Manual Sheet on his website! You were supposed to double in this problem! I hope this helps!!

Kailani_Dial_2K
Posts: 114
Joined: Wed Sep 30, 2020 9:44 pm
Been upvoted: 4 times

Re: Delta V value

Hello, did you check to see if this was one of the questions in the textbook with an incorrect solution? The correct way to approach this problem would be to double the 5 to get a change in velocity of 10. You would not double the velocity if it said something like the change in velocity is equal to 1% of the speed of light. Because you would just take the 1% of the speed of light and that would be your delta v. I hope this helps

Victoria Dao 3G
Posts: 65
Joined: Wed Sep 30, 2020 9:50 pm

Re: Delta V value

Selena Quispe 2G wrote:Hi! So the textbook answer is wrong and Lavelle clarifies this through his Solution Manual Sheet on his website! You were supposed to double in this problem! I hope this helps!!

Ah thank you so much! I was so confused haha.

Victoria Dao 3G
Posts: 65
Joined: Wed Sep 30, 2020 9:50 pm

Re: Delta V value

Kailani_Dial_3G wrote:Hello, did you check to see if this was one of the questions in the textbook with an incorrect solution? The correct way to approach this problem would be to double the 5 to get a change in velocity of 10. You would not double the velocity if it said something like the change in velocity is equal to 1% of the speed of light. Because you would just take the 1% of the speed of light and that would be your delta v. I hope this helps

Thank you, that makes a lot of sense!

Vanessa Perez
Posts: 76
Joined: Wed Sep 30, 2020 9:56 pm

Re: Delta V value

wow haha I was literally stuck on this problem for a while, it did not cross my mind that it was a mistake. Thank you all!


text:
# SSD7 Training Tutorial¶

This tutorial explains how to train an SSD7 on the Udacity road traffic datasets, and just generally how to use this SSD implementation.

Disclaimer about SSD7: As you will see below, training SSD7 on the aforementioned datasets yields alright results, but I'd like to emphasize that SSD7 is not a carefully optimized network architecture. The idea was just to build a low-complexity network that is fast (roughly 127 FPS or more than 3 times as fast as SSD300 on a GTX 1070) for testing purposes. Would slightly different anchor box scaling factors or a slightly different number of filters in individual convolution layers make SSD7 significantly better at similar complexity? I don't know, I haven't tried.

In [ ]:
from keras.optimizers import Adam
from keras.callbacks import ModelCheckpoint, EarlyStopping, ReduceLROnPlateau, TerminateOnNaN, CSVLogger
from keras import backend as K
from math import ceil
import numpy as np
from matplotlib import pyplot as plt

from models.keras_ssd7 import build_model
from keras_loss_function.keras_ssd_loss import SSDLoss
from keras_layers.keras_layer_AnchorBoxes import AnchorBoxes
from keras_layers.keras_layer_DecodeDetections import DecodeDetections
from keras_layers.keras_layer_DecodeDetectionsFast import DecodeDetectionsFast

from ssd_encoder_decoder.ssd_input_encoder import SSDInputEncoder
from ssd_encoder_decoder.ssd_output_decoder import decode_detections, decode_detections_fast

from data_generator.object_detection_2d_data_generator import DataGenerator
from data_generator.object_detection_2d_misc_utils import apply_inverse_transforms
from data_generator.data_augmentation_chain_variable_input_size import DataAugmentationVariableInputSize
from data_generator.data_augmentation_chain_constant_input_size import DataAugmentationConstantInputSize
from data_generator.data_augmentation_chain_original_ssd import SSDDataAugmentation

%matplotlib inline

## 1. Set the model configuration parameters¶

The cell below sets a number of parameters that define the model configuration. The parameters set here are being used both by the build_model() function that builds the model as well as further down by the constructor for the SSDInputEncoder object that is needed to to match ground truth and anchor boxes during the training.

Here are just some comments on a few of the parameters, read the documentation for more details:

• Set the height, width, and number of color channels to whatever you want the model to accept as image input. If your input images have a different size than you define as the model input here, or if your images have non-uniform size, then you must use the data generator's image transformations (resizing and/or cropping) so that your images end up having the required input size before they are fed to the model. to convert your images to the model input size during training. The SSD300 training tutorial uses the same image pre-processing and data augmentation as the original Caffe implementation, so take a look at that to see one possibility of how to deal with non-uniform-size images.
• The number of classes is the number of positive classes in your dataset, e.g. 20 for Pascal VOC or 80 for MS COCO. Class ID 0 must always be reserved for the background class, i.e. your positive classes must have positive integers as their IDs in your dataset.
• The mode argument in the build_model() function determines whether the model will be built with or without a DecodeDetections layer as its last layer. In 'training' mode, the model outputs the raw prediction tensor, while in 'inference' and 'inference_fast' modes, the raw predictions are being decoded into absolute coordinates and filtered via confidence thresholding, non-maximum suppression, and top-k filtering. The difference between latter two modes is that 'inference' uses the decoding procedure of the original Caffe implementation, while 'inference_fast' uses a faster, but possibly less accurate decoding procedure.
• The reason why the list of scaling factors has 5 elements even though there are only 4 predictor layers in tSSD7 is that the last scaling factor is used for the second aspect-ratio-1 box of the last predictor layer. Refer to the documentation for details.
• build_model() and SSDInputEncoder have two arguments for the anchor box aspect ratios: aspect_ratios_global and aspect_ratios_per_layer. You can use either of the two, you don't need to set both. If you use aspect_ratios_global, then you pass one list of aspect ratios and these aspect ratios will be used for all predictor layers. Every aspect ratio you want to include must be listed once and only once. If you use aspect_ratios_per_layer, then you pass a nested list containing lists of aspect ratios for each individual predictor layer. This is what the SSD300 training tutorial does. It's your design choice whether all predictor layers should use the same aspect ratios or whether you think that for your dataset, certain aspect ratios are only necessary for some predictor layers but not for others. Of course more aspect ratios means more predicted boxes, which in turn means increased computational complexity.
• If two_boxes_for_ar1 == True, then each predictor layer will predict two boxes with aspect ratio one, one a bit smaller, the other one a bit larger.
• If clip_boxes == True, then the anchor boxes will be clipped so that they lie entirely within the image boundaries. It is recommended not to clip the boxes. The anchor boxes form the reference frame for the localization prediction. This reference frame should be the same at every spatial position.
• In the matching process during the training, the anchor box offsets are being divided by the variances. Leaving them at 1.0 for each of the four box coordinates means that they have no effect. Setting them to less than 1.0 spreads the imagined anchor box offset distribution for the respective box coordinate.
• normalize_coords converts all coordinates from absolute coordinate to coordinates that are relative to the image height and width. This setting has no effect on the outcome of the training.
In [2]:
img_height = 300 # Height of the input images
img_width = 480 # Width of the input images
img_channels = 3 # Number of color channels of the input images
intensity_mean = 127.5 # Set this to your preference (maybe None). The current settings transform the input pixel values to the interval [-1,1].
intensity_range = 127.5 # Set this to your preference (maybe None). The current settings transform the input pixel values to the interval [-1,1].
n_classes = 5 # Number of positive classes
scales = [0.08, 0.16, 0.32, 0.64, 0.96] # An explicit list of anchor box scaling factors. If this is passed, it will override min_scale and max_scale.
aspect_ratios = [0.5, 1.0, 2.0] # The list of aspect ratios for the anchor boxes
two_boxes_for_ar1 = True # Whether or not you want to generate two anchor boxes for aspect ratio 1
steps = None # In case you'd like to set the step sizes for the anchor box grids manually; not recommended
offsets = None # In case you'd like to set the offsets for the anchor box grids manually; not recommended
clip_boxes = False # Whether or not to clip the anchor boxes to lie entirely within the image boundaries
variances = [1.0, 1.0, 1.0, 1.0] # The list of variances by which the encoded target coordinates are scaled
normalize_coords = True # Whether or not the model is supposed to use coordinates relative to the image size

## 2. Build or load the model¶

You will want to execute either of the two code cells in the subsequent two sub-sections, not both.

### 2.1 Create a new model¶

If you want to create a new model, this is the relevant section for you. If you want to load a previously saved model, skip ahead to section 2.2.

The code cell below does the following things:

1. It calls the function build_model() to build the model.
2. It optionally loads some weights into the model.
3. It then compiles the model for the training. In order to do so, we're defining an optimizer (Adam) and a loss function (SSDLoss) to be passed to the compile() method.

SSDLoss is a custom Keras loss function that implements the multi-task log loss for classification and smooth L1 loss for localization. neg_pos_ratio and alpha are set as in the paper.

In [3]:
# 1: Build the Keras model

K.clear_session() # Clear previous models from memory.

model = build_model(image_size=(img_height, img_width, img_channels),
n_classes=n_classes,
mode='training',
l2_regularization=0.0005,
scales=scales,
aspect_ratios_global=aspect_ratios,
aspect_ratios_per_layer=None,
two_boxes_for_ar1=two_boxes_for_ar1,
steps=steps,
offsets=offsets,
clip_boxes=clip_boxes,
variances=variances,
normalize_coords=normalize_coords,
subtract_mean=intensity_mean,
divide_by_stddev=intensity_range)

# 2: Optional: Load some weights

# 3: Instantiate an Adam optimizer and the SSD loss function and compile the model

ssd_loss = SSDLoss(neg_pos_ratio=3, alpha=1.0)

### 2.2 Load a saved model¶

If you have previously created and saved a model and would now like to load it, simply execute the next code cell. The only thing you need to do is to set the path to the saved model HDF5 file that you would like to load.

The SSD model contains custom objects: Neither the loss function, nor the anchor box or detection decoding layer types are contained in the Keras core library, so we need to provide them to the model loader.

This next code cell assumes that you want to load a model that was created in 'training' mode. If you want to load a model that was created in 'inference' or 'inference_fast' mode, you'll have to add the DecodeDetections or DecodeDetectionsFast layer type to the custom_objects dictionary below.

In [ ]:
# TODO: Set the path to the .h5 file of the model to be loaded.
model_path = 'ssd7.h5'

# We need to create an SSDLoss object in order to pass that to the model loader.
ssd_loss = SSDLoss(neg_pos_ratio=3, alpha=1.0)

K.clear_session() # Clear previous models from memory.

'compute_loss': ssd_loss.compute_loss})

## 3. Set up the data generators for the training¶

The code cells below set up data generators for the training and validation datasets to train the model. You will have to set the file paths to your dataset. Depending on the annotations format of your dataset, you might also have to switch from the CSV parser to the XML or JSON parser, or you might have to write a new parser method in the DataGenerator class that can handle whatever format your annotations are in. The README of this repository provides a summary of the design of the DataGenerator, which should help you in case you need to write a new parser or adapt one of the existing parsers to your needs.

Note that the generator provides two options to speed up the training. By default, it loads the individual images for a batch from disk. This has two disadvantages. First, for compressed image formats like JPG, this is a huge computational waste, because every image needs to be decompressed again and again every time it is being loaded. Second, the images on disk are likely not stored in a contiguous block of memory, which may also slow down the loading process. The first option that DataGenerator provides to deal with this is to load the entire dataset into memory, which reduces the access time for any image to a negligible amount, but of course this is only an option if you have enough free memory to hold the whole dataset. As a second option, DataGenerator provides the possibility to convert the dataset into a single HDF5 file. This HDF5 file stores the images as uncompressed arrays in a contiguous block of memory, which dramatically speeds up the loading time. It's not as good as having the images in memory, but it's a lot better than the default option of loading them from their compressed JPG state every time they are needed. Of course such an HDF5 dataset may require significantly more disk space than the compressed images. You can later load these HDF5 datasets directly in the constructor.

Set the batch size to to your preference and to what your GPU memory allows, it's not the most important hyperparameter. The Caffe implementation uses a batch size of 32, but smaller batch sizes work fine, too.

The DataGenerator itself is fairly generic. I doesn't contain any data augmentation or bounding box encoding logic. Instead, you pass a list of image transformations and an encoder for the bounding boxes in the transformations and label_encoder arguments of the data generator's generate() method, and the data generator will then apply those given transformations and the encoding to the data. Everything here is preset already, but if you'd like to learn more about the data generator and its data augmentation capabilities, take a look at the detailed tutorial in this repository.

The image processing chain defined further down in the object named data_augmentation_chain is just one possibility of what a data augmentation pipeline for unform-size images could look like. Feel free to put together other image processing chains, you can use the DataAugmentationConstantInputSize class as a template. Or you could use the original SSD data augmentation pipeline by instantiting an SSDDataAugmentation object and passing that to the generator instead. This procedure is not exactly efficient, but it evidently produces good results on multiple datasets.

An SSDInputEncoder object, ssd_input_encoder, is passed to both the training and validation generators. As explained above, it matches the ground truth labels to the model's anchor boxes and encodes the box coordinates into the format that the model needs.

### Note:¶

The example setup below was used to train SSD7 on two road traffic datasets released by Udacity with around 20,000 images in total and 5 object classes (car, truck, pedestrian, bicyclist, traffic light), although the vast majority of the objects are cars. The original datasets have a constant image size of 1200x1920 RGB. I consolidated the two datasets, removed a few bad samples (although there are probably many more), and resized the images to 300x480 RGB, i.e. to one sixteenth of the original image size. In case you'd like to train a model on the same dataset, you can download the consolidated and resized dataset I used here (about 900 MB).

In [5]:
# 1: Instantiate two DataGenerator objects: One for training, one for validation.

# Optional: If you have enough memory, consider loading the images into memory for the reasons explained above.

# 2: Parse the image and label lists for the training and validation datasets.

# TODO: Set the paths to your dataset here.

# Images
images_dir = '../../datasets/udacity_driving_datasets/'

# Ground truth
train_labels_filename = '../../datasets/udacity_driving_datasets/labels_train.csv'
val_labels_filename   = '../../datasets/udacity_driving_datasets/labels_val.csv'

train_dataset.parse_csv(images_dir=images_dir,
labels_filename=train_labels_filename,
input_format=['image_name', 'xmin', 'xmax', 'ymin', 'ymax', 'class_id'], # This is the order of the first six columns in the CSV file that contains the labels for your dataset. If your labels are in XML format, maybe the XML parser will be helpful, check the documentation.
include_classes='all')

val_dataset.parse_csv(images_dir=images_dir,
labels_filename=val_labels_filename,
input_format=['image_name', 'xmin', 'xmax', 'ymin', 'ymax', 'class_id'],
include_classes='all')

# Optional: Convert the dataset into an HDF5 dataset. This will require more disk space, but will
# speed up the training. Doing this is not relevant in case you activated the load_images_into_memory
# option in the constructor, because in that cas the images are in memory already anyway. If you don't
# want to create HDF5 datasets, comment out the subsequent two function calls.

train_dataset.create_hdf5_dataset(file_path='dataset_udacity_traffic_train.h5',
resize=False,
variable_image_size=True,
verbose=True)

val_dataset.create_hdf5_dataset(file_path='dataset_udacity_traffic_val.h5',
resize=False,
variable_image_size=True,
verbose=True)

# Get the number of samples in the training and validations datasets.
train_dataset_size = train_dataset.get_dataset_size()
val_dataset_size   = val_dataset.get_dataset_size()

print("Number of images in the training dataset:\t{:>6}".format(train_dataset_size))
print("Number of images in the validation dataset:\t{:>6}".format(val_dataset_size))

Number of images in the training dataset:	 18000
Number of images in the validation dataset:	  4241

In [6]:
# 3: Set the batch size.

batch_size = 16

# 4: Define the image processing chain.

data_augmentation_chain = DataAugmentationConstantInputSize(random_brightness=(-48, 48, 0.5),
random_contrast=(0.5, 1.8, 0.5),
random_saturation=(0.5, 1.8, 0.5),
random_hue=(18, 0.5),
random_flip=0.5,
random_translate=((0.03,0.5), (0.03,0.5), 0.5),
random_scale=(0.5, 2.0, 0.5),
n_trials_max=3,
clip_boxes=True,
overlap_criterion='area',
bounds_box_filter=(0.3, 1.0),
bounds_validator=(0.5, 1.0),
n_boxes_min=1,
background=(0,0,0))

# 5: Instantiate an encoder that can encode ground truth labels into the format needed by the SSD loss function.

# The encoder constructor needs the spatial dimensions of the model's predictor layers to create the anchor boxes.
predictor_sizes = [model.get_layer('classes4').output_shape[1:3],
model.get_layer('classes5').output_shape[1:3],
model.get_layer('classes6').output_shape[1:3],
model.get_layer('classes7').output_shape[1:3]]

ssd_input_encoder = SSDInputEncoder(img_height=img_height,
img_width=img_width,
n_classes=n_classes,
predictor_sizes=predictor_sizes,
scales=scales,
aspect_ratios_global=aspect_ratios,
two_boxes_for_ar1=two_boxes_for_ar1,
steps=steps,
offsets=offsets,
clip_boxes=clip_boxes,
variances=variances,
matching_type='multi',
pos_iou_threshold=0.5,
neg_iou_limit=0.3,
normalize_coords=normalize_coords)

# 6: Create the generator handles that will be passed to Keras' fit_generator() function.

train_generator = train_dataset.generate(batch_size=batch_size,
shuffle=True,
transformations=[data_augmentation_chain],
label_encoder=ssd_input_encoder,
returns={'processed_images',
'encoded_labels'},
keep_images_without_gt=False)

val_generator = val_dataset.generate(batch_size=batch_size,
shuffle=False,
transformations=[],
label_encoder=ssd_input_encoder,
returns={'processed_images',
'encoded_labels'},
keep_images_without_gt=False)

## 4. Set the remaining training parameters and train the model¶

We've already chosen an optimizer and a learning rate and set the batch size above, now let's set the remaining training parameters.

I'll set a few Keras callbacks below, one for early stopping, one to reduce the learning rate if the training stagnates, one to save the best models during the training, and one to continuously stream the training history to a CSV file after every epoch. Logging to a CSV file makes sense, because if we didn't do that, in case the training terminates with an exception at some point or if the kernel of this Jupyter notebook dies for some reason or anything like that happens, we would lose the entire history for the trained epochs. Feel free to add more callbacks if you want TensorBoard summaries or whatever.

In [7]:
# Define model callbacks.

# TODO: Set the filepath under which you want to save the weights.
model_checkpoint = ModelCheckpoint(filepath='ssd7_epoch-{epoch:02d}_loss-{loss:.4f}_val_loss-{val_loss:.4f}.h5',
monitor='val_loss',
verbose=1,
save_best_only=True,
save_weights_only=False,
mode='auto',
period=1)

csv_logger = CSVLogger(filename='ssd7_training_log.csv',
separator=',',
append=True)

early_stopping = EarlyStopping(monitor='val_loss',
min_delta=0.0,
patience=10,
verbose=1)

reduce_learning_rate = ReduceLROnPlateau(monitor='val_loss',
factor=0.2,
patience=8,
verbose=1,
epsilon=0.001,
cooldown=0,
min_lr=0.00001)

callbacks = [model_checkpoint,
csv_logger,
early_stopping,
reduce_learning_rate]

I'll set one epoch to consist of 1,000 training steps I'll arbitrarily set the number of epochs to 20 here. This does not imply that 20,000 training steps is the right number. Depending on the model, the dataset, the learning rate, etc. you might have to train much longer to achieve convergence, or maybe less.

Instead of trying to train a model to convergence in one go, you might want to train only for a few epochs at a time.

In order to only run a partial training and resume smoothly later on, there are a few things you should note:

1. Always load the full model if you can, rather than building a new model and loading previously saved weights into it. Optimizers like SGD or Adam keep running averages of past gradient moments internally. If you always save and load full models when resuming a training, then the state of the optimizer is maintained and the training picks up exactly where it left off. If you build a new model and load weights into it, the optimizer is being initialized from scratch, which, especially in the case of Adam, leads to small but unnecessary setbacks every time you resume the training with previously saved weights.
2. You should tell fit_generator() which epoch to start from, otherwise it will start with epoch 0 every time you resume the training. Set initial_epoch to be the next epoch of your training. Note that this parameter is zero-based, i.e. the first epoch is epoch 0. If you had trained for 10 epochs previously and now you'd want to resume the training from there, you'd set initial_epoch = 10 (since epoch 10 is the eleventh epoch). Furthermore, set final_epoch to the last epoch you want to run. To stick with the previous example, if you had trained for 10 epochs previously and now you'd want to train for another 10 epochs, you'd set initial_epoch = 10 and final_epoch = 20.
3. Callbacks like ModelCheckpoint or ReduceLROnPlateau are stateful, so you might want ot save their state somehow if you want to pick up a training exactly where you left off.
In [ ]:
# TODO: Set the epochs to train for.
# If you're resuming a previous training, set initial_epoch and final_epoch accordingly.
initial_epoch   = 0
final_epoch     = 20
steps_per_epoch = 1000

history = model.fit_generator(generator=train_generator,
steps_per_epoch=steps_per_epoch,
epochs=final_epoch,
callbacks=callbacks,
validation_data=val_generator,
validation_steps=ceil(val_dataset_size/batch_size),
initial_epoch=initial_epoch)

Let's look at how the training and validation loss evolved to check whether our training is going in the right direction:

In [70]:
plt.figure(figsize=(20,12))
plt.plot(history.history['loss'], label='loss')
plt.plot(history.history['val_loss'], label='val_loss')
plt.legend(loc='upper right', prop={'size': 24});

Out[70]:
<matplotlib.legend.Legend at 0x7f02e97f2eb8>

The validation loss has been decreasing at a similar pace as the training loss, indicating that our model has been learning effectively over the last 30 epochs. We could try to train longer and see if the validation loss can be decreased further. Once the validation loss stops decreasing for a couple of epochs in a row, that's when we will want to stop training. Our final weights will then be the weights of the epoch that had the lowest validation loss.

### 5. Make predictions¶

Now let's make some predictions on the validation dataset with the trained model. For convenience we'll use the validation generator which we've already set up above. Feel free to change the batch size.

You can set the shuffle option to False if you would like to check the model's progress on the same image(s) over the course of the training.

In [14]:
# 1: Set the generator for the predictions.

predict_generator = val_dataset.generate(batch_size=1,
shuffle=True,
transformations=[],
label_encoder=None,
returns={'processed_images',
'processed_labels',
'filenames'},
keep_images_without_gt=False)

In [23]:
# 2: Generate samples

batch_images, batch_labels, batch_filenames = next(predict_generator)

i = 0 # Which batch item to look at

print("Image:", batch_filenames[i])
print()
print("Ground truth boxes:\n")
print(batch_labels[i])

Image: ../../datasets/Udacity_Driving/driving_dataset_consolidated_small/1479503098787107173.jpg

Ground truth boxes:

[[  1  12 141  60 177]
[  1  50 142 123 184]
[  1 112 143 134 161]
[  1 126 144 141 160]
[  1 196 141 208 150]
[  1 213 139 223 149]
[  1 219 140 244 158]
[  1 369 110 479 217]]

In [24]:
# 3: Make a prediction

y_pred = model.predict(batch_images)

Now let's decode the raw predictions in y_pred.

Had we created the model in 'inference' or 'inference_fast' mode, then the model's final layer would be a DecodeDetections layer and y_pred would already contain the decoded predictions, but since we created the model in 'training' mode, the model outputs raw predictions that still need to be decoded and filtered. This is what the decode_detections() function is for. It does exactly what the DecodeDetections layer would do, but using Numpy instead of TensorFlow (i.e. on the CPU instead of the GPU).

decode_detections() with default argument values follows the procedure of the original SSD implementation: First, a very low confidence threshold of 0.01 is applied to filter out the majority of the predicted boxes, then greedy non-maximum suppression is performed per class with an intersection-over-union threshold of 0.45, and out of what is left after that, the top 200 highest confidence boxes are returned. Those settings are for precision-recall scoring purposes though. In order to get some usable final predictions, we'll set the confidence threshold much higher, e.g. to 0.5, since we're only interested in the very confident predictions.

In [25]:
# 4: Decode the raw prediction y_pred

y_pred_decoded = decode_detections(y_pred,
confidence_thresh=0.5,
iou_threshold=0.45,
top_k=200,
normalize_coords=normalize_coords,
img_height=img_height,
img_width=img_width)

np.set_printoptions(precision=2, suppress=True, linewidth=90)
print("Predicted boxes:\n")
print('   class   conf xmin   ymin   xmax   ymax')
print(y_pred_decoded[i])

Predicted boxes:

class   conf xmin   ymin   xmax   ymax
[[  1.     0.95 363.69 123.34 494.48 223.61]
[  1.     0.91 217.38 140.01 240.73 160.38]
[  1.     0.91  53.77 145.21 118.32 187.84]
[  1.     0.62  13.87 145.2   56.61 176.59]
[  1.     0.62 110.87 143.69 134.8  163.92]
[  1.     0.52 216.01 130.4  248.78 156.57]]

Finally, let's draw the predicted boxes onto the image. Each predicted box says its confidence next to the category name. The ground truth boxes are also drawn onto the image in green for comparison.

In [26]:
# 5: Draw the predicted boxes onto the image

plt.figure(figsize=(20,12))
plt.imshow(batch_images[i])

current_axis = plt.gca()

colors = plt.cm.hsv(np.linspace(0, 1, n_classes+1)).tolist() # Set the colors for the bounding boxes
classes = ['background', 'car', 'truck', 'pedestrian', 'bicyclist', 'light'] # Just so we can print class names onto the image instead of IDs

# Draw the ground truth boxes in green (omit the label for more clarity)
for box in batch_labels[i]:
xmin = box[1]
ymin = box[2]
xmax = box[3]
ymax = box[4]
label = '{}'.format(classes[int(box[0])])
current_axis.add_patch(plt.Rectangle((xmin, ymin), xmax-xmin, ymax-ymin, color='green', fill=False, linewidth=2))
#current_axis.text(xmin, ymin, label, size='x-large', color='white', bbox={'facecolor':'green', 'alpha':1.0})

# Draw the predicted boxes in blue
for box in y_pred_decoded[i]:
xmin = box[-4]
ymin = box[-3]
xmax = box[-2]
ymax = box[-1]
color = colors[int(box[0])]
label = '{}: {:.2f}'.format(classes[int(box[0])], box[1])
current_axis.add_patch(plt.Rectangle((xmin, ymin), xmax-xmin, ymax-ymin, color=color, fill=False, linewidth=2))
current_axis.text(xmin, ymin, label, size='x-large', color='white', bbox={'facecolor':color, 'alpha':1.0})


text:
: pid

1. .

nyannaco
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7. internet PID AUBE, Honeywell PIA. e mail postaro . .

Hello Mr.

Hydronic system, react much slower compared with Hot air system.
So preferably use longer cycles 20-30 minutes

PIA
The thermostat calculates the best proportion of time to heat up within the cycle per hour configuration setting.
Varying between 10% and 100%, below 10% it stops completely.
It readapt itself continuously within all these parameters cycle after cycle.
The shorter the cycle is the most precise span will be.

PID
Proportional integral derivative
The thermostat calculate a time to heat up to approach a 50% cycle duty on the cycle per hour configuration setting.
At 50% the thermostat would have a better control of the temperature.
This method also include an artificial anticipation of 2C within 2 minutes of operation.
So when the thermostat start the system, the temperature readout will show an artificial rise of 2 within 2 minutes, simply to compensate for the systems heat propagation delay.

Sincerely
Honeywell

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