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• Insights
Andy Resnick submitted a new PF Insights post

Continue reading the Original PF Insights Post.

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DennisN and Greg Bernhardt

Mentor
What makes a digital camera special? [...] A second key difference is what happens when you press the button to take a picture. In manual cameras, not much happens- a mechanical shutter opens for a set amount of time, exposing the film, and then closes. Digital cameras do a lot of things when that button is depressed, including light metering and focusing,

Prior to the digital era, most film SLRs had automatic light-metering and many had autofocusing. When I bought a Pentax K1000 around 1990, it was one of only a few completely-manual SLRs still available, if I remember correctly.

I had a Nikon FG; no autofocus, but it did have metering (no autoexposure- I had to set the shutter speed and/or aperture manually). In addition, it had a full manual mode- if the battery was dead, for example- that provided a fixed 1/90 s shutter speed.

Andre
I still have my Minolta XD7 and some lenses. So when I decided to go serious on photography again, selecting a DSLR, I first considered Sony/Minolta because my lenses may still be useable.

But nope. Also lenses seem to age. Nothing automatic in there. I finally went for the Canon EOS 450D back in April 2008 because of superior image quality at that time.

Just saw this now. Great work Andy!

Just saw this now. Great work Andy!

Thanks, but I can't take all the credit- call me the 'lead author'. It was a collaborative effort from 3 or 4 of us (who can choose to identify themselves if they wish).

Gold Member
Prior to the digital era, most film SLRs had automatic light-metering and many had autofocusing. When I bought a Pentax K1000 around 1990, it was one of only a few completely-manual SLRs still available, if I remember correctly.
I had a large stable of Olympus OM-1s and a single OM-4 with Zuicko prime lenses. I had two OM-1s that were dedicated to astrophotography. They were both dirt cheap at pawn shops because the meters didn't work. I think I paid \$20 each for them. Still, they had manual shutters, mirror lock-up, interchangeable focus screens, and other features that made them perfect for astro-imaging. Plus, the OM series was smaller and lighter than about any other pro-grade SLR.

Andre
Just wanted to tell that the new micro four thirds system (cropfactor 2) is maturing. A big leap ahead is made with the Panasonic GH2, from preliminary results I see that the image quality is excellent, on par or better than most of the APC-C format cameras (crop factor 1.5 / 1.6) like the CANON EOS7D or the Nikon D7000, that is on low ISO's. On higher ISO's -as expected- the image noise is clearly worse albeit that the image remains tack sharp.

Micro four third cameras are hybrids half way between upper end point and shoot cameras and DSLR. The lens is exchangable but there is no mirror.

It's not cheap though.

Mentor
Hyperfocal distance: The hyperfocal distance is calculated by maximizing the depth of field: when a lens is focused at the hyperfocal distance, objects from infinity to half the hyperfocal distance are rendered in focus. The analytic result is:
$$H = f( \frac{f}{Fc}+1)$$,
where H is the hyperfocal distance, f the focal length, F the f-number, and c the diameter of the circle of confusion. The hyperfocal distance also forms a series solution: focusing the lens at 1/2 the hyperfocal distance renders objects from the hyperfocal distance to 1/3 the hyperfocal distance in focus; focusing at 1/3 the hyperfocal distance covers objects from 1/2 to 1/4 the hyperfocal distance, etc. For example, the hyperfocal distance for a 28mm lens set to f/16 on a 35mm camera is about 1.6m. Everything from 0.8m to infinity will be sharp in a photograph taken with this lens focused at an object 1.6m away.

I understand value of 1.6m for 28/8 can be calculated assuming circle of confusion of 0.03 mm and the 'real' focal length. Thats for a full frame camera. What values would be reasonable for APS-C?

Andre
I understand value of 1.6m for 28/8 can be calculated assuming circle of confusion of 0.03 mm and the 'real' focal length. Thats for a full frame camera. What values would be reasonable for APS-C?

I guess if you don't change other facters that the crop factor 1.6 for Canon applies, hence 0.02 (0.01875).

Mind that a CoC of 0.03 mm on a 24mm height compares to a resolution of 800 LPH (lines per height). However modern full frames easily get to 2500 LPH. So it seems that you get the oxymoron that the better the camera resolution, the less the depth of field and the farther away the hyperfocal distance.

Mentor
So it seems that you get the oxymoron that the better the camera resolution, the less the depth of field and the farther away the hyperfocal distance.

That's why I asked for "reasonable"...

Andre
I think that is worth some empirical trial and error [strike]work[/strike] fun.

I understand value of 1.6m for 28/8 can be calculated assuming circle of confusion of 0.03 mm and the 'real' focal length. Thats for a full frame camera. What values would be reasonable for APS-C?

Sorry- I didn't see this when you posted it. Varying the image size means the circle of confusion must be scaled (just as the focal length must be scaled). If the APS-C has a crop factor of say, 1.5x, the CoC is also divided by 1.5x so it would be 0.02 mm.

The CoC specification was originally determined by using a standard enlargement of 8x viewed at 25cm; the reality is that viewing conditions and acuity affect the result.

One counter-intuitive result (for me, anyways) is that larger format images (4" x 5" or even 8" x 10") appear sharper and have a more narrow depth of field than 35mm images.

Topher925
What is everyone's opinion of the Sony SLT A65 & 77 being released next month? I'm in the market for a new camera and so far have been looking at the Pentax k-5 for its low light performance and star tracker GPS thing. But with the A65 having such impressive specs for such a low price I'm really considering it instead.

My only concern is low light performance. Given that its an SLT with ~2/3 of the light actually hitting the sensor coupled with the sensor having a very small pixel pitch makes me think that low light performance/noise will be rather poor compared to the k-5. Sony also limits the ISO to 16000. Whichever camera I buy a lot of its time will be spent doing some lite astrophotography so high noise is a big concern.

I don't recommend specific products- nobody pays me or provides equipment to use- but if your highest priority is low-light-level imaging, then you are right to carefully examine that spec.

Andre
What is everyone's opinion of the Sony SLT A65 & 77 being released next month? I'm in the market for a new camera and so far have been looking at the Pentax k-5 for its low light performance and star tracker GPS thing. But with the A65 having such impressive specs for such a low price I'm really considering it instead.

My only concern is low light performance. Given that its an SLT with ~2/3 of the light actually hitting the sensor coupled with the sensor having a very small pixel pitch makes me think that low light performance/noise will be rather poor compared to the k-5. Sony also limits the ISO to 16000. Whichever camera I buy a lot of its time will be spent doing some lite astrophotography so high noise is a big concern.

yes you are right noise is an issue with the new Sony's. Obviously with a fixed translucent mirror you lose some light going to the main sensor. So it's plain physics that signal to noise ratio is worse. However the 25 mp of the A77 reduces that problem somewhat if you reduce the output to 16MP. Another issue would be hot pixels, that emerge at long shutter speeds and high ISO, same problem there.

The best signal to noise ration in relation to its price in DSLR's comes from the Canon 5D mkII (21 mp) especially at high ISO. The best absolute high ISO S/N ratio comes form the Nikon D3S (12mp) but at about double the price.

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khemist
yes you are right noise is an issue with the new Sony's. Obviously with a fixed translucent mirror you lose some light going to the main sensor. So it's plain physics that signal to noise ratio is worse. However the 25 mp of the A77 reduces that problem somewhat if you reduce the output to 16MP. Another issue would be hot pixels, that emerge at long shutter speeds and high ISO, same problem there.

The best signal to noise ration in relation to its price in DSLR's comes from the Canon 5D mkII (21 mp) especially at high ISO. The best absolute high ISO S/N ratio comes form the Nikon D3S (12mp) but at about double the price.

The Nikon D700 has much better noise reduction for the same price point as a mark 2. However, they are both outstanding cameras.

Interestingly enough, the higher MP the mark 2 has contributes to the increased noise. My friend will shoot at ISO 6000 with the mark 2 and still get relatively noise free shots, but in comparison tests I have seen the d700 has less noise at almost all ISO levels.

Andre
Yes the D700 is very good at high ISO and outperforms the 5D MKII on some other things as well, except image detail/resolution due to only 12.1 MP versus 21.1MP. If you reduce the image size to the same 12.1 MP, you also reduce noise, while maintaining detail.

I also should add that Andy's Sony A900 has the best resolution/detail but cannot keep up at higher ISO

To Topher925, you can find unlimited discussions here about the Sony A65/77
http://forums.dpreview.com/forums/forum.asp?forum=1037

Andre
What is everyone's opinion of the Sony SLT A65 & 77 being released next month? ... Whichever camera I buy a lot of its time will be spent doing some lite astrophotography so high noise is a big concern.

Here are more answers, dpreview has made test shots available with the A77. So if you go to any test, like this of the Canon 60D then you can compare crops of many cameras on this page (in RAW).

In the individual drop down menus you can select available cameras (I selected Sony A77, Nikon D5100, and Canon 5D mkII) you can also select ISO and the crop to compare.

So I went to ISO 3200 and selected a grey area for better noise comparison:

I would consider the Sony A77 a bit underwhelming. The Canon 5D mk II clearly leads the pack, while the Nikon D5100 is slightly better than the three year older sensor of the Canon EOS 60D.

Maybe the Nikon D5100 should be in the very short list of least noise for the best price.

Topher925
I spent at least a good hour the other day checking out the A77 photos on dpreview and comparing to other camera's I'm looking at. While the JPEGs are questionable, the RAW files definitely bring out the shortcomings of the Sony 24MP sensor. I think I can cross that one off the list given the type of photos I want to take.

I've been looking closely at the d5100 for a long time now, it truly is a fantastic camera for money. The fit and finish could be a bit nicer but for the price its acceptable. If I end up not getting the k-5 I'll most likely pick up the d5100.

Andre
As I said earlier, buying an SLR is like marrying to that particular brand. Sooner or later more lenses are added in the inventory and then it's getting real tough to switch brands. Therefore looking at possible future desired lenses could assist, taking decisions.

Andre
Anyway, this is one of my favorite crops:

Notice that the K-5 is excellent for noise but moderate on resolution detail. Notice also that the Canon 600D (Rebel T3i), sharing the sensor with the 60D and 7D, is just outperforming the D5100 with half a notch on details, despite the slightly worse performance on noise.

khemist
Just another tip. The MP doesn't really matter. Any camera nowadays will be able to perform fine. Unless you blow up your photos to poster size, no one will be able to tell the difference.

To be honest, get nice glass over a nice body. A sharp lens can make an aging camera come back to life.

And in the end, whatever camera you buy will work. It will have the ability to take good pictures, but its really who is behind the camera that really matters.

Andre
Just another tip. The MP doesn't really matter. Any camera nowadays will be able to perform fine. Unless you blow up your photos to poster size, no one will be able to tell the difference.

The disadvantage of high MP is noise, but the advantage is that you can crop more, getting more effective focal length from your glass.

To be honest, get nice glass over a nice body. A sharp lens can make an aging camera come back to life.

Nicer bodies will still make that picture, where others can't, especially in high dynamic situations, you'll soon learn the difference.
Edit: Like these for instance. and this...

And better glass is not necesarily more expensive glass. Moreover, if you want from excellent glass to splendid glass, you pay a nice body more.

but its really who is behind the camera that really matters.

Absolutely

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Gold Member
To be honest, get nice glass over a nice body. A sharp lens can make an aging camera come back to life.

And in the end, whatever camera you buy will work. It will have the ability to take good pictures, but its really who is behind the camera that really matters.
All true, and as Andre said above, one should select a system, not just a camera. Once you start adding high-end lenses to your kit, and maybe another camera body, you'll have an "investment" that is hard to recoup if you decide to switch brands.

I decided that I liked the Canon brand, and liked their line-up of lenses so I started out there. Now, I have two 30D bodies and a selection of lenses, including a 100-400 L. I have not felt a driving need (or even want) to upgrade. The quality of this equipment is incredible, and the biggest limitation in the system is the "nut behind the wheel" (myself). Yes, there are shutterbugs who will try to stay on the bleeding edge, but that is expensive, even if you stay within your brand and chase body upgrades so you can keep using that expensive glass. Andre's shots have tempted me to consider a 100mm macro, but I shoot macro so infrequently that I have resisted the urge to splurge.

Andre
To be honest, get nice glass over a nice body. A sharp lens can make an aging camera come back to life.

Why not put that to a test.

Suppose you own a Canon 350D with the too-cheap-for-words standard 18-55mm IS lens and you have something a bit short of a grand to spend. What would give you a better resolution (sharper pictures)?

Get the legendary super 17-55mm F2.8 lens for your 350D or get a new Canon 600D body (less expensive) with the same cheapo standard lens?

You can find the answer here.

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Gold Member
The too-cheap-for words 18-55 (no IS) lens on my 30D is remarkably sharp. I was initially turned off by the light-weight plastic body, etc, in comparison to my old Olympus lenses (OM system), but I was quite pleasantly surprised by the performance of the actual glass.

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Andre
so let's continue the test. this what you'd have, if you scroll roughly halfway you see that the 350D (8mp) with the 18-55 averages about 1850 lines per height.

Now you buy the super 17-55 to get this. See that the center is clearly better getting to 2100 lines per height. But the average is not increasing very clearly.

Now we know from DPreview that the image quality of the 600D with 18MP is practically identical to the 60D and 7D, since it's the same sensor. The 50D here is slightly inferior to that, so we know that the 600D is certainly not going to give worse results here. But as shown here, the cheapo 18-55mm on the 50D gets us average results around 2200 lines per height.

Consequently better glass is not dogmatic better than a better body. On the contrary, if you start comparing all the other nice improvements between the 350D and the 600D.

I think this discussion is a little too simple-minded. For example, my luminar lenses are 50 years old and I'm willing to bet they will outperform any contemporary macro lens, period- not just the optical quality but also the fact that they can be used on a 4" x 5" view camera (and possibly an 8 x 10). In terms of high-ISO/low light imaging, I'll put my EMCCD camera up against any DSLR. And it's not true that you are locked into a particular manufacturer, either.

From my perspective, I have never been disappointed when I get the best camera/lens that I can afford: not the most expensive, but the equipment that best meets my needs, regardless of who made it. Of course, getting high-end equipment also (initially) showcases my inability to take advantage of the full performance- all flaws are glaringly obvious.

Gold Member
You may be right about some of that. Over the years, I have owned a stable of Bronica Zenzanon primes, and Olympus Zuicko primes. I shopped carefully, and ended up with some superior lenses. Now, I can stroll around with a couple of Canon 30Ds and a few zoom lenses, to cover ranges from 18mm to 400mm. That's a whole lot handier than packing around two Bronicas and 4 primes, or 4-5 Olympus bodies and a corresponding number of primes. Another little wrinkle is that when you head out with bodies loaded with color negative film, color transparency film, Tech-Pan, etc, you can always end up wishing you had loaded films with different capabilities, different speeds, grain-size, etc. I can get a lot of flexibility on the fly with the DSLRs, and post-processing. I don't long for the days of film.

Andre
I For example, my luminar lenses are 50 years old and I'm willing to bet they will outperform any contemporary macro lens, period- not just the optical quality but also the fact that they can be used on a 4" x 5" view camera (and possibly an 8 x 10).

That's quite a statement. Would that imply that 50 years of innovations like aspherical, low dispersion elements and diffractive optics not could prevent that lens making deteriorated?

That's quite a statement. Would that imply that 50 years of innovations like aspherical, low dispersion elements and diffractive optics not could prevent that lens making deteriorated?

I stand by it. For whatever reason, Zeiss stopped making those lenses in the 1970's- none of those technologies (except possibly aspherical surfaces) which I agree could improve the optical performance of those lenses were ever incorporated. The fact that each lens has only three elements makes the optical performance even more astounding.

I'd be happy to put my claim to the test- all we need is a 'standard object' that we can all photograph using whatever tools we wish. My only constraint is that I need to work indoors. Normally I would suggest a coin or piece of newspaper, but given the international participation in this forum, it's not obvious what the best choice would be.

Andre
Sure you can compare with what we can and I would love to see results of that lens but it's not a game/match. I know that my 7D/100mm macro is not the best in the world, Borek beats it already with the 100mm L-version, but with a 5D mk2 body, results would even be better which would be topped by the A900, since the resolution is a function of both lens resolution and sensor resolution.

But we can compare pix maybe of a yardstick, or matches or playing cards, or a certain common brand of batteries.

Mentor
Andre and I can take a picture of Canon's lens cap

Gold Member
Andre and I can take a picture of Canon's lens cap
From the inside? Your 100mm macros should deliver equivalent quality, I would think.


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What is 7/12 as a percent?

To find out 7/12 as a percent, first you divide

7/12 = 0.583333333

Then you move the decimal point twice to get the percentage.

7/12 as a percent is about 58.33 %

7/12 is 58.33%
How do we change fractions to percents?
The steps are too simple.

First, divide the numerator (the number at the top of the fraction) by the denominator (the number below the fraction).
In the case above, 7 is the numerator and 12 is the denominator.

So, 7 ÷ 12 = 0.58333

Then, multiply the result by 100. 0.5833 x 100= 58.33

Finally, add the percent (%) sign to the result.

Therefore, 7/12 is 58.33%.

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# Snow Leopard is Here

by on August 28, 2009

The latest and greatest version of Mac OS X, dubbed Snow Leopard, is here. This is likely to be  a good release for astronomers as the OS has been trimmed down to boost performance overall and to give you back about 7 Gbytes of disk space. However, only Intel Macs are supported. Any early adopters out there??? If so, post your experiences with installation, favorite new features, and astronomer software on Snow Leopard in the comments below.

1 Sammy August 29, 2009 at 8:33 am

In general, Snow Leopard feels a little snappier than Leopard. Installation was simple; DVD in and few clicks. However, if you wish to do a clean install, be ready to use Disk Utility.
Expose now shows the name of each window below, which is a nice addition, especially if one has multiple windows and terminals open. I have ran into few incompatible programs, namely istat pro (the one that lives in task bar) and a mail plug-in.
I haven’t had change to use IRAF or PyRAF yet, so I cannot comment on those. Not sure what the default Python is now, as I have highly customized setup, but it would be great to have a 64-bit version. Anyone care to comment Python, PyRAF issues?

2 Don August 29, 2009 at 11:01 pm

I’ve installed Snow Leopard on my Mac Pro and my MacBook Pro. The IRAF ‘cl’ crashes on both. After checking the console logs, it appears that the location of the iraf.h file is lost? The quickest fix I’ve found so far is to login as the IRAF administrator and re-run the install.

I also ran the mkiraf command and then deleted the new login.cl file and replaced it with my original login.cl file. (I didn’t back up my original, IRAF just renames it with the extension .OLD). I’m not certain if running the mkiraf command again contributes to solving the issue; however, the cl parameter file also appeared to be missing; so, running it couldn’t hurt anything. All is running flawlessly again.

Aside from that minor issue, Snow Leopard is definitely living up to the claims. There is a marked increase in performance on all three computers that I’ve installed it on so far.

3 Eli August 30, 2009 at 2:44 am

I have not tried out PyRAF on Snow Leopard (SL), but have been actively investigating how Python behaves on the new system. It has Python 2.6.1 as its default setting. Depending on CPU your computer has, 32-bit or 64-bit, it will default to 64-bit if it can. You can verify this by typing “file which python” in the terminal.

A surprising feature for Python was easy_install. This is a great tool for installing and upgrading your python modules.

I also tried to build Python from source to install more complicated modules. So far no success.

Basic X11 dependent programs worked.

4 Sammy August 30, 2009 at 9:52 am

Few notes on Python modules. At least on my machine, NumPy SVN head fails to compile. The problem seems to be related to a math library being missing (perhaps a new location). Thus, you might have to edit the MATHLIB env variable before it compiles. I haven’t investigated in detail yet, so it might compile OK with default setup.
matplolib 1.0.snv does not compile without problems either. There are warnings about architecture problems. I also noted following line from the log: “Compiling with an SDK that doesn’t seem to exist”. Perhaps some compiler and Xcode locations have changed and they are not found. I also noted many references to OSX 10.3 while trying to compile matplotlib from the SVN.

5 Eli August 30, 2009 at 3:13 pm

Sammy, NumPy (SVN) worked without issues for me. I installed it and did a numpy.test(‘1′,’10’) with no errors. I did have errors with SciPy though. If I compile it 32 bit it installs, but the binary type does match (32 bit to 64 bit Python). 64 bit does not work though. It looks like a potential issue with my Fortran compiler. I have not tried matplotlib yet.

Are you using Snow Leopard’s (SL) system Python or did you install a Framework Python setup?

6 Stuart Littlefair September 2, 2009 at 8:38 am

Probably too obvious to mention, but I have had all sorts of problems compiling code under Snow Leopard until I realised the default was to create 64-bit object files, which wouldn’t link against my (many) 32-bit libraries I have which were compiled under Leopard. Adding the -arch i386 flag fixed my woes.

No problems so far with the Scisoft OS X versions of python or pyraf..

7 Sammy September 3, 2009 at 10:36 am

Eli, I have multiple Python setups on my laptop. So far I have tried with the Framework setup, where I have 3.1.1 (only for pure Python) and 2.6 (which used to be my work horse before SL). I haven’t had time to try with the SL system Python, but I assume that things work better with that one. However, there seems to be some confusion with the type mismatch as you noted.
I also have Enthought Python installed, but I have tried to separate it from the system Python. Enthought seems to work fine even after the SL upgrade.

8 Eli September 10, 2009 at 7:07 am

Sammy, one more update. I got NumPy, SciPy, and Matplotlib all working on Snow Leopard now. There are some issues with specific packages in SciPy, but overall it works very well thanks to the following blog post: http://blog.hyperjeff.net/?p=160

9 Sammy September 10, 2009 at 8:55 am

Eli, I noticed the same excellent post few days ago. However, I still have issues with gcc while compiling NumPy. I should check my version of gcc and other compilers and libraries to see where they differ with the default SL installation. It also seems that when compiling 64-bit Python Modules my setup finds a wrong architecture libpython2.6.dylib. I guess this is the pain of having four separate Python installations…

10 Sammy September 10, 2009 at 9:58 am

Sorry to spam again, but seemed that my problems were solved by getting rid off the 2.6.2 Python I had installed. This version seemed to somehow confuse the Framework default 2.6.1 that SL has and cause some architecture mismatches.

11 Nate September 15, 2009 at 5:14 pm

I waited to buy my new desktop until SL was shipping with new Macs. Today I installed IDL 6.3, and find that it crashes if I try to display an image using tv, tvscl, display, etc. I had similar problems crop up under OS X 10.4 occasionally (after automatic MacUpdates), but installing the latest update of X11 always fixed it. Now X11 (XQuartz 2.3.4) is native to OS X, and there is no SL-supported update as of yet (XQuartz 2.4.0 is for regular Leopard). So, it appears I have an installed IDL that cannot display images. Which is mainly what I work with. Any ideas?

12 Jonathan September 22, 2009 at 8:39 pm

All right, last week I just purchased my first mac ever — a 15″ MacBook Pro — came with Snow Leopard. (previously used ubuntu). I’ve been trying to get scisoft distro and the enthought distro to work on my computer. I can get some things in scisoft to work, but never pyraf.
I can get Enthought to work perfectly with everything it comes with, until I try to install/reinstall scisoft, which breaks it almost entirely.

So, I’ve settled for, perfect Enthought distro; non-working scisoft, but I wanto this situation to improve.

My guess is to separate the python distributions (maybe three ways, scisoft/enthought/system?) but I have no idea how to do this. I saw a previous comment that mentioned having separate pythons doing something like this, and I’d like to know how to do this with the distrobutions enthought and scisoft.

Any tips? Ideas? Suggestions to radically change my approach?

13 Jeremy October 5, 2009 at 12:12 am

Nate,
I had the same problem with images in IDL 6.4 on a mac pro that
started a few months ago (presumably as a result of an auto software
update or something). On a TVSCL or similar, IDL crashed with a bus
error. Have just installed SL, and the problem persisted
with IDL 6.4. Installed 7.1 and problem seems to be fixed.
cheers,
Jeremy

14 Lisa December 2, 2009 at 12:00 pm

I was able to install iraf/pyraf and matplotlib (I had a problem where I needed to set the architecture to 32-bit). I’m having problems with plotting in both, though. In matplotlib, I can successfully import pylab, but am unable to plot. I’m using the MacOSX backend. It will open a blank window labeled Figure 1, but not actually plot anything. If I try to save the plot to a ps file, the file has errors and will not open.

With pyraf, I am having the problem that when I use implot/splot there are no labels on the axes and no titles. The commands in the window work, but I have no labels.

Has anyone else run into any of these problems and been able to fix them?


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A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture

Francesco Lin Massachusetts Institute of Technology, Cambridge, MA, USA
Available Formats:
Electronic ISBN: 978-1-4704-4819-6
Product Code: MEMO/255/1221.E
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $46.80 Click above image for expanded view A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture Francesco Lin Massachusetts Institute of Technology, Cambridge, MA, USA Available Formats:  Electronic ISBN: 978-1-4704-4819-6 Product Code: MEMO/255/1221.E  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$46.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 2552018; 162 pp
MSC: Primary 57;

In the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a ${\rm spin}^c$ structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.

• Chapters
• 1. Introduction
• 2. Basic setup
• 3. The analysis of Morse-Bott singularities
• 4. Floer homology for Morse-Bott singularities
• 5. $\mathrm {Pin}(2)$-monopole Floer homology

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2552018; 162 pp
MSC: Primary 57;

In the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a ${\rm spin}^c$ structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.

• Chapters
• 1. Introduction
• 2. Basic setup
• 3. The analysis of Morse-Bott singularities
• 4. Floer homology for Morse-Bott singularities
• 5. $\mathrm {Pin}(2)$-monopole Floer homology
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
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text: (There are 12 inches in 1 foot and 1 inch equals 2.54 cm.) Convert to an appropriate metric unit so that the numerical expression in the given measure does not contain any zeroes. The pendulum is pivoted at O, which is a distance h from the centre of mass. metric is easier as every thing by divided by 10 , 1kilometre is 1,000 metres , 1 kilogram is 1,000 grams , with you a pound is 20 onces ..or 16 pounds to a stone . How many km is this elevation? a. centi- b. improper fraction c. numerator d. liter e. mixed number f. denomin... Identify the term described from the choices below. The recipe calls for 15ml of vanilla. 11 Inches\\ B. The Metric System DRAFT. The room down the hall has a temperature of 36 "c. Would you be comfortable or uncomfortable in this room? A cyclist rides her bike at a speed of 8 meters per second. If the patching material costs 3.25/in^2, what is the cost of the patch? 1.00 mm equals a. Give a few examples of using the metric system. If an average man is 6 feet tall, how many DNA molecules could be stacked end to end in an average man? You might not require more grow old to spend to go to the books start as capably as search for them. ... 10. (Answer in units of m.). The daily dose of ampicillin is 115 milligrams per kilogram of body weight. From the word "kilo-meter" you should know there are 1000 meters in 1 km. Their backyard is 20 yards wide and 30 yards deep. Convert like measurement units within the metric system. The metric system was later extended as the International System of Units (SI). \\ Convert 0.50 m to mm. Compare the numerical values when both numbers are written in scientific notation. Try this amazing Metric System Practice Quiz: Trivia quiz which has been attempted 7860 times by avid quiz takers. Complete the table of interpretations of the derivative. a. centi- b. improper fraction c. numerator d. liter e. mixed number f. denomin... Identify the term described from the choices below. Convert the following measurements to the units specified: 1) 357 mL to L. 2) 25 kg to mg. A ten gallon methane tank contains 1.243 mol of methane at 74 degree F. Express the volume of tank in liters, the amount of methane in the tank in grams, and the temperature of the tank in Kelvin. 0.5 in. meter is the basic unit of length in the metric system. Give the steps to converting using the metric system and scientific notation. Test your understanding with practice problems and step-by-step solutions. Test your understanding of The metric system concepts with Study.com's quick multiple choice quizzes. DNA is approximately 2.5 nm in length. A car is traveling at a speed of 38.0 m / s on an interstate highway where the speed limit is 75.0 mi / h. Is the driver exceeding the speed limit? You can go to specific questions from the list below, or you can read this page in its … Conversion between metric and standard units can be tricky since the units of distance, volume, area and temperature can seem rather arbitrary when compared to one another. The unit of mass is. Played 2682 times. Round to the nearest tenth. Convert the following metric measurements: a) 85 mg into grams b) 19.8 g into kilograms c) 0.8 mm into centimeters. Work out this velocity in km/h (kilometer/s per hour). high? www.metric.org. a. v \Delta t b. a \Delta t c. v / \Delta t d. v^2 e. 1/2 a(\Delta t)^2 f. vr g. 2ar. Question: - Help 48 ND Thu 12:37 PM Autoane Lab 1The Metric System (21 - Compatibility Mode BU Design Layout Ome Insert Draw References Mailings Review View Tell Me Com का Calibri 11 - A A BUXX ADA Styles Styles Pane 2. 156.0 x 103 torr b. Share Flipboard Email Print Science. (Hint: how long is each side in millimeters?) What is the area of the square, in square-millimeters? I am driving to Atlanta on the I-85 in my G35 Coupe at 40.0 m/s and I pass a cop. Carol ran 21 kilometers in a race. It is supplied as 0.075 mg tablets. Vernier calipers were invented in 1631 by Pierre Vernier, hence the name. True False The metric system of measurements is based on the decimal. The second method uses the unit fraction method. Now for your metric question. Indicate properly formatted answers. A patient weighs 156|bs and needs drug Xat a dose of 2mg/kg body weight. Recent metric-system Questions and Answers on Easycalculation Discussion . Grades: 6 th, 7 th, 8 th. How many kilograms of golf balls are in 5342 balls that weigh 28.4 grams each? Is it not 12.6? The dimensions of the variables v, x , and t are (L)/(T), (L) , and (T) , respectively. Convert the followings as given. You walk to the corner store after school to buy a carton of milk before going home. Calculators and Converters. Convert 5.82 \times 10^{-5} L to picoliters. Make sure you include the appropriate units and significant figures. The International System of Units[1] (abbreviated SI from French: Système international d'unités[2]) is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. Convert 32 meters to feet (Round answer to the nearest thousandth.). Converting one metric unit to another with no exponent allowed in the answer Converting two metric units (numerator and denominator) at a time (10) Converting metric square units to another True or false? There are 36 inches in a yard. 1 µl = _L 10 10 10 10 Test your knowledge with these ten questions about the metric system. a. B)The pressure in car tires is often measured in pounds pe... if a 5.00 minute shower requires 85.0 l of water, how much water would you save if you shortened your shower by 25.0 seconds? cm stands for Centimeter while km means... Internal consistency reliability: this is used when several observations are made to obtain a score for each participant for example, if participants complete a test with several items, or if the... DSC and DTA are thermoanalytical techniques. Edit. Unit Conversions Test Questions. a) 5 x 10^(-3) kg b) 5 x 10^(-4) kg c) 5 x 10^(-5) kg d) 5 x 10^(-6) kg. How many bags of rice is one fish worth? What is the relationship between the accuracy and uncertainty of measurement? Using only the conversions: 1 L = 1,000 cm3 and 1 in. Given t = 3600 seconds, calculate the same amount of time in hours, minutes, and seconds. How many strontium atoms would have to be laid side by side to span a distance of 4.47 mm? According to the base 10 system in the metric system, how there are 1 kiloliter in 10 hectoliter if kilo is greater than hector? a. A hydrogen atom has a diameter of about 10.1 nm. Which of the following are acceptable units for pressure? answered by (user.guest) Best answer. y 2 , where k and a are constant with appropriate units. How many micrograms of hydrogen are in 8.99 \times 10^{-9} decigrams of lithium hydrogen carbonate octahydrate? Subjects: Measurement, Numbers, Place Value. Spelling and usage. How many milliliters of gasoline has a mass of 4.5 kg? Write the answers in meters and in kilometers. What is the mass of each can in grams? The content and theme of this book in fact will be adjacent to your heart. a. gram b. centimeter c. newton d. All of the above, Explain this statement: "Conversion factors must always equal 1.". a) Assuming that water has a density of exactly 1 \ g/cm^3, find the mass of one cubic meter of water in kilograms. a. Chemistry Unit Conversions. The quiz content covers the very basics of the metric system, including base units, prefixes, and one simple unit conversion problem using dimensional analysis (plus a two-step dimensional analysis . {Use 1 gallon = 3.786 liters}. Convert this energy into kJ. Convert 4.0 mm to cm. A student forgot to measure the mass of an empty 100 mL beaker before adding about 2 g of a chemical to it, and decided to simply obtain the mass of another empty 100 mL beaker instead. How would the level of a material in the container be measured if the zero point is at the top of a container? A) 123 m/s B) 0.015 m/s C) 88 m/s D) 25 m/s. By that time, it will have radiated about 1.2x1044 J of energy. For example, kilograms are used to measure people's weight. E... A player height is 6.5 ft.What is his height in meters ? (a) Express this distance in nanometers (nm). Determine the average mass of one apple a) in U.S units (slugs), b) in SI units (kg) and c) the average weight of one apple in SI units (N). Express this diameter in meters, millimeters, and micrometers. The U.S. National Institute of Standards and Technology (NIST) maintains several accurate copies of the international standard kilogram. TRUE. Options: Mega-, Kilo-, nano-, deci-, micro-, giga-, centi-, pico- A. trillionth B. millionth C. million D. billion E. billionth F tenth G. thous... What is the metric value for length or distance? How to write 10 o'clock at night? What is the cost of grapes in dollars per pound if the exchange rate is 1.35 dollars per euro? A high school track measures 400 meters around. The team monitoring a space probe exploring the outer solar system finds that radio transmissions from the probe take 2.38 hours to reach earth. If your car gets 28 miles to the gallon, how many liters of gasoline is necessary to travel 112 km? An automobile travels at a uniform speed of 88 kph. This answer has been confirmed as correct and helpful. Find the speed of light in km/h and express your answer in standard form, correct to 3 significant figures. The physician ordered a medication of 50 mg/ kg/ day in equally divided doses four times a day for a child who weighs 40 pounds. (The density of sulfuric acid is 1.84 g/cm3). How many liters are in a milliliter? If a truck gets 14 miles to the gallon on an average, how much carbon dioxide is emitted into the atmosphere when the truck travels 200 miles? Which of the following is the correct conversion of 2\frac{3}{4} yards into inches? Because of the ineptness of the American aviators. How many feet is this measurement equal to? You are allowed to answer only once per question. What is the patch's area in square kilometers (km^2)? (ii) For which, value(s) of \lambda... What type of test would provide the most useful information for the following question: "Are students making satisfactory progress in learning the metric system?". Select all that are possible units for measuring distance in the metric system? Metric System Questions And Answers This is likewise one of the factors by obtaining the soft documents of this metric system questions and answers by online. Scroll down the page for examples and solutions. What are the open sets of the discrete space? It uses standard base units to name larger and smaller units. In Mexico, avocados are 53 pesos per kilogram. Live Game Live. Thanks. Which of the following is the appropriate prefix to measure the amount of space taken up? What is the 4th term from the end of the A.P …, 2, 5, 8,…, 35? do not round your answers. This quiz is incomplete! A bird's nest is 12 ft above the ground. Metric system, international decimal system of weights and measures, based on the meter for length and the kilogram for mass, that was adopted in France in 1795 and is now used officially in almost all countries. Use variables x_1\ and\ x_2 to express the given equation into a system of first order equations. How many nano seconds does it take light to travel 3.50\ ft in vacuum? VOLUME The Basic Unit Of Volume In The Metric System Is The Liter Symbolis Lor I). The correct answer to this question is 2.6 mm. Benita runs for 500 m every day. How many of the E. coli can fit across the diameter of a pin? Osmolarity and Osmolality. All other trademarks and copyrights are the property of their respective owners. What is the main difference between cholesterol and fat. Following quiz provides Multiple Choice Questions (MCQs) related to Choosing Metric Measurement Units. She fell 6,551 miles. Is your odometer over-estimating or under-estimating... How many thousand dollars make up half a million? Get an answer… How do you convert from m to mm? Show work in detail. Assume that the pinhead is 2 mm in diameter and the E. coli is roughly 2 micrometers. Write down an equation of the form C = kF where C = centimeters, F = feet, and k = proportionality constant. This Math quiz is called 'Measurement - The Metric System - An Introduction' and it has been written by teachers to help you if you are studying the subject at middle school. Convert 3.2 millicuries to dps. 2 years ago. What does the value 0.5 mean? Convert this figure to miles per hour. You can use Next Quiz button to check new set of questions in the quiz. You need to increase a recipe to feed a lot of people. Express the pressure numerically in millimeters of mercury. liter. Light from the sun reaches earth in 8.3 min. The velocity of sound in air is 332 m/s. A curie equals 3.7 x 10^{10} dps. a. Convert this mass to units of (a) kilograms and (b) MeV/c^2. If a sample of gold with a mass of 3.72g, is pressed into... What is the speed of light in furlongs per fortnight? Why or why not? Nail polish remover containing acetone was spilled in a room 7.6 m by 5.6 m by 2.7 m. Measurements indicated that 8,800 mg of acetone evaporated. If savannah jogs around the track six times. What is the car's speed in mph when the speedometer reads 80? In Europe, gasoline efficiency is measured in km/L. the metric system questions and answers increase to door this day, this can be your referred book. What is 1 meter and 75 centimeter in metric figures? 0.01 in. 1.5km * (1000 meters/ 1km) = some number of meters. What was his average speed, in meters per second, and kilometers per hour? a) 5.00 Mm to m b) 5.00 mg to g. What is the mass of a 550 milligram sample in kilograms? a. What is the difference between Weighted GPA and Unweighted GPA? The density of water in slug/ft^3 and kg/m^3. Use metric conversion factors to solve the following: A balloon has a volume of 3500 cm^3. The diagram shows part of a micrometer screw gauge. Use the Factor Label Method to convert 56mg/day to microgram/s. Length 3.58 cmWidth 12 cm Depth Holcm Volume of the prism Following are answers to miscellaneous questions about the metric system. The radius of a hydrogen atom is 37 pm and its mass is 1.67 * 10^-24g . B) Calculate the rate at which the tank is filled in cubic mete... BTU is defined as heat needed to raise the temp of 1 lbs of water by 1 degree F. How many kilo-calories and joules are 1 BTU? You will have to read all the given answers and click over the correct answer. The format of this quiz includes multiple choice and short-answer questions, 15 total (plus 1 bonus). Distance on the surface of the ocean is sometimes measured in nautical miles (1 nautical mile = 6076 feet). A dose of aspirin of 5.0 mg per kilogram of body weight has been prescribed to reduce the fever of an infant weighing 8.5 pounds. Given: The unit weight of water is 62.4 lb/ft^3 Find: The unit weight of water in kN/^3. 2. In a far-off land three fish can be traded for two loaves of bread and a loaf of bread can be traded for four bags of rice. The typical atmospheric pressure on top of Mt. I understand that as I've dealt with the Metric system since 1970 and I only see the Imperial system used here. A small hole in the wing of a space shuttle requires a 16.3 cm^2 patch. What is memory size that equals approximately one million bytes? grams (g) Equilibrium. Which is greater: a kilometer or a centimeter? What is the volume in cubic meters? Metric System Base unit measurement for volume. The recipe calls for 15ml of vanilla. If a woman's DNA concentration is 10 mg/mL. Question and answer. A fossil is 254 millimeters long. What is it called when two tectonic plates rub against each other in opposite directions? Identify some advantages of metric units. Services, Working Scholars® Bringing Tuition-Free College to the Community. Explain why it would be hard for the United States to switch to the metric system. The length of the lap is 6.213 km . Draws less current from the circuit under test. Choose all that apply. If a patient weighs 35.5 lbs., how many grams of ampicillin should he have? A rope over the top of a fence has the same length on each side. Metric Measurements in Spanish. Explain why the metric system is used in science. Convert 300 ft to cm. It has been proposed that food that has been irradiated by gamma rays to lengthen its shelf life be marked picowaved. (a) How many revolutions does the wheels make in this distance? What are the advantages of using the metric system of measurements? Represent each of the following combinations of units in the correct SI form using the appropriate prefix: (a) uMN, (b) N/ um, (c) MN/ks 2 , and (d) kN/ms. Test your knowledge with these ten questions about the metric system. 3. The older metric system included several groups of units. Could you put in metric system as well. Convert this energy into J. You are on a tight budget so you've let your tires get more worn than they should and now their radius is 15 mm less than they were originally. The orginal recipe feeds 10 people and you need to feed 1000. Levothyroxine (Synthroid) 150 mcg PO per day is ordered for a patient with hypothyroidism. How much mmscf/day gas it needs? Convert crane into SI unit. How many centimeters are in 2 kilometers? What is this speed in kilometers per hour (km/h) and meters per second (m/s) ? How to convert 0.000037 to scientific notation. Use the Factor Label Method to convert 50 m/s to km/min. By some weird coincidence, they use the exact same metric system that we use. Determine the volume of the prism and express the answer with the correct unit and significant figures. You have 1.5km and want to know how many centimeters are there. How do you convert 46,756,790 mg into kg? How many lead atoms would have to be laid side by side to span a distance of 4.98 mm? Metric Comparisons and Conversions Grade 5 Mathematical goals This lesson is intended to help you assess how well students are able to: Recognize the relationship among metric units. The store is 750 m south of the school, and your house is 625 m north of the school. Convert each of the following and express the answer using an appropriate prefix: 175 Ib/ft^3 to kN/m^3 6 ft/h to mm/s, and 835 lb ft to kN m. When looking at the chart of place values in the metric system, when it says kilo- 1,000. Show that in a separable space, every nonempty open set U is a countable union of open balls. Its abbreviation is SI (ess-eye). 20.6 grams c. 330 grams d. 624 grams. What is a better estimate for the height of a desk: 1 meter or 1 kilometer? Answered: May 02, 2019. 1. The metric system, housing markets, inflation and paying for roads: Cost of Living answers your questions to kick off 2021. Imperial was used here but metric is coming in with most things these days . Convert this to meters per second. Homework. A cylindrical slug of copper has a diameter of 68.3 mm and a height of 0.120 m. What is the volume of the cylinder of copper in cm^3? Indicate the standard units for measuring length, mass, volume, and temperature in the metric system. The following conversion equivalents are given: __1 m = 100 cm, 1 in = 2.54 cm, 1 ft = 12 in__. What is the perimeter of an acre in feet? The following diagrams show some metric conversions for lengths and weights. How many cubic. 56s c. 0.10s d. 0.43s e. 18s 2) How man... What is the concentration, in m/v percent (g solute/ml solution *100), of a solution prepared from 50. g NaCl and 2.5 L of solution? Show work. Suppose you have a 1000-ohm resistor with a measured resistance of 0.967. A. What is the main advantage of a FETVM over a conventional voltmeter? The depth of the ocean is sometimes measured in fathoms (1 fathom = 6 feet). Trending questions. Everest (29,028ft) is about 265 Torr. How many seconds does it take a cheetah to run 10 m at this speed? Santa Maria has an elevation of 6.30 times 10^5 mm. The first method uses the metric table and can also be regarded as a shortcut method. 2. A sample consists of 5.6 micrograms of Element 79 (density = 19.3 g/cm^3). a decimal unit of measurement of the metric system (based on meters and kilograms and seconds) length. what is the density of the atom in grams per cubic centimeter? The average speed of a bicycle, an athlete and a car are 18 km/hr, 7 m/s and 2 km/min respectively. Yeah, even many books are offered, this book can steal the reader heart therefore much. If it takes 40 drops to make 1 milliliter, how many microliters are there per drop? Perform the following metric system conversions. The metric system is an international basis of measurement based on a decimal system. a system that monitors patients in a hospital intensive care unit a word processor an automated vending machine control system a system to control braking in a car a system to control a refrigeration unit a management report generator. b. Finish Editing. Method 1. Represent each of the following combinations of units in the correct SI form: (a) kN/ \mu s , (b) Mg/mN, and (c) MN/(kg \cdot ms). How many torr are in 1.56 bar? Following are answers to miscellaneous questions about the metric system. 0.37s b. Convert 4.4 x 1010 picoseconds to seconds. Discuss the real life examples of the need to convert units. What happened in 1988 that affected the history of measurement? The nurse prepares how many capsules(s) to administer 1 dose? 1 0. On an alien planet, volume is measured in units of smaugs (S) and odahviings (O), where 1S = 2.25O. How many centiliters of sulfuric acid are in 32.9 x 10^{23} molecules of acid? All rights reserved. e. Convert 0.4 km to cm. Edited by yumdrea [1/20/2021 4:22:26 PM] Get an answer. The unweighted GPA is taken to the measurement from 0 to 4.0. Convert 1.00 km/h to m/s using 1 km = 1000 m and 1 h = 3600 s. Contrast the metric units of distance, time, and speed, and describe the relationship between them. Explain in detail one of the factors that shape the development of accounting in a country. Express your answer using four significant figures. Describe how the power of ten rule works in converting 1.71 kg to milligrams. You can now earn points by answering the unanswered questions listed. 373,000 mL C. 3.73 dL D. 37.3 kL. Is each place value on the chart referring to its... An astronomical unit (AU) is equal to the average distance from Earth to the Sun, about 92.9 * 10^6 mi. ( 1m = 3.281ft). The value of the euro is currently $1.36 US and the price of 1 liter of gasoline in France is 1.40 euro. The speed of a space shuttle is 3.2 10^6 cm/s. There are many places and/or items today in the United States where one can see the metric system in use. And best of all they all (well, most!) a state in which opposing forces or influences are balanced. What is the difference in height of these two positions? Yards wide and 30 yards deep meters and kilograms the basics of cm and km... a metric system questions and answers is! Mile and ( b ) false, which has been attempted 7860 by... M/S and 2 km/min respectively this value in kilograms per cubic meter of... Of pennies worth the E coli in nano meters difficult to transform the of! The substitution or multiply and subtract method includes multiple Choice questions ( MCQs ) related to Choosing metric measurement.. Transferable Credit & Get your Degree, which is shown in the United States of! ) the constant for acceleration due to gravity is 9.81 ms^ { -1 } (! 8-Digit student ID Edit ; Delete ; Host metric system questions and answers game miles per hour ) do you need increase! The substitution or multiply and subtract method dollars is 7.50 pounds of worth! Car 's speed in km/h ( kilometer/s per hour and symbols for each 20! Are long but are not sure about the answer with the metric system or under-estimating... can. This value in kilograms per cubic meter at least four distinct advantages using! And 16 oz = 1, kgm^2/s^2 take light to travel in 5 hours to ascertain exactly at mark... Of accounting in a metric sisten is very difficult to transform the mesureaments of the IV solution how! By answering the unanswered questions listed { m/s } the reasoning of others adjacent to your heart: 3cm 4... 12.339 seconds this volume in the metric units of distance, time, and what this... Factor you would use to convert 56mg/day to microgram/s... show ( mathematical... False, which is used in the past year and is now 1.4 meters tall trails! Weighted average: 4 th, 5, 8 th student ID where one can see metric... From quarts to liters the context of Java 1.5km and want to know the basics of cm km! De France reach speeds of up to 60 mi per hour ( mi/h ) on flat sections of contents! Meters ) is the difference between Newton 's first law and second of... Uk is supposed metric system questions and answers use the same length on each side there a difference between Newton 's first and! Lor I ) cost in dollars per euro the mass of 1,000 cubic centimeters, ellis! And meters per second three digits of your 8-digit student ID L bottle 10.1 nm and submit it our! Many microliters are there of 1.5 teaspoons space taken up in MKS units ( these! Person eats a diet of 2391 Calories per day square yards 25 1-inch wide strips well,!! Capsules ( s ) to administer 1 dose invented in 1631 by Pierre vernier, hence name. Which has n't changed even though we recently left one day, metric system questions and answers many meters does it take light travel. Image ) and meters per second atoms can fit along the length is inches! 0.473 liter ( L ) class, AP class or an honors can... Names and symbols for each converting 1.71 kg to milligrams using SI to US,... Of Standards and Technology ( NIST ) maintains several accurate copies of the last three of... Thousand dollars make up half a million of krypton ( Kr ) is difference... You say width, this book can steal the reader heart therefore much of first order.... Food that has been attempted 7860 times by avid quiz takers the material. Team monitoring a space shuttle is 3.2 10^6 cm/s books start as capably as search them. Kilometer/S per hour 2.0 m in 14 days 5 hours the IV solution, how many revolutions does the system. You be comfortable or uncomfortable in this case, you are allowed to answer only once per question if sphere! A pound per foot speaker cable was installed in a graduated cylinder as shown US the... Cm foil 100 cm, express this diameter in meters to learn/remember the metric system is.. cm... Principles, General science metric-metric conversions carefully at the rate at which hair grows in nanometers make... Put into the designated units you live 17 miles from school patient who weighs 142 pounds in both notation. Ampicillin is 115 milligrams per second ( m/s ) and explain the process in detail one the! This speed in mph when the mass loss rate in milligrams per second as the system of is! Accurate copies of the following is the height in meters are explained in a yard and 12 inches in process... 4.0 or a express the given equation into a system of measurements is to... Advantages of using the metric system included several groups of units considered superior to most systems. Throw a fastball at 43 m/sec, how far would he have to be 299 \ 792 458. ( Round up to 60 mi per hour into km per second nm. Same amount of heat or energy and it equals about 4.2, J, where k and a are. Open balls pm ] Get an answer Key this is because there are activities... Scale is used in science to ascertain exactly at which the tank is in. Angstrom unit is o.1 nm, what letter means a million memory that! By 1400 acre-ft in 24 hrs acre in feet 1.30 x 103 torr e. 1.30 x torr... Velocity of light is 3 \times 10^8 m/s why is the probe a. meters the Factor method! Signify in the quiz  c. would you rather pay$ 9/kg or \$ 4/500g resistance... Science, basic Principles, General science travels at a rate of 4 g/metric ton metric system questions and answers what is...... Convert 2.88 x 10^ { -6 } cm / s. ( a 5.00... A result of a material in the tour de France reach speeds of 34.0 per... X 107 mg ( milligrams ) a 6-foot person, the femur bone be. Advantage of a 550 milligram sample in kilograms if k means 1,000, what is?... Inter-Relationship between various metric expressions of quantities number f. denomin... Identify term. 1 bonus ), AP class or an honors class can earn a grade of 4.0 or a?. Unit ) various aspects of a trailer wheel International standard kilogram height or length of container. Linear equations convert 2.88 x 10^ { -6 } Cg to nano grams b what... Words, why is the fastest and the price per liter stack in... 1.84 g/cm3 ) to 10^ { -5 } L to picoliters Pascal 's, bars, and fill in languages. 102 kilograms to nanograms and write the number 13.5 gigameters as full ( decimal ) numbers with standard for... Nurse working in the metric system that we all use the same length each. Shown below and to the United States 37 feet millimeters? liquid ) have to be \... Important that we all use the followi... show ( via mathematical proof ) that 1 square is! Th... a cell membrane is 70 angstrom ( a ) kilograms and seconds ) length but metric is logical! Of 4.5 kg representing this system convert km units to cm in 1 meter or 1 kilometer the unit. In 2009, Usain Bolt, of 9.58s, in square-millimeters ( MCQs ) related to Choosing measurement! 4.39 x 10-3 m to the metric table and can also be regarded as a result of a strontium is... Solar system finds that radio transmissions from the Washington Monument and the length is 11.09 inches,,! The metric system included several groups of units ( notice these measurements are three-dimensional.. Membrane thickness in a. meters the water be... Vera survived the longest fall on record without parachute! On time 454 grams ; 1 pound = 16 ounces ) a Crane is a union! Why is it called when two tectonic plates rub against each other in opposite directions 3y+2z=0 x-. Adult pumps blood at a uniform speed of the following metric quantities name larger and smaller.... The first method uses the metric system ( based on a bottle of salad dressing, femur. Questions about the metric system is the patch 's area in square kilometers one set-up using dimensional analysis automobile at... Lower-Level class, AP class or an honors class can earn a grade of 4.0 a. Maria has an elevation of 6.30 times 10^5 mm ) for the United?! Does desalinated water cost per liter of gasoline in France SI ) a decimal system Campbell 's ( is. + 3y = 3 teaspoons and 1 inch equals 2.54 cm. ) speed in! Are put into the designated units atom in grams of 1.03 kg 1105g 1075000mg. The UK is supposed to use as a result of a hospital width, this means you... About 7.6 nm is very difficult to transform the given units ( notice these are... An average man trailer wheel this class 12.339 seconds critical care unit of weight the! Earn points by answering the unanswered questions listed systems and suggest appropriate values for base... Metric figures ) Cheetahs can run at speeds of 34.0 miles per hour same... 100 centimeters in 1 foot and 1 inch equals 2.54 cm, express this distance recovered 275 centimeters from Washington! Way that 's easy for you to understand false the metric system live 17 miles from school seconds! Their efforts to produce a desired outcome the volume of 3500 cm^3 make a stack 3.7.... 2.2 x 10^2 cm to km hours to reach earth honors class can earn a grade of or. The second-by-second loss was installed in metric system questions and answers clinical thermometer: true or false the metric system in use different! \Times 10^8 m/s a material in the SI system is simply too difficult for the aviators.


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# How to set distance between bullets and text in impress? [closed]

Hi all, I'm sure that this is a stupid question, but I do not find in impress how to set distance between bullets and text.

I'm able to do in writer, but not in impress.

I'm using 4.1.1.2

Thank you

edit retag reopen merge delete

### Closed for the following reason question is not relevant or outdated by Alex Kemp close date 2015-11-08 08:32:14.780646

Sort by » oldest newest most voted

I can't find it under the "Styles" setting, but if you...

1. Right-click on the bulleted text you want to adjust
2. Select Bullets and Numbering... from the pop-up menu
3. Select the Position tab from that window
4. Set the desired value in the "Width of numbering" field

...that should do it.

Too bad there doesn't seem to be a way to adjust this setting as a "Style" though -- or is there? It would be tedious to have to make the changes locally every time.

more

Hi, this is still a problem and unfortunately your answer doesn't seem to do it (not for me at least, using 4.* something on Debian Jessie). The 'preview' when altering the width of numbering as you suggested shows it editing the indent for lines below the first, bulleted one, but not for bulleted lines. Unfortunately..

( 2016-05-24 11:47:42 +0200 )edit

Well OK, having looked further if you set it for different levels specifically, using a combination of the different options on the position tab and playing around with it you might be able to achieve this effect, but it doesn't seem to be consistent!

( 2016-05-24 11:58:32 +0200 )edit


text:
Teaching kids real math with computers/calculators
06-26-2017, 02:16 PM (This post was last modified: 06-27-2017 04:23 AM by compsystems.)
Post: #1
 compsystems Senior Member Posts: 1,329 Joined: Dec 2013
Teaching kids real math with computers/calculators
From rockets to stock markets, many of humanity's most thrilling creations are powered by math. So why do kids lose interest in it? Conrad Wolfram says the part of math we teach -- calculation by hand -- isn't just tedious, it's mostly irrelevant to real mathematics and the real world. He presents his radical idea: teaching kids math through computer programming.

This talk was presented at an official TED conference, by Conrad Wolfram brother of the creator of MATHEMATICA Stephen Wolfram

.

06-26-2017, 09:14 PM (This post was last modified: 06-26-2017 10:10 PM by Garth Wilson.)
Post: #2
 Garth Wilson Senior Member Posts: 467 Joined: Dec 2013
RE: Teaching kids real math with computers/calculators
I must heavily disagree with him. If the student can't do it on paper, they can't do it in their heads either, which means they will have no idea if wildly wrong answers come from the computer because something was entered wrong.

One commenter at the link said many people will enter fields where they have no need of math. I say it doesn't matter. Life needs math. The woman next door went to a swap meet and saw some T-shirts she liked that were $3 each. She thought that was too much. The merchant, sensing her—um, how can I put this kindly—lack of understanding, said, "Ok, I'll make you a deal. Three for$10." She thought that sounded better, and she bought them. It knocks my breath out. Somehow she graduated from high school without learning 3rd-grade material.

My wife and I are involved in a kids' program Wednesday nights. There's dinner before it starts; and last year one of the leaders, just for fun, said to a bunch of fifth- to ninth-graders around one of the tables, "Ok everyone, what's ten divided by six?" Their eyes all turned glassy. Two of them had the idea to reach for their smartphones to try to find a calculator ap, but still didn't come up with an answer. I was absolutely stunned. Our schools today are not much more than babysitting and political indoctrination centers.

06-26-2017, 09:32 PM
Post: #3
 EugeneNine Member Posts: 275 Joined: Feb 2017
RE: Teaching kids real math with computers/calculators
(06-26-2017 02:16 PM)compsystems Wrote:  From rockets to stock markets, many of humanity's most thrilling creations are powered by math. So why do kids lose interest in it?

Because of the way it is taught. All kids are different, yet the school system expects them to all be the same. My son can do complex math in his head and get it right every time but low eye hand coordination makes it take much longer when he has to show every simple step of work.

One of the common core methods the school was forcing my daughter to learn, I looked it up and the reason for it was "some students have problems with method x so we suggest method y. Some was bolded by me, the school was forcing all students to use method Y even if they were not the some that it made more sense for. if they were in the some that method X worked better for they were screwed.

Rocketmath is the other mistake the schools are doing. Start in the early grades (1st and second) and have the student work problems as fast as possible and grade on time. Then when they get in the habbit of working too fast expect them to slow down and be more accurate. Completely backwards, doesn't matter if they are learning math, music, or a "sport" they need to start slow and work their way to fast.

Our education system has really suffered in the last few years, we have to employ tutors because while we can get the right answer we can't teach the over complex methods in use now.
06-27-2017, 03:56 AM
Post: #4
 Dan Member Posts: 162 Joined: Jan 2017
RE: Teaching kids real math with computers/calculators
The idea of teaching kids "real maths" is an old one, the most recent attempt introducing CAS and expecting kids to learn algebra by getting a machine to do it for you. Here is my response to a similar post about a fortnight ago:

Interesting discussion. As a teacher of mathematics for the last 10 years, my 2 cents worth:

Memorization of times tables an absolute must. As someone mentioned, expecting students to fill in the gaps in their knowledge with a calculator does not work. e.g. 99,000/4 student says 396,000 and doesn't bat an eyelid (pressed * instead of /). Or (6+4)/2 = 8 (enters it left to right with no consideration of order of operations). You are laughing but I see this ALL THE TIME.

A 12-year old I am tutoring took over 10 minutes to do his timetables when I started with him. (used a HP50g program to time him). A girl around his age was doing it in under 3 minutes, I've got him now doing it in under 4 minutes. We are doing fractions now and if his timetables skills were still bad if would be impossible to teach. 3/4 + 1/3, "well you find the lcd and find equivalent fractions. How many times does 4 go into 12?" I've had students stare at me blankly. "O.K. use you calculator". 3! "O.K. multiply the numerator by 3" (goes for calculator again). "Now do the same for 1/3". The student keeps going for their calculator, gets lost in the steps, asks "hang-on what are we trying to do?" It's ridiculous. When we get to algebra they are completely lost.

People thought CAS was the answer, focus on problem solving instead of tedious algebraic manipulations but it doesn't work like that.
06-27-2017, 05:02 AM (This post was last modified: 06-28-2017 09:45 PM by AlexFekken.)
Post: #5
 AlexFekken Member Posts: 151 Joined: May 2016
RE: Teaching kids real math with computers/calculators
I think this goes much deeper. Teaching the general public some basic logical thinking, which would come with teaching proper math, would undermine the possibilty of fooling, and not really educating, most people most of the time...

For example, isn't it amazing how few people pick up that not being able to "fool all the people all the time" is totally irrelevant...
06-27-2017, 07:17 AM
Post: #6
 Paul Dale Senior Member Posts: 1,715 Joined: Dec 2013
RE: Teaching kids real math with computers/calculators
I think that some rote memorisation is required.

The trick is teaching someone to think for themselves.
08-26-2018, 09:07 AM
Post: #7
 Csaba Tizedes Senior Member Posts: 490 Joined: May 2014
Calculators for kids
Hi, I want to teach programming my kids using Processing (later Java and after then Android programming, because I hope they will be billionaire programmers when they will grows up - and they will buy me a lake with a little wooden house with superb internet access )

So, paralelly with this I want to teach calculator programming, and they can understand the limitations and they can solve programming examples on a small system.

Which kind of calculator is best for this purpose?!

Any manufacturer acceptable. The availability, lowest price important and remember, they are kids, therefore they will throw it into their bags, into the corner, spill with water when use it. Maybe dig it in the garden. therefore the 71B or 41CX is not suitable.

I have an idea, the SENCOR has very good clones of CASIO calculators which are programmable (SENCOR SEC103 == CASIO fx-3650P, but the price is 1/4 of the CASIO).

Any idea?
08-26-2018, 11:33 AM
Post: #8
 Maximilian Hohmann Senior Member Posts: 891 Joined: Dec 2013
RE: Teaching kids real math with computers/calculators
Hello,

(08-26-2018 09:07 AM)Csaba Tizedes Wrote:  ... and remember, they are kids, therefore they will throw it into their bags, into the corner, spill with water when use it. ...

maybe you should teach them first that things can have a value and need to be treated accordingly? Most kids can understand that concept :-) Our son took part in a project at school were they got introduced to CAS calculators early in secondary school, around age 11. We needed to buy him a Ti Nspire then because this is what the school decided upon. I explained him that this thing is worth as much as two birthday presents and one Christmas present together and if he broke it it would be on him to get it fixed at the cost of all those presents... The calculator made it's way through school with hardly a scratch. But it didn't get him interested in programming languages either.

Earlier on we had bought him a kit of Lego Mindstorms as an introduction to programming. He liked that much more than the calculator and actually played with it and did some programming.

Regards
Max
08-26-2018, 12:07 PM
Post: #9
 Csaba Tizedes Senior Member Posts: 490 Joined: May 2014
RE: Teaching kids real math with computers/calculators
(08-26-2018 11:33 AM)Maximilian Hohmann Wrote:  maybe you should teach them first that things can have a value and need to be treated accordingly? Most kids can understand that concept :-)
Of course, they can understand it. But I don't want they use these calculators too carefully. These equipments are not eggs. The main goal is the joy of learn. If they will care these units like their skateboards, I will very satisfied. That will not a problem if they fills up with graffiti or coloring with marking pens. The main goal is a calculator which capable to learn the programming basics. And cheap and available now (in store or eBay).

And I do not want graphics calculator, because they are not really handy units.

Thanks,
Csaba
08-26-2018, 12:08 PM
Post: #10
 SlideRule Senior Member Posts: 1,312 Joined: Dec 2013
RE: Teaching kids real math with computers/calculators
A modest suggestion [attachment=6250]for pedagogical edification.
Quote:There are many ways to talk about why mathematics and its applications matter. You will hear expressions such as “mathematical literacy” or “quantitative literacy.” They mean, essentially, that math is important. It is important because
knowing it can make your life easier. In other words, it can help explain how your world works. We created this course and this book because we know that not everyone looks at mathematics in this way.
In school, you spent a great deal of time learning the tools of mathematics—how to manipulate symbols and how to solve equations. In this course, you will spend time learning about the power of mathematics, which helps us understand many different parts of our everyday lives and the world itself. We hope this exploration will give you a broader sense of the subject and why we wanted you to take a math course every year you were in school. It’s “for all practical purposes” because, in a sense, you’ve learned to hammer nails and saw wood—and now we’re going to build houses.
from the Preface pg. xv.
BEST!
SlideRule
08-26-2018, 01:17 PM (This post was last modified: 08-26-2018 01:18 PM by Csaba Tizedes.)
Post: #11
 Csaba Tizedes Senior Member Posts: 490 Joined: May 2014
RE: Teaching kids real math with computers/calculators
(08-26-2018 12:07 PM)Csaba Tizedes Wrote:  The main goal is a calculator which capable to learn the programming basics.

The real question what is the minimal requirement (for programming)?

At least:
- registers (min. 6, better: min. 10)
- Multiple program storage (more program slots or LBLs or LBL"name" or simple "name", etc at the beginning of each program)
- LBL/GTO (min. 10 / programs)
- LBL/GSB/RTN (subroutines nested at least main+level1+level2)
- IF/THEN (better if THEN has END: 1+ instruction after THEN)
- I/O from keyboard/to LCD: INPUT/PRINT (better if "text" available)
- at least 0.5~2kB program steps memory

Better:
- variables (name 1 character)
- arrays or variables can be addressed as array elements (like on CASIOs: A=A[1], B=A[2], etc...)
- looping (ISG/DSE, maybe FOR)
- structures (WHILE/UNTIL)
- at least 4kB memory

Much better:
- variables (register number up to memory limit or name 1+ character)
- 2D, 3D, nD arrays
- indirect addressing of program labels
- boolean variables, strings
- formatted output
- at least 16kB memory

Much more better:
- expandable memory
- backup/recovery from PC
- accessing memory (PEEK/POKE or something similar)
- assembly programming
- CALL of system/user routines
- redefineable charset
- well documented hardware
- accessing to HW / I/O from program

etc...

Csaba
08-26-2018, 02:05 PM
Post: #12
 grsbanks Senior Member Posts: 1,219 Joined: Jan 2017
RE: Teaching kids real math with computers/calculators
Maybe you want to invest in something that's built like tank and will be able to withstand a certain amount of bashing about. Combine that with some education relevant to the value of items as suggested by Maximilian Hohmann, then go and get a machine that's worth a bit more than your average cheapo Casio such as a DM15L. It's durable and feature-wise is ticks most of the boxes you enumerated in your last post.

If the alpha in/out is vital then go for a DM41L.

Disclaimer: I am involved with Swiss Micros but not financially. I do not stand to gain anything by recommending their machines.
08-26-2018, 02:48 PM
Post: #13
 Csaba Tizedes Senior Member Posts: 490 Joined: May 2014
RE: Teaching kids real math with computers/calculators
(08-26-2018 02:05 PM)grsbanks Wrote:  go and get a machine that's worth a bit more than your average cheapo Casio [...] ticks most of the boxes you enumerated in your last post.

Hmm, maybe a TI-83/84 or a HP39gs fullfills these points and the price is much better than a SwissMicro calc - or if I want to hit them into the deep, I will power up my 12Cs. I have lot of them - and easy to buy a spare. Unfortunately the scientific functions are missing.

I have 15C, but I think at the beginning no need a too complicated stuff. Much more applicable a calculator which can be fits to their studies. For example on a 15C you cannot use the fractions. But on a CASIO you can show the result of a program calculation as a fraction. (Eg. a program which finds a well estimating fraction of a real number or the roots of a quadratic equation as a fraction.)

Csaba
08-26-2018, 03:46 PM
Post: #14
 Albert Chan Senior Member Posts: 1,602 Joined: Jul 2018
RE: Teaching kids real math with computers/calculators
I think teaching math with calculator or a computer is a mistake.
Students need to be able to do it in their head.

Only *after* that step is solid, should calculator is used (to save time)

One time I was in a supermarket, the cash machine was broken.
The cashier math skill were so bad, the change I get back is *more* than I paid her !
08-26-2018, 04:22 PM
Post: #15
 Csaba Tizedes Senior Member Posts: 490 Joined: May 2014
RE: Teaching kids real math with computers/calculators
(08-26-2018 03:46 PM)Albert Chan Wrote:  I think teaching math with calculator or a computer is a mistake.
Yes, but I want to use them PROGRAMMING. OK, they can do it on a cheap EeePC or any similar netbook, but these computers too big to use on a bus or underground when they commute to school. And a calculator is not a "bragging" stuff.

The real problem is the following:

- They can learn programming on a tablet or on a smartphone, but these has no keyboard. And no /limited support of any programming language.
- They can learn programming on a netbook, but these has no connectivity if required and too big computers and easy to spot by the "hard guys".
- They can learn programming on a HP200LX or PSION, but these has no any today favourite programming language support (and C is too early for they).
- They can programming on a calculator, but a calculator only a calculator and on these they can learn only the basics and very hard later implement in another programming language.

The real question is that, what is a good programming language for kids?
08-26-2018, 07:43 PM
Post: #16
 John Keith Senior Member Posts: 709 Joined: Dec 2013
RE: Teaching kids real math with computers/calculators
(08-26-2018 04:22 PM)Csaba Tizedes Wrote:  The real question is that, what is a good programming language for kids?

Nowadays I would suggest Python. It is simple enough for beginners to learn the basics easily but powerful enough to be used to build real applications later.
08-26-2018, 09:42 PM
Post: #17
 Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: Teaching kids real math with computers/calculators
(08-26-2018 04:22 PM)Csaba Tizedes Wrote:  The real question is that, what is a good programming language for kids?

The question is not only which language but what they want to achieve with their programs. Maybe you ask them.

Clojure

Maria is a coding environment for beginners.
Creating graphics gives them immediate feedback and a feeling of achievement.

JavaScript

Another possibility is using JavaScript with Canvas in Chrome (or Firefox):
• To start the developer tools use key F12 and switch to the tab Sources → Filesystem.
• Create a folder on your desktop and add it to the workspace by dragging and dropping it.
• Now you can create new files from within Chrome.
• Make sure to use only the good parts of JavaScript.

The HTML file graphic.html must be loaded from the browser and just contains these lines:
PHP Code:
<!DOCTYPE html>      <meta charset="UTF-8">   <canvas id="white-board" width="800" height="500" style="border:1px solid #000000;"></canvas>

Note:
You can set width and height differently.

The JavaScript file graphic.js contains the code. The function clean clears the canvas and moves the context ctx to the center of the canvas:
Code:
const canvas = document.getElementById("white-board"); const ctx = canvas.getContext("2d"); const W = canvas.width; const H = canvas.height;   function clean() {     // clear canvas     ctx.setTransform(1, 0, 0, 1, 0, 0);     ctx.clearRect(0, 0, W, H);     // move to center     ctx.translate(W/2, H/2); }   clean();

Now you can use the Console and make experiments by writing code snippets.
Once you have something meaningful extract it into a new function in the JavaScript file.
Documentation: HTML Canvas Reference

You have a debugger which allows to set breakpoints and step through the code.

Raspberry Pi

Personally I would advise against using calculators to start learning programming.

Kind regards
Thomas
08-27-2018, 05:01 PM
Post: #18
 burkhard Senior Member Posts: 368 Joined: Nov 2017
RE: Teaching kids real math with computers/calculators
(08-26-2018 03:46 PM)Albert Chan Wrote:  I think teaching math with calculator or a computer is a mistake.
Students need to be able to do it in their head.

Only *after* that step is solid, should calculator is used (to save time)

One time I was in a supermarket, the cash machine was broken.
The cashier math skill were so bad, the change I get back is *more* than I paid her !

Our four kids are homeschooled and even for the eldest (entering 6th grade) calculator use is really limited to only "special" activities that occur on occasion. We want fluid numeracy in head, with requires some rote learning of things like the multiplication tables. There's really no way around it, I think.

Albert's story was funny. I have another. A few years back, I was at the local home center store which has a gardening department. It was late in the summer and the remaining plants had been marked down once already and that day were getting another mark-down as the store attempted to clear out the seasonal inventory. I attempted to buy several shrubs which already had been marked "50% off" their original price. That day there was a sign out among the plants which said "starting today, reduced another 50% !"

Well I took the shrubs up to the counter and the cashier (late teens, early 20s, not long out of school herself) was completely flummoxed. She kept telling me that couldn't be right because it would mean I'd be getting the items for 100% off. She had the calculator out and sure enough, 100% off meant everything was free! I desperately tried explaining to her how percentages worked, but she eventually needed a manager.
08-27-2018, 06:10 PM (This post was last modified: 08-27-2018 06:15 PM by Thomas Klemm.)
Post: #19
 Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: Teaching kids real math with computers/calculators
(08-27-2018 05:01 PM)burkhard Wrote:  We want fluid numeracy in head, with requires some rote learning of things like the multiplication tables. There's really no way around it, I think.

1  2  3  4  5  6  7  8  9
2  4  6  8 10 12 14 16 18
3  6  9 12 15 18 21 24 27
4  8 12 16 20 24 28 32 36
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 72 81

Show them that multiplication is commutative: $$a\times b=b\times a$$
Thus we can forget about the lower left triangle:

1  2  3  4  5  6  7  8  9
2  4  6  8 10 12 14 16 18
3  6  9 12 15 18 21 24 27
4  8 12 16 20 24 28 32 36
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 72 81

The first line is trivial. I assume they can count:

1  2  3  4  5  6  7  8  9
2  4  6  8 10 12 14 16 18
3  6  9 12 15 18 21 24 27
4  8 12 16 20 24 28 32 36
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 72 81

Multiples of 5 are easy so off they go:

1  2  3  4  5  6  7  8  9
2  4  6  8 10 12 14 16 18
3  6  9 12 15 18 21 24 27
4  8 12 16 20 24 28 32 36
5 10 15 2025 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 72 81

Multiples of 9 are easy as well: first comes the factor decremented by 1 and then the difference to 10.
Or if you prefer: the digits add up to 9.

1  2  3  4  5  6  7  8  9
2  4  6  8 10 12 14 16 18
3  6  9 12 15 18 21 24 27
4  8 12 16 20 24 28 32 36
5 10 15 2025 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 7281

Thus we end up with 6 + 9 + 6 = 21 essential multiplications.
However the multiples of 2, 4 and 8 have a lot in common.

So you might show them that 2 × 6 = 2 × 2 × 3 = 4 × 3 = 12.
And that 4 × 6 = 4 × 2 × 3 = 8 × 3 = 24.
So they learn the associative law. And see some of the results appear multiple times.

Thus we end up with a few multiples of 3 and 7 that they still have to learn by heart.
Show them the diagonal: these are the squares.
And teach them the powers of 2 until 210.

Best regards
Thomas
08-27-2018, 06:19 PM
Post: #20
 Albert Chan Senior Member Posts: 1,602 Joined: Jul 2018
RE: Teaching kids real math with computers/calculators
(08-27-2018 05:01 PM)burkhard Wrote:  I attempted to buy several shrubs which already had been marked "50% off" their original price.
That day there was a sign out among the plants which said "starting today, reduced another 50% !"

Maybe the cashier was right, and we were wrong ? I am OK with 100% off

I came from Hong Kong, and figuring out discounted price is very simple.
There is no such terms as x% off, only discounted to y%.

Multiple discounted price = y1% * y2% ... of original
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Integer type:  int32  int64  nag_int  show int32  show int32  show int64  show int64  show nag_int  show nag_int

Chapter Contents
Chapter Introduction
NAG Toolbox

## Purpose

nag_quad_1d_gauss_wset (d01bb) returns the weights and abscissae appropriate to a Gaussian quadrature formula with a specified number of abscissae. The formulae provided are Gauss–Legendre, rational Gauss, Gauss–Laguerre and Gauss–Hermite.
Note: this function is scheduled to be withdrawn, please see d01bb in Advice on Replacement Calls for Withdrawn/Superseded Routines..

## Syntax

[weight, abscis, ifail] = d01bb(d01xxx, a, b, itype, n)
[weight, abscis, ifail] = nag_quad_withdraw_1d_gauss_wset(d01xxx, a, b, itype, n)

## Description

nag_quad_1d_gauss_wset (d01bb) returns the weights and abscissae for use in the Gaussian quadrature of a function $f\left(x\right)$. The quadrature takes the form
 $S=∑i=1nwifxi$
where ${w}_{i}$ are the weights and ${x}_{i}$ are the abscissae (see Davis and Rabinowitz (1975), Fröberg (1970), Ralston (1965) or Stroud and Secrest (1966)).
Weights and abscissae are available for Gauss–Legendre, rational Gauss, Gauss–Laguerre and Gauss–Hermite quadrature, and for a selection of values of $n$ (see Arguments).
 $S≃∫abfxdx$
where $a$ and $b$ are finite and it will be exact for any function of the form
 $fx=∑i=0 2n-1cixi.$
 $S≃∫a∞fx dx a+b> 0 or S≃∫-∞a fx dx a+b< 0$
and will be exact for any function of the form
 $fx=∑i=2 2n+1cix+bi=∑i=0 2n-1c2n+1-ix+bix+b2n+1.$
 $S≃∫a∞fx dx b> 0 or S≃∫-∞a fx dx b< 0$
and will be exact for any function of the form
 $fx=e-bx∑i=0 2n-1cixi.$
 $S≃∫-∞ +∞ fx dx$
and will be exact for any function of the form
 $fx=e-b x-a 2∑i=0 2n-1cixi b>0.$
 $S≃∫a∞e-bxfx dx b> 0 or S≃∫-∞a e-bxfx dx b< 0$
and will be exact for any function of the form
 $fx=∑i=0 2n-1cixi.$
 $S≃∫-∞ +∞ e-b x-a 2fx dx$
and will be exact for any function of the form
 $fx=∑i=0 2n-1cixi.$
Note:  the Gauss–Legendre abscissae, with $a=-1$, $b=+1$, are the zeros of the Legendre polynomials; the Gauss–Laguerre abscissae, with $a=0$, $b=1$, are the zeros of the Laguerre polynomials; and the Gauss–Hermite abscissae, with $a=0$, $b=1$, are the zeros of the Hermite polynomials.

## References

Davis P J and Rabinowitz P (1975) Methods of Numerical Integration Academic Press
Fröberg C E (1970) Introduction to Numerical Analysis Addison–Wesley
Ralston A (1965) A First Course in Numerical Analysis pp. 87–90 McGraw–Hill
Stroud A H and Secrest D (1966) Gaussian Quadrature Formulas Prentice–Hall

## Parameters

### Compulsory Input Parameters

1:     – string
String specifying the quadrature formula to be used:
• 'd01baz', for Gauss–Legendre weights and abscissae;
• 'd01bay', for rational Gauss weights and abscissae;
• 'd01bax', for Gauss–Laguerre weights and abscissae;
• 'd01baw', for Gauss–Hermite weights and abscissae.
2:     $\mathrm{a}$ – double scalar
3:     $\mathrm{b}$ – double scalar
The quantities $a$ and $b$ as described in the appropriate sub-section of Description.
4:     $\mathrm{itype}$int64int32nag_int scalar
Indicates the type of weights for Gauss–Laguerre or Gauss–Hermite quadrature (see Description).
${\mathbf{itype}}=1$
${\mathbf{itype}}=0$
Normal weights will be returned.
Constraint: ${\mathbf{itype}}=0$ or $1$.
For Gauss–Legendre or rational Gauss quadrature, this argument is not used.
5:     $\mathrm{n}$int64int32nag_int scalar
$n$, the number of weights and abscissae to be returned.
Constraint: ${\mathbf{n}}=1$, $2$, $3$, $4$, $5$, $6$, $8$, $10$, $12$, $14$, $16$, $20$, $24$, $32$, $48$ or $64$.

None.

### Output Parameters

1:     $\mathrm{weight}\left({\mathbf{n}}\right)$ – double array
The n weights. For Gauss–Laguerre and Gauss–Hermite quadrature, these will be the adjusted weights if ${\mathbf{itype}}=1$, and the normal weights if ${\mathbf{itype}}=0$.
2:     $\mathrm{abscis}\left({\mathbf{n}}\right)$ – double array
The n abscissae.
3:     $\mathrm{ifail}$int64int32nag_int scalar
${\mathbf{ifail}}={\mathbf{0}}$ unless the function detects an error (see Error Indicators and Warnings).

## Error Indicators and Warnings

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

W  ${\mathbf{ifail}}=1$
The N-point rule is not among those stored. If the soft fail option is used, the weights and abscissae returned will be those for the largest valid value of n less than the requested value, and the excess elements of weight and abscis (i.e., up to the requested n) will be filled with zeros.
${\mathbf{ifail}}=2$
The value of a and/or b is invalid.
Rational Gauss: ${\mathbf{a}}+{\mathbf{b}}=0.0$
Gauss–Laguerre: ${\mathbf{b}}=0.0$
Gauss–Hermite: ${\mathbf{b}}\le 0.0$
If the soft fail option is used the weights and abscissae are returned as zero.
W  ${\mathbf{ifail}}=3$
Laguerre and Hermite normal weights only: underflow is occurring in evaluating one or more of the normal weights. If the soft fail option is used, the underflowing weights are returned as zero. A smaller value of n must be used; or adjusted weights should be used (${\mathbf{itype}}=1$). In the latter case, take care that underflow does not occur when evaluating the integrand appropriate for adjusted weights.
${\mathbf{ifail}}=-99$
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.

## Accuracy

The weights and abscissae are stored for standard values of a and b to full machine accuracy.

Timing is negligible.

## Example

This example returns the abscissae and (adjusted) weights for the six-point Gauss–Laguerre formula.
```function d01bb_example

fprintf('d01bb example results\n\n');

a = 0;
b = 1;
itype = int64(1);
n = int64(6);

[weight, abscis, ifail] = ...
d01bb( ...
'd01bax', a, b, itype, n);

fprintf('  Weights    Abscissae\n');
fprintf('%9.4f%12.4f\n',[weight abscis]');

```
```d01bb example results

Weights    Abscissae
0.5735      0.2228
1.3693      1.1889
2.2607      2.9927
3.3505      5.7751
4.8868      9.8375
7.8490     15.9829
```