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Giuseppe Veronese

Quick Info

Born
7 May 1854
Chioggia (now Italy)
Died
17 July 1917

Summary
Giuseppe Veronese was an Italian mathematician who worked on the geometry of multidimensional spaces, model theory and transfinite numbers.

Biography

Giuseppe Veronese was born and brought up in Chioggia which was a small fishing village not far from Venice. His father was a house painter and his mother Elenora Duse was related to a famous actress. However, it was a poor family and they could not afford to finance Giuseppe through university. In 1872, at age eighteen, Veronese had give up his education to take a job in Vienna.

Veronese was fortunate, however, and the following year he was able to begin his studies again. He found himself a patron in Count Nicolò Papadopoli who supported him financially so that he could go to Zürich Polytechnic in 1873. There he set out on a course of study which involved both engineering and mathematics. However, he began to correspond with Cremona, who was at the University of Rome, on mathematical topics. He started work on a paper on Pascal's hexagram but, following Cremona's advice, he moved to Rome to complete his undergraduate degree.

In 1876 Veronese was appointed as assistant in analytical geometry on the strength of his paper on Pascal's hexagram which he had completed by this time. This is quite remarkable for one should remember that at this point Veronese was still studying the undergraduate course in Rome. He graduated in 1877 and continued to work for his doctorate in Rome. Veronese was in contact with Klein who was about to take up a chair of geometry at the University of Leipzig. It was arranged that Veronese would go to Leipzig in 1880 and to spend the year 1880-81 undertaking research under Klein.

Bellavitis died in November 1880 and his chair of algebraic geometry in Padua became vacant. The chair was filled by holding a competition which Veronese won and he was appointed to the chair in 1881. He held this chair throughout his life.

Freguglia, in [5], describes Veronese's study of geometry in higher dimensions. In 1880 Veronese described an $n$-dimensional projective geometry, showing that simplifications could be obtained in passing to higher dimensions. He illustrated the fact that difficulties arose when a simple surface in high dimension was projected onto 3-space. This was a very original approach to higher-dimensional projective geometry that Veronese developed. He is certainly considered to be one of the founders of that topic for with him what others had considered as linear algebra viewed geometrically became geometry.

This original approach was based on the supremacy of geometric intuitive techniques over the analytic and algebraic viewpoints. Veronese provided both logical and psychological motivations for his approach which greatly influenced the Italian school of geometry for many years.

Veronese invented non-Archimedean geometries which he proposed around 1890. However Peano strongly criticised the notion due to the lack of rigour of Veronese's description and also for the fact that he did not justify his use of infinitesimal and infinite segments. The resulting argument was extremely useful to mathematics since it helped to clarify the notion of the continuum. Any fears that non-Archimedean systems would not be consistent were shown to unnecessary soon after this when Hilbert proved that indeed they were consistent.

We should mention one or two further aspects of Veronese's life. He wrote a number of useful secondary school texts on mathematics and he also became involved in politics. He served as a member of the Parliament of Chioggia from 1897 to 1900, then later he served as a member of the Padua City Council, finally being a Senator from 1904 until his death.

He had two particularly famous pupils. Castelnuovo, one of the greatest algebraic geometers of the Italian school, was his pupil in the mid 1880s and Levi-Civita was one of his pupils about ten years later.

References (show)

1. F G Tricomi, Biography in Dictionary of Scientific Biography (New York 1970-1990). See THIS LINK.
2. L Boi, The influence of the Erlangen Program on Italian geometry, 1880-1890 : n-dimensional geometry in the works of D'Ovidio, Veronese, Segre and Fano, Arch. Internat. Hist. Sci. 40 (124) (1990), 30-75.
3. B Busulini, La retta non-archimedea di Giuseppe Veronese, Ist. Veneto Sci. Lett. Arti Atti Cl. Sci. Mat. Natur. 128 (1969/70), 239-263.
4. G Fisher, Veronese's non-Archimedean linear continuum, in Real numbers, generalizations of the reals, and theories of continua (Dordrecht, 1994), 107-145.
5. P Freguglia, The foundations of higher-dimensional geometry according to Giuseppe Veronese (Italian), in Geometry Seminars, 1996-1997 (Bologna, 1998), 253-277.
6. C F Manara, Giuseppe Veronese ed il problema del continuo geometrico, Rendiconti del Seminario matematico e fisico di Milano 56 (1986), 99-111.
7. C Segre, Commemorazione del socio nazionale Giuseppe Veronese, Atti dell'Accademia nazionale dei Lincei. Rendiconti 26 (1917), 249-258.


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## LATEX-L@LISTSERV.UNI-HEIDELBERG.DE

 Options: Use Forum View Use Monospaced Font Show Text Part by Default Show All Mail Headers Message: [<< First] [< Prev] [Next >] [Last >>] Topic: [<< First] [< Prev] [Next >] [Last >>] Author: [<< First] [< Prev] [Next >] [Last >>]

 Subject: Re: Guidelines on the new hook management From: Michal Hoftich <[log in to unmask]> Reply To: Mailing list for the LaTeX3 project <[log in to unmask]> Date: Thu, 23 Jul 2020 14:37:09 +0200 Content-Type: text/plain Parts/Attachments: text/plain (76 lines)
Hello Joseph,

> # \shipout
>
> There are very few packages that actually modify the \shipout primitive:
> almost everyone uses either everyshi or atbegshi, and we have arranged
> for those to be emulated. As such, the only packages that need to be
> modified here are those that *directly*, which is limited as far as we
> know to pgf, crop and a few other packages. There are then a number of
> hooks one can use
>
> - shipout/before
> - shipout/foreground
> - shipout/background
> - shipout/firstpage
> - shipout/lastpage
>
> as described in "texdoc ltshipout".

We patch \shipout on one occasion:

\let\:shipout=\shipout
\def\shipout{\vfil\break\let\shipout=\:shipout \shipout}

If I understand correctly, it is executed only in the first use of
\shipout  and it doesn't seem to do anything useful, although I am
sure there was a use case at some point for that.

Is this code OK? It should work even in Plain.

> # \document
>
> Many more packages patch \document. Those adding code using
> \AtBeginDocument will have no issues: this kernel-level hook will
> continue to be available, although it is now a wrapper around
> \AddToHook. Many others will be using etoolbox's hooks: they are already
> aware of the new kernel hooks and again will need no work from package
> authors.
>

Yes, we use \AtBeginDocument a lot. It is good that this will continue to work.

> For people directly altering \document, the need to take action will
> depend on the exact nature of the changes. For example, I have had to
> adjust beamer, but siunitx, which also patches \document, continues to
> work with no action. (I will update to use 'best practice', but that is
> not a *requirement*.) Basically, anything that starts messing with the
> detail of \document needs action, whereas simply adding a macro to the
> end of \document works out OK.
>
> Where you do need to take action, there are now a number of hooks
>
> - env/document/before: Occurs as soon as \begin{document} is seen,
>      before the group is opened
> - env/document/begin: Occurs just after environment group is opened:
>     for \document this is not really different from the above due to
>     the special nature of \document
> - begindocument: Replaces \AtBeginDocument, occurring after the .aux
> - begindocument/end: Occurs right at the end of \document, followed
>      only by \ignorespaces: where many people add 'last minute' stuff to
>      \document
>

This seems really useful, thanks.

BTW, I was able to find the main clashes between TeX4ht and new LaTeX
code, so it works for the test file. I hope it will work also for real
world documents.

Best regards,
Michal

format: plain


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# Difference polynomials

(Redirected from Stirling polynomial)

In mathematics, in the area of complex analysis, the general difference polynomials are a polynomial sequence, a certain subclass of the Sheffer polynomials, which include the Newton polynomials, Selberg's polynomials, and the Stirling interpolation polynomials as special cases.

## Definition

The general difference polynomial sequence is given by

$p_n(z)=\frac{z}{n} {{z-\beta n -1} \choose {n-1}}$

where ${z \choose n}$ is the binomial coefficient. For $\beta=0$, the generated polynomials $p_n(z)$ are the Newton polynomials

$p_n(z)= {z \choose n} = \frac{z(z-1)\cdots(z-n+1)}{n!}.$

The case of $\beta=1$ generates Selberg's polynomials, and the case of $\beta=-1/2$ generates Stirling's interpolation polynomials.

## Moving differences

Given an analytic function $f(z)$, define the moving difference of f as

$\mathcal{L}_n(f) = \Delta^n f (\beta n)$

where $\Delta$ is the forward difference operator. Then, provided that f obeys certain summability conditions, then it may be represented in terms of these polynomials as

$f(z)=\sum_{n=0}^\infty p_n(z) \mathcal{L}_n(f).$

The conditions for summability (that is, convergence) for this sequence is a fairly complex topic; in general, one may say that a necessary condition is that the analytic function be of less than exponential type. Summability conditions are discussed in detail in Boas & Buck.

## Generating function

The generating function for the general difference polynomials is given by

$e^{zt}=\sum_{n=0}^\infty p_n(z) \left[\left(e^t-1\right)e^{\beta t}\right]^n.$

This generating function can be brought into the form of the generalized Appell representation

$K(z,w) = A(w)\Psi(zg(w)) = \sum_{n=0}^\infty p_n(z) w^n$

by setting $A(w)=1$, $\Psi(x)=e^x$, $g(w)=t$ and $w=(e^t-1)e^{\beta t}$.


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## The Dirac equation as a quantum walk: higher dimensions, observational convergence    [PDF]

Pablo Arrighi, Marcelo Forest, Vincent Nesme
The Dirac equation can be modelled as a quantum walk, with the quantum walk being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a lattice); homogeneous (i.e. translation-invariant and time-independent), and causal (i.e. information propagates at a bounded speed, in a strict sense). This quantum walk model was proposed independently by Succi and Benzi, Bialynicki-Birula and Meyer: we rederive it in a simple way in all dimensions and for hyperbolic symmetric systems in general. We then prove that for any time t, the model converges to the continuous solution of the Dirac equation at time t, i.e. the probability of observing a discrepancy between the model and the solution is an O({\epsilon}^2), with {\epsilon} the discretization step. At the practical level, this result is of interest for the quantum simulation of relativistic particles. At the theoretical level, it reinforces the status of this quantum walk model as a simple, discrete toy model of relativistic particles. Keywords: Friedrichs symmetric hyperbolic systems, Quantum Walk, Quantum Lattice Gas Automata, Quantum Computation, Trotter-Kato, Baker-Campbell-Thomson, Operator splitting, Lax theorem
View original: http://arxiv.org/abs/1307.3524


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Posted 2015-03-31 16:27:13 +0200

# Bluetooth low energy Advertising, a beginner's tutorial

The purpose of this tutorial is to get you started with the basics of the nRF5x and Bluetooth Low Energy (BLE). The tutorial is fairly superficial and is meant to be a hands-on introduction to BLE advertising and broadcasting of a limited payload. It is intended to be a fun way to get you started with something functional, and maybe inspire you to go further with BLE. Here you will not learn details of the BLE protocol, but we will have a quick look at what you should know before making an advertising device.

# Before we begin

### Table of context

1. Before we begin
2. The "Hello world" example
• Bonding
5. Scan response data

Change Log 2016.03.14: Updated tutorial to suit SDK V11.0.0 and the possibility to use both nRF51 and nRF52 kits.

### Equipment and software

To complete this tutorial you will need the following:

Other kits, dongles and software versions might work as well, but this is what I have used. This tutorial will not cover how to install and setup the software. Please search the forum if you run into trouble before posting questions here.

### Necessary prior knowledge

It is expected that you have basic knowledge of how to use Keil, MCP and nRFgo Studio and how to download your application to your kit. Please browse the Tutorial section and the Infocenter to find guides on how to use your equipment and compile your first BLE application. Here is an excellent blogpost that I highly recommend you read. It provides a more in depth explanation on how advertising works and is a natural supplement to this tutorial.

If you run into troubles please browse devzone, look for documentation on our Infocenter, and read the user guides for your kits. I urge you to post any questions you might have on the forum and not below the tutorial. This makes it is easier for other users and Nordic employees to see and search for your question and you will actually most likely get a faster response(!).

# The “Hello world” example

First thing first: download the example code from github. It is based on the template example found in the SDK V11.0.0, but stripped of all code that is not necessary for our purpose. There is still quite a lot of code left though, which is used to initiate and utilize processes running in the background. The code is not essential for this tutorial and can be left as is. If you are curious of what it is anyway then here are some links to documentation on some of the modules that are used in the code:

1. The Device Manager. This is a module that handles active and bonded connections. Since this tutorial is about advertising and not connections it is not really relevant. Still I chose to leave it in the code as it is extensively used in more advanced examples, so I figured you might just as well get used to it being there and it doesn't do any harm.
2. The Button Support Package (bsp). This module is used to handle the LEDs and the buttons. In this example you will notice that an LED is blinking when your board is advertising. After 180 seconds the board will stop advertising and go to sleep. Then you can push Button 1 and the board will wake up and start advertising again. All this is handled by the bsp module.
3. Various _evt() and _dispatch() functions. These are functions that handle BLE and system events that originates in the Softdevice. They also allow your application to take various actions based on what is going on in the Softdevice. We will not dwell on these functions in this tutorial.

To compile the example download the files and copy the folder "nrf5x-ble-tutorial-advertising" to "your_SDK_folder\examples\ble_peripheral". Your main.c file should then be found in the folder "your_SDK_folder\examples\ble_peripheral\nrf5x-ble-tutorial-advertising". If you need help with this please have a look at this thread on devzone: Compiling github projects. Open the project file "ble_app_tutorial_advertising.uvprojx" and hit “Build”. It should compile without any errors or warnings.

Now, let us have some fun right away. Make sure you have programmed the correct SoftDevice to your nRF5x DK kit and compiled the example successfully. Then hit the download button in Keil and load the example onto your kit as well. Open MCP and start discovery using your nRF51 Dongle as master emulator. To learn how to use MCP and a master emulator read this tutorial: Testing and using a simple BLE application. A device named “HelloWorld” should show up in the list of discovered devices as shown in the picture below.

What you see in the picture is:

• The device name as defined in our main.c file. Try to search for #define DEVICE_NAME in your code and change the string to something of your own choice (just don’t make it too long). Now compile and download your application again and see how your device name has changed.
• The Bluetooth Device Address. Similar to a Media Access Control address (MAC address), but not necessarily universally unique.
• The Received Signal Strength Indicator (RSSI). This is a value of how good your signal strength is. Move your kit around or lay your hand over the PCB antenna on your kit and see how the RSSI changes.

Now expand the "HelloWorld" device tree by clicking on the little cross to the left. You should see something similar to the next image.

What you see here is:

The Received Signal Strength Indicator as mentioned above.

The Bluetooth Device Address as mentioned above.

Address type as defined in the Bluetooth Core specification. See this post on devzone for more on address types. The default address type in our example is “Random static address”. Try to go into gap_params_init() in main.c and add these four lines at the end of the function:

ble_gap_addr_t gap_address;
APP_ERROR_CHECK(err_code);// Check for errors

This will set the address type to “Private Resolvable address”.The Address type will still show up as “Random”, but try to reset your board a few times. You should see that after each reset your device shows up with a different address in the device list. This functionality might be handy in certain situations demanding higher security. Remove the lines again to change the address type back to “Random static address”.

To keep it simple there are two advertising types; connectable and non-connectable. Non-connectable might be useful if you just need one-way communication and only need to broadcast a couple of bytes. One use case for this might for example be location awareness. If you want to send more data to a specific device, on the other hand, you need a connectable device. Examples here might be a heart rate sensor connected to an app on your phone or a Bluetooth headset.

### Bonded

This shows whether the device is bonded to another device or not. The purpose of bonding is described in the Bluetooth Core Specification 4.2 as:

"The purpose of bonding is to create a relation between two Bluetooth devices based on a common link key (a bond). The link key is created and exchanged (pairing) during the bonding procedure and is expected to be stored by both Bluetooth devices, to be used for future authentication[...]"

Now to the fun part! Go to the advertising_init() function. The advertising data fields contained in the advdata variable are the fields where you can configure your first advertising packet. The advertising packet in this example already contains your full device name. It also contains flags defining some of the advertising options. The flag field is mandatory, but we will discuss it here.

Search for the definition of the ble_advdata_t advertising data structure in your project files (right click on ble_advdata_t and click "Go To Definition Of 'ble_advdata_t'. This works on all functions and variables). When you find it you can see that it is a list of options and data structures with some very brief descriptions. There are quite a few options, but it is important to know that an advertising packet can consist of no more than 31 bytes, so you might need to select your data with care. Here is a useful discussion on advertising bytes.

First let us play with the name and pretend that we need a really long one. Find the "DEVICE_NAME" define again and change the string to “ThisIsAReallyLongName”. Compile and download the code and make sure your new name shows in the device list. This name consumes a lot of our precious 31 byte long advertising packet. So let us say we want to keep our long name, but only advertise the first few letters of it. The advertising_init() function should now look something like this:

static void advertising_init(void)
{
uint32_t      err_code;

APP_ERROR_CHECK(err_code);
}

Change the advertising name type to:

advdata.name_type = BLE_ADVDATA_SHORT_NAME; // Use a shortened name

Then right below this add the line:

advdata.short_name_len = 6; // Advertise only first 6 letters of name

Compile and download again. In the “Discovered devices” list your device should now show up with the name “ThisIs”, the first 6 letters of the full name. However, if you connect to your device by clicking “Select device”, “Connect” and then “Discover services” you will see that the full name is still there. In our case, this frees up 15 bytes in the advertising packet.

### Manufacturer Specific Data

One of the most interesting fields in the advertising data structure might be the p_manuf_specific_data field. This is a field where you can place whatever data you want. So copy the advertising_init() function below:

static void advertising_init(void)
{
uint32_t      err_code;

ble_advdata_manuf_data_t        manuf_data; // Variable to hold manufacturer specific data
uint8_t data[]                      = "SomeData!"; // Our data to adverise
manuf_data.company_identifier       = 0x0059; // Nordics company ID
manuf_data.data.p_data              = data;
manuf_data.data.size                = sizeof(data);

APP_ERROR_CHECK(err_code);
}

Now compile, download and check your MCP. You can see that there is a new field in the “Advertising Data” list called “ManufacturerSpecificData”. It contains a cryptic string of hexadecimal numbers. The first two numbers are the company ID (0x0059) with the least significant byte first. The company ID is a unique 16-bit value assigned to Bluetooth SIG members. It is not allowed to broadcast a custom company ID value without being a member. If you are curious you can see a list of the Bluetooth SIG member IDs here. As described at the bottom of the page the value 0xFFFF "may be used in the internal and interoperability tests before a Company ID has been assigned. This value shall not be used in shipping end products". When you are ready for shipping you will need to apply for a Bluetooth SIG membership to get your own unique ID. "Adopter level" membership is free, but you will need to be associated with a valid company. The next 10 bytes in the manufacturer specific data field are the actual data. If you compare with an ASCII table you will recognize the string “SomeData!”, most significant byte first this time. The last two zeroes at the end represent a termination character in the string.

Challenge 1: Try to add and populate the "p_tx_power_level" field in "advdata" with a value of your own choice and see what happens in MCP. This field is meant to advertise the transmit power of your device. This value might, e.g., enable other units to roughly estimate the distance to your device. (Keep in mind that you will have to use one of the valid tx power levels shown in Chapter 8.5.3 in the nRF51 Product Specification V3.3. It is also important to know that this doesn't change the actual transmit power, just the information that is advertised).

Challenge 2: Set the "include_appearance" field in "advdata" to "true" and see what happens in MCP. Then search for sd_ble_gap_appearance_set(0) in your main file and change the ‘0’ to “BLE_APPEARANCE_HID_MOUSE” and see what happens. The appearance feature might be useful to developers of e.g. mobile phone apps. If you have a BLE enabled phone (or a laptop) your kit should now show up with the name "ThisIs" and a computer mouse icon if you search for BLE devices.

This is what I can see on my phone:

## Scan response data

But what if you really, really want to advertise more than 31 bytes? Then there is a solution for you and that is the Scan response data. This is an optional "secondary" advertising payload which allows scanning devices that detect an advertising device to request a second advertising packet. This allows you to send two advertising frames with a total payload of 62 bytes.

Challenge: In your code, immediately above the line err_code = ble_advdata_set(&advdata, NULL), do the following:

1. Declare a new "ble_advdata_manuf_data_t" type variable called "manuf_data_response".
2. Populate "manuf_data_response" with data as we did with the first advertising packet.
6. Change the line

err_code = ble_advertising_init(&advdata, NULL, &options, on_adv_evt, NULL);

to

err_code = ble_advertising_init(&advdata, advdata_response, &options, on_adv_evt, NULL);

This should make your device look something like this in MCP:

In case you need help your advertising_init() function should now look similar to this:

static void advertising_init(void)
{
uint32_t      err_code;

ble_advdata_manuf_data_t        manuf_data; // Variable to hold manufacturer specific data
uint8_t data[]                      = "SomeData!"; // Our data to adverise
manuf_data.company_identifier       = 0x0059; // Nordics company ID
manuf_data.data.p_data              = data;
manuf_data.data.size                = sizeof(data);

int8_t tx_power                 = -4;

// Prepare the scan response Manufacturer specific data packet
uint8_t                                 data_response[] = "Many_bytes_of_data"; // Remember there is a 0 terminator at the end of string
manuf_data_response.company_identifier       = 0x0059;
manuf_data_response.data.p_data              = data_response;
manuf_data_response.data.size                = sizeof(data_response);

// Always initialize all fields in structs to zero or you might get unexpected behaviour
// Populate the scan response packet

APP_ERROR_CHECK(err_code);
}

## Summary

And there you go. Your first nRF5x DK kit advertising its name, various options, and a small payload. Once again I recommend that you take a look at this blog post: Bluetooth Smart and the Nordic's Softdevices - Part 1 GAP Advertising. The next step will be to add services and characteristics: BLE Services, a beginner's tutorial

Posted April 18, 2015, 12:01 a.m.

after downloading the github file, where should one extract the file to? I can never get downloaded github projects to work? any insight would be a massive help

Posted April 19, 2015, 3:42 p.m.

Hi, You should move into the directory

nRF51_SDK_8.0.0_5fc2c3a/examples/ble_peripheral

git clone https://github.com/NordicSemiconductor/nrf51-ble-tutorial-advertising.git

after that you can proceed compiling as you always did with other example projects :)

I hope it helped,

Francesco

Posted April 21, 2015, 7:48 p.m.

Thanks for this Guide! (I guess. Haven't tried it out yet, but soon I will!)

What am I suppose to use for "manuf_data.company_identifier" as I don't work for a Bluetooth SIG Company ? ;-)

Posted April 22, 2015, 9:16 a.m.

Hi. Thank you for your comment. I have updated the text to make it clearer for future readers. As stated in your link:

This value [0xFFFF] may be used in the internal and interoperability tests before a Company ID has been assigned. This value shall not be used in shipping end products.

Any other values are reserved and forbidden to use in an end product. When you are ready for shipping you will need to apply for a Bluetooth SIG membership to get your own unique ID. "Adopter level" membership is free, but you will need to be associated with a valid company.

Posted May 9, 2015, 5:48 a.m.

Thanks for this guide and it's great. When will have Advertise UUID/flag tutorial? I'm waiting for this.

Posted May 12, 2015, 10:41 a.m.

@EL34PP The next tutorial is a work in progress, but I can't make any promises for a "release date".

Posted May 14, 2015, 12:40 a.m.

Hi all,

I followed this instruction from github.

To compile it, clone the repository to "your_SDK_v8.0.0_folder\examples\ble_peripheral". Download and extract the zipped version of the SDK. It will not work with the Pack installer. If you need help with this please have a look at this thread on devzone:

My path is C:\Keil_v5\ARM\Pack\NordicSemiconductor\nRF_Examples\8.0.0\ble_peripheral. However, it showed me an error.

John

Posted May 14, 2015, 9:29 a.m.

I tried the things mentione above . I have PC10003 EK (nRF51422), for check i turned on my TICK_LED(LED_0) function in main. But it seems the control is not transferring to the main functions. And I tried with various example but I never seen PC10003 board ble get turned on.

IROM1: 0x18000 size 0x28000

IRAM : 0x2000200 size : 0x6000

This is how I configured the memory address.

Please help me now, this is situation of give up , Don't know where and what I am missing. Soft Device version S110 BLE_STACK using right now .

Please help me asap. Or is there any hardware fault? How could I check that BLE module of PCA10003 board for any hardware issues?

Posted May 15, 2015, 10:44 a.m.

@John: I can see that you have used the Pack installer. The third sentence in your quote actually states that the example will not work with pack installer. Download the SDK 8.0.0 .zip-file from here, ectract it to a folder of your own chosing and then extract the example as instructed. I know the Pack vs .zip-file is confusing and we have a lot of people struggling with the same issue. In general we recommend the .zip-file solution as this will get rid of the "file not found" errors you have.

Posted May 15, 2015, 11:01 a.m.

@ Shubham Kumar Mishra : The PCA10003 has an old revision 2 nRF51422 on it. As you can see in the Compatibility Matrix this is not compatible with SDK V8.0.0 and SoftDevice S110 V8.0.0. Hence, it is not guaranteed to work with this example either. However, I did try the tutorial on my PCA10003 and it seems to work, but I haven't tested it thoroughly. Also, as a sidenote, the PCA10003 only has 16kB of RAM and you should set your IRAM1 size to 0x2000 instead of 0x6000. If this is a problem with your function TICK_LED() we can't help you unless you post your code.

PS: if your problem is related to your question here then lets continue our problem solving there.

Posted May 15, 2015, 8:30 p.m.

@Martin Børs-Lind Yeah, you were right. I just moved it to SDK8.0.0 I downloaded. It seems fine now. I have almost completed this tutorial except for challenge 1. I'm still struggling with changing the transmit power level.

Posted May 18, 2015, 12:21 p.m.

Posted May 26, 2015, 5 p.m.

Can I use this example with SDK 8.1.0 ?

I tried and I got a build error.

Step to reproduce and find:

• Clone github files in the right place under SDK 8.1.0
• Open the project and build
• In nRF_Libraries -> app_button.c I see (line 19) #include "nrf_drv_gpiote.h"

The error is that nrf_drv_gpiote.h isn't found.

I tried to import the example in the SDK 8.0.0 and all works fine; so I tried to open the app_button.c of the SDK 8.0.0 and it's different from app_button.c of the SDK 8.1.0.

If app_button.c is part of the nRF_Libraries of SDK 8.1.0, and If it includes nrf_drv_gpiote.h that's part of the library too. Could be a bug or I'm doing something wrong? Thanks

Posted May 27, 2015, 9:43 a.m.

I'm afraid that you can't use it with SDK 8.1.0. If you look at the advertising_init() function in main.c in SDK V8.1.0 you can see that is has some differences from V8.0.0 as well. But the example code used in the tutorial is very similar to the ble_app_template examples so with a little extra effort you can use this. You just need to take a close look at advertising_init() and ble_advertising_init() (called in advertising_init() and located in ble_advertising.c) and you should be able to recognize a lot of stuff.

I say that it might be easy, but to make the tutorial compatible with SDK 8.1.0 I'll need to rewrite a lot of text and make new example code so I probably won't prioritize that.

Posted May 29, 2015, 6:51 p.m.

Why is it that nRF Beacon Android app cannot detect the development kit after uploading this project, whereas nRF Master control app can?

Posted June 2, 2015, 11:13 a.m.

Becons have a specific configuration of the adveritisng packet. The Beacon app is scanning for and shows only devices with this configuration. Take a look at the ble_app_beacon example in the SDK.

Posted June 18, 2015, 9:03 a.m.

Could you create the same type of tutorial for S120?

Posted June 18, 2015, 4:13 p.m.

Hello Nordic Comunity :) When I change the code as instructed in the tutorial

My dongle does not even detect the device. Meanwhile when I comment out the following code

   // err_code = ble_advdata_set(&p_advdata, NULL);
//  APP_ERROR_CHECK(err_code);// Check for errors

My device becomes detected yet on the advertise data of MCP nothing shows up. Why is this happening and What is the purpose of this challange ?

Posted June 18, 2015, 6:14 p.m.

Hi Milad. Could it be that you advertising packet is already full? Remember that you can only have 31 bytes in the packet in total. Have a look at this explanation and see if that helps.

Posted June 18, 2015, 8:54 p.m.

Hey Martin, I am only sending an integer value.

power=0x3A;

I do not think that this would be a problem. What other issues might be the reason? Thanks

Posted June 18, 2015, 9:54 p.m.

Meanwhile where is the continuation to this tutorial and as for the GATT communication ?

Thanks

Posted June 19, 2015, 9:50 a.m.

Do you have control over how many bytes you have in your packet? Adding the tx power level value will actually add 3 more bytes, not just the value; a length byte, a type byte and the tx power level byte. Can you post your .c-file? You can't attach files in the tutorial comment sections, so maybe you can post it in the thread I linked to above or send it to me on PM.

The next tutorial is still a work in progress.

Posted June 25, 2015, 6:47 a.m.

Hi~ Thansks for this post. I tried to implement the challanges but I am unable to implement the challange regarding "scan data response" for advertising data more than 31 bytes.

Please share some code example for reference related to modifications in advertising_init().

Thanks. /Ash

Posted July 19, 2015, 4 p.m.

@martinbl :Thank you for the tutorial. It is very helpful!

I have a question on writing the ADC value to the manufacturer specific data. It looks like this data is only written to the packet during the advertising initialisation.

I have tried out the adc_simple example code as it was (without S100). Can I use the same ADC code in this tutorial code?

Posted Aug. 26, 2015, 6:55 p.m.

i amusing SDK 6.0 since i am using nRF51822 EK. Is this tutorial still valid for me?

Posted Sept. 1, 2015, 2:51 p.m.

Sorry for the late response guys. Holidays and busy days in general...

@HSA: Did you try to copy paste the code at the bottom of the tutorial to get scan response working? Are you getting any errors returned from ble_advdata_set()?

@Johnson: Yes, you should be able to use the adc example code alongside the tutorial. To put adc values in your advertising packet you will have to update the manufacturer data and run advdata_set() once more to actually change det packet.

@harsha: Not directly I'm afraid, but with some work you should be able to port it.

I will encourage you all to ask your questions on the forum's main page and not here in the tutorial comment field. That way it will be easier for all users and Nordic employees to see and search for your post. You will probably also get an answer faster that way. Tips and comments about the tutorial are welcome here. You can also send me a PM.

Posted Sept. 16, 2015, 10:39 a.m.

int8_t *       tx_power_level; // Variable to hold manufacturer specific data
uint8_t data[]                      = "4DBM";
tx_power_level.data.p_data              = data;
tx_power_level.data.size             = sizeof(data);

i added this line for challenge on ebut it shows me error can anyonbe guide how to solve this issue? in order to tranmit the power?

Posted Sept. 16, 2015, 1:41 p.m.

Remove the star (*). You should not declare a pointer. And remember to assign a value to tx_power_level. Try this:

int8_t tx_power_level = 4;

Posted Oct. 9, 2015, 4:50 p.m.

Hello,

So, a regular advertisement is done continuously while the the scan response is only sent when there is a request from a central.

Then, is it more power efficient to put the data in the scan response or in the regular advertisement? Are there any other criteria we have to consider when deciding which attribute to place where? Thanks

Posted Nov. 3, 2015, 9:51 a.m.

Hi There, I have an nRF52 DK, is there a way to run this tutorial on it? Thanks!

Posted Feb. 10, 2016, 9:03 a.m.

As of yesterday it is :)

Posted Feb. 19, 2016, 3:24 p.m.

There's an error in your 'Scan Response Data' section where you refer toerr_code = ble_advdata_set(&advdata, NULL), which does not exist in the code. It seems to now be this function err_code = ble_advertising_init(&advdata, NULL, &options, on_adv_evt, NULL);

Posted Feb. 29, 2016, 2:08 p.m.

Thanks. Fixed it now.

Posted March 26, 2016, 4:20 p.m.

Any reason why Keil is the compiler of choice here? I would appreciate arm-gcc make files to make it easier of Linux/Mac users.

Posted April 22, 2016, 2:43 p.m.

I have added GCC files to the SDK11 project now. Please PM me if they don't work.

Keil has been the prefered IDE here at Nordic for a while. Partly because it is easier to set up than GCC and free to use (within the code size limitation of course).

Posted May 3, 2016, 8:22 a.m.

Thank you for the tutorial. :-)

## just minor fix needed. you missed "&"

to

Posted May 25, 2016, 6:39 p.m.

Hi,

I think it is worth mentioning that example project won't compile with SDK 11.0.0 alpha version. I assumed the changes from alpha to stable 11.0.0 couldn't be so big and tried to use previously installed v11.0.0-2.alpha which didn't work (due to the changes in softdevice api I think). Using recent nRF5_SDK_11.0.0_89a8197 solved the issues with compilation. I took me a lot of hair scratching until I figured it out, so maybe this post will help someone.

Posted July 13, 2016, 4:46 p.m.

Hi,

Can you explain how to advertise for limited time say 120 seconds.

Thanks.

Posted July 14, 2016, 8:29 p.m.

Hi, im a Teacher in a community college in Mazatlan, Mexico, it is posible, to do all tutorials, using only open source software like Linux, gcc, etc.? (No Keils for example)

Posted July 17, 2016, 7:57 p.m.

Great tutorial!!!! Thanks for putting this together.

For Challenge 2 I made the changes as described in the tutorial.

could not see any changes in the MCP nor was the device seen on my BLE enabled device (Ipad). Any ideas?

Thanks

Posted Aug. 16, 2016, 9:12 a.m.

Hi, I think there is a mistake in the SDK "ble_advertising.c" in the function ble_advertising_init() used in this tutorial.

The code:

if(p_advdata->p_tx_power_level != NULL)
{
}

should probably be

if(p_advdata->p_tx_power_level != NULL)
{
}

as I think it is the value which should be copied into the local static m_tx_power_level.

I apologise if this has already been fixed. Regards.

Posted Aug. 31, 2016, 10:25 a.m.

Can I change the advertising data dynamically during program running? Just by calling advertising_init()?

Posted Sept. 6, 2016, 10:26 p.m.

Hello, I'm using a nRF52835 pc10040, I have all the libs (SDK V11.0.0 zip) and I can compile with succesfully with out any errors and warnings. But the software is not doing anything, dosen't blink the LED when I press the button, and I can't see the device with the dongle in the MCP. This example is compatible with my setup?

Best regards

Posted Dec. 15, 2016, 7:17 a.m.

Great tutorials, best that i could find in web. Thanks

Posted Jan. 14, 2017, 2:15 a.m.

Is there any other way to do this than with the dongle? I live in Europe and ordered the nrf52-DK via Express Delivery because I wanted to quickly test how it is to work with this device. I didn't realize that this dongle would be helpful/needed in order to progress through the tutorials.

Posted Feb. 17, 2017, 1:43 a.m.

Great tutorial.

But I was struggling because I want it to advertise a beacon, now I took a look to the ble_app_beacon example, there the name has to be hidden: advdata.name_type = BLE_ADVDATA_NO_NAME; and many other changes.

The funny part is, when I flash the final firmware, some scanners app show that the name is what I defined in the firmware that was prevously installed. Why is that happening? Could be that the softdevice was modified? I was looking for a solution to change the device name AND advertise at the same time, is that possible?

## Recent blog posts

• ### ble_app_hrs_freertos running in Atollic TrueSTUDIO

Posted 2017-08-14 02:55:30 by jmag999
• ### OLED display support for nRF52832 (SSD1306, Adafruit GFX)

Posted 2017-08-11 08:21:31 by Mahesh Venkitachalam
• ### I tried 5 different debugger IDEs for nRF52 and STM32. Here are my results.

Posted 2017-08-09 10:56:19 by Jonathan
• ### Things you should know about Bluetooth mesh

Posted 2017-08-07 12:37:22 by Eirik Midttun
• ### Support pairing on NUS profile for Central and Peripheral

Posted 2017-08-01 08:42:41 by Eugene Yu

## Recent questions

• ### getting incorrect output using the timer_example_timer_mode example

Posted 2017-08-16 23:21:55 by Nikhil
• ### Sampo S1 simple "read, notify" protocol/bytestream example

Posted 2017-08-16 21:33:31 by Christian
• ### How to get softdevice state in my application

Posted 2017-08-16 20:54:24 by ypearson
• ### nRF Cloud Gateway Error connecting gateway

Posted 2017-08-16 20:05:14 by carlos carrizosa
• ### nrf52 GPIO sink & source current

Posted 2017-08-16 19:04:24 by dingari


text:
# Definition:Convergent Filter Basis

## Definition

Let $\left({X, \tau}\right)$ be a topological space.

Let $\mathcal B$ be a filter basis of a filter $\mathcal F$ on $X$.

Then $\mathcal B$ converges to a point $x \in X$ if and only if:

$\forall N_x \subseteq X: \exists B \in \mathcal B: B \subseteq N_x$

where $N_x$ is a neighborhood of $x$.

That is, a filter basis is convergent to a point $x$ if every neighborhood of $x$ contains some set of that filter basis.


text:
1. ## Simple speed/distance/time questions

Hello I'm stuck on a particular 'genre' of sorts of speed/distance/time questions where you have to incorporate two objects travelling.

Apart from trial and error I don't know how to do these.

For example:
A car travelling at 90km/h is 500m behind another car travelling at 70km/h in the same direction. How long will it take the first car to catch the second?

or

A train of length 180m approaches a tunnel of length 620m. How long will it take the train to pass completely through the tunnel at a speed of 54km/h?

I have several of these questions so I would please like a method...

I've tried different tactics but I can't seem to figure out how to do these type of questions.

2. Furthermore I have a simpler question of a different ty[pe that I can't do.

This is the question:
A car must complete a journey at an average speed of 40mph. At what speed must it travel on the return journey if the average speed for the complete journey is 60mph?

I started off:

Average speed = $\frac{2D}{T1+T2}$

Then because T1 = $\frac{D}{40}$

Average speed = $\frac{2D}{1}\cdot \frac{40+T2}{2D}$

To which I think I can cancel the 2D's. I'm left as T2 = 20mph but that's not the answer.

3. Originally Posted by Mukilab
Hello I'm stuck on a particular 'genre' of sorts of speed/distance/time questions where you have to incorporate two objects travelling.

Apart from trial and error I don't know how to do these.

For example:
A car travelling at 90km/h is 500m behind another car travelling at 70km/h in the same direction. How long will it take the first car to catch the second?

or

A train of length 180m approaches a tunnel of length 620m. How long will it take the train to pass completely through the tunnel at a speed of 54km/h?

I have several of these questions so I would please like a method...

I've tried different tactics but I can't seem to figure out how to do these type of questions.

Hi Mukilab,

For the car catching up to the one in front,
it's travelling 20km/hr "faster" than the one in front.

Hence, you can imagine the one in front stopped
and the car in behind travelling at 20km/hr effectively.

Hence it will bridge the 500m gap in $t=\frac{d}{v}=\frac{0.5}{20}$ hours.

For the train,

the nose of it has to travel a distance it's own length plus the tunnel's length
in order for the tail of it to exit the tunnel.

You then have the speed and distance,
so you can calculate the time.

$v=\frac{d}{t}$

$d=vt$

$t=\frac{d}{v}$

4. Thanks for those but I'm confused with this one know x_xx

An earthworm of length 15cm is crawling along at 2cm/s. An ant overtakes the worm in 5 seconds. How fast is the ant walking?

I'm just confused. I thought I wrote something worthwhile but it turns out I didn't because I assumed the... nevermind, no point in me rambling. Please could you show me?

5. Originally Posted by Mukilab
Thanks for those but I'm confused with this one know x_xx

An earthworm of length 15cm is crawling along at 2cm/s. An ant overtakes the worm in 5 seconds. How fast is the ant walking?

I'm just confused. I thought I wrote something worthwhile but it turns out I didn't because I assumed the... nevermind, no point in me rambling. Please could you show me?
If the ant overtakes the worm in 5 seconds,
then given that the worm will have moved 10cm in those 5 seconds, due to it's own speed,
and is 15cm long, the ant will have moved 25cm in those 5 seconds,

so the ant's speed is 5cm/s

6. Originally Posted by Archie Meade
If the ant overtakes the worm in 5 seconds,
then given that the worm will have moved 10cm in those 5 seconds, due to it's own speed,
and is 15cm long, the ant will have moved 25cm in those 5 seconds,

so the ant's speed is 5cm/s

sorry, I thought thise question was the same but it's totally differnt, I need to call upon your help again.

A train of length 100m is moving at a speed of 50km/h. A horse is running alongside the train at a speed of 56km/h. How long will it take the horse to overtake the train?

Also please could you help me with the question I posed on post #2?

7. Originally Posted by Mukilab
Furthermore I have a simpler question of a different ty[pe that I can't do.

This is the question:
A car must complete a journey at an average speed of 40mph. At what speed must it travel on the return journey if the average speed for the complete journey is 60mph?

I started off:

Average speed = $\frac{2D}{T1+T2}$

Then because T1 = $\frac{D}{40}$

Average speed = $\frac{2D}{1}\cdot \frac{40+T2}{2D}$

To which I think I can cancel the 2D's. I'm left as T2 = 20mph but that's not the answer.
You haven't handled the division properly here, Mukilab

$Av=\frac{2D}{\frac{40}{D}+T_2}=\frac{2D}{\frac{40+ DT_2}{D}}=\frac{2D^2}{40+DT_2}$ etc

However, because we are dealing with average speeds, the situation is linear, so we can choose a distance of 40 miles for convenience.

$\frac{2D}{1+x}=60$

since the car will cover the 40 miles in 1 hour, so since D=40

$\frac{80}{1+x}=60$

$80=(1+x)60=60+60x$

$20=60x$

$x=\frac{1}{3}$ hours = 20 minutes.

On the return journey the car covers 40 miles in 20 minutes,
so what is it's average speed on the return journey?

8. Originally Posted by Archie Meade
You haven't handled the division properly here, Mukilab

$Av=\frac{2D}{\frac{40}{D}+T_2}=\frac{2D}{\frac{40+ DT_2}{D}}=\frac{2D^2}{40+DT_2}$ etc

However, because we are dealing with average speeds, the situation is linear, so we can choose a distance of 40 miles for convenience.

$\frac{2D}{1+x}=60$

since the car will cover the 40 miles in 1 hour, so since D=40

$\frac{80}{1+x}=60$

$80=(1+x)60=60+60x$

$20=60x$

$x=\frac{1}{3}$ hours = 20 minutes.

On the return journey the car covers 40 miles in 20 minutes,
so what is it's average speed on the return journey?

I got lost when you put 40+DT2. No idea where you got D*T2...

I also have no idea where you get 1.

or + x

9. Originally Posted by Mukilab
sorry, I thought thise question was the same but it's totally differnt, I need to call upon your help again.

A train of length 100m is moving at a speed of 50km/h. A horse is running alongside the train at a speed of 56km/h. How long will it take the horse to overtake the train?

Also please could you help me with the question I posed on post #2?
This one (horse and train) is the same type as the one with the two cars.
The "effective" speed of the horse is 6km\hr relative to the train,
(ie as if the train was stopped).

Have a shot at it.

10. Originally Posted by Mukilab
I got lost when you put 40+DT2. No idea where you got D*T2...

I also have no idea where you get 1.

or + x
As it's convenient to choose D=40 miles, then $T_1=1\ hour$

The return time is x.

You could choose D as other distances too, but as this is a linear model,
you will keep getting the same answer for the return average speed.

You chose a more complicated way.

$\frac{2D}{\frac{40}{D}+T_2}=\frac{2D}{\frac{40}{D} +\frac{DT_2}{D}}$ getting a common denominator under the line.

$=\frac{2D}{\frac{40+DT_2}{D}}$

When you divide by a fraction, just turn the fraction upside-down and multiply instead.

Divide by 2 is multiply by $\frac{1}{2}$

Divide by $\frac{1}{2}$ is multiply by 2 etc.

Hence

$\frac{2D}{\frac{40+DT_2}{D}}=2D\frac{D}{40+DT_2}$

11. Originally Posted by Archie Meade
As it's convenient to choose D=40 miles, then $T_1=1\ hour$

The return time is x.

You could choose D as other distances too, but as this is a linear model,
you will keep getting the same answer for the return average speed.

You chose a more complicated way.

$\frac{2D}{\frac{40+DT_2}{D}}$

When you divide by a fraction, just turn the fraction upside-down and multiply instead.

Divide by 2 is multiply by $\frac{1}{2}$

Divide by $\frac{1}{2}$ is multiply by 2 etc.

Hence

$\frac{2D}{\frac{40+DT_2}{D}}=2D\frac{D}{40+DT_2}$

I understand everything apart from how you got T1 as 1hour.

Thank you for your complete perserverance

to get the time for the first one you would do:

$T1=\frac{D}{40}$

You have two unknowns and no simultaneous equation so how could you solve?

12. Originally Posted by Mukilab
I understand everything apart from how you got T1 as 1hour.

Thank you for your complete perserverance
Hi Mukilab,

To obtain a "pain-free" answer, I choose D=40 miles,
so that the outward journey would take 1 hour exactly.

You could choose D as any other distance
and you really should verify that regardless of D (within reason)
you will keep getting the same answer for reverse journey average speed.

So my choice of D=40 miles was to simplify everything.
If you choose D=80 miles, you get the same answer, or D=100 miles etc.

for practice, you should experiment with a few different distances,
calculate the average return speed and verify that the entire journey average speed is 60mph.

13. 120minutes

14. Hi Mukilab,

If the outward journey is 40 miles in 1 hour,
the return journey is 40 miles in 20 minutes,

that's one hour and 20 minutes, which is 60+20 minutes
(rather that 100+20 minutes).

15. Originally Posted by Mukilab
I understand everything apart from how you got T1 as 1hour.

Thank you for your complete perserverance

to get the time for the first one you would do:

$T1=\frac{D}{40}$

You have two unknowns and no simultaneous equation so how could you solve?
Yes, it gets a bit complex,
so it's better to experiment by choosing a value for D.

Page 1 of 2 12 Last

,

,

,

# the first train of length 100m moving at a speed

Click on a term to search for related topics.


text:
# Waecmaths

Title waecmaths question
Question 1

Evaluate  ${{({{111}_{two}})}^{2}}$ and leave your answer in base 2

Question 2

\begin{align} &\text {Find the LCM of} \\ & {{2}^{3}}\times 3\times {{5}^{2}} \\ & 2\times {{3}^{2}}\times 5 \\ & {{2}^{2}}\times {{3}^{3}}\times 5 \\\end{align}

Question 3

Simplify $(0.3\times {{10}^{5}})\div (0.4\times {{10}^{7}})$ leaving your answer in the standard form

Question 4

If $p\propto \frac{1}{q}$  which of the following is true

Question 5

Simplify $3\sqrt{45}-12\sqrt{5}+16\sqrt{20}$ leaving your answer in surd form

Question 6

Which of the following statements is true for the set $P=\{-3.2\le x<5\}$ where x is an integer?

Question 7

Simplify $\frac{3{{x}^{3}}}{{{(3x)}^{3}}}$

Question 8

N140.00 is shared between Abu, Kayode  and Uche. Abu has twice as much as kayoed and Kayode as twice as much as Uche. What is kayode’s share?

Question 9

I am x years old and my brother is 3 years older. How old was my brother last year

Question 10

For what value of x is the expression $\frac{2x-1}{x+3}$ not defined?

Question 11

If x = 3, y = 2 and z = 4. What is the value of $3{{x}^{2}}-2y+z$

Question 12

Solve the simultaneous equations\begin{align} & x+y=2 \\ & 3x-2y=1 \\\end{align}

Question 13

If ${{8}^{x+1}}=\frac{1}{4}$ fins x

Question 14

The area of a square field is 110.25m. Find the cost of fencing it round as N75.00 per metre

Question 15

A chord of length 6cm is drawn in a circle of radius 5cm. Find the distance of the chord from the centre of the circle

Question 16

A sector of a circle of radius 14cm containing an angle of 60o is folded to form a cone. Calculate the radius of the base of the cone

Question 17

In the diagram $\left| LN \right|=4cm,\angle LNM={{90}^{\circ }}$ and $\tan y=\tfrac{2}{3}$What is the area of $\triangle LMN$

Question 18

Find the volume of a solid cylinder with base radius 10cm and height 14cm (take $\pi =\tfrac{22}{7}$)

Question 19

From the diagram, find the value of x

Question 20

Find the value of x in the diagram

Question 21

Each interior angle of a regular polygon is 162o. How many sides has the polygon?

Question 22

From the diagram, find the value of x

Question 23

In the diagram $\left| SP \right|=\left| SR \right|$ and $\angle PRS={{50}^{\circ }}$ Calculate $\angle PQR$

Question 24

In the diagram, O is the centre of the circle and $\angle PQR={{106}^{\circ }}$ .Find the value of y

Question 25

In a $\Delta PQR,\text{ }\angle PQR=\angle PRQ={{45}^{\circ }}$ which of the following statement is correct?

I. $\triangle PQR$is an equilateral triangle

II. $\triangle PQR$ is an isosceles triangle

III. $\triangle PQR$ is a right angled triangle

Question 26

The table gives the distribution  of the marks of a number of students in a test

 Marks 1 2 3 4 5 6 Frequency 5 3 6 4 2 5

Find the mode of the distribution

Question 27

If the probability of an event occurring is x, what is the probability of the event not occurring?

Question 28
 Ages 1 2 3 4 5 Number of Children 2 3 5 6 4

The table shows the ages (in years) of twenty children chosen at random from a community

What is the mean age?

Question 29
 Ages 1 2 3 4 5 Number of Children 2 3 5 6 4

The table shows the ages (in years) of twenty children chosen at random from a community

What is the median of the distribution?

Question 30

Q is 32km away from P on a bearing of 042o and R is 25km from P on a bearing of 132o. Calculate the bearing of R from Q

Question 31

In the diagram$\left| PQ \right|=4cm$, $\left| QR \right|=6cm,\text{ }\left| RS \right|=12cm$ $\angle QRS={{90}^{\circ }}$. Find the value of x

Question 33

The bearing of a point P from another point Q is 310o. If $\left| PQ \right|=200M$ how far east of Q is P?

Question 34

Find the value of a if ${{\log }_{10}}a+{{\log }_{10}}{{a}^{2}}=0.9030$

Question 35

A messenger was paid N2.50  an hour during the normal working hours and N4.00 an hour during overtime. If he received N31.00 for 10 hours works, how many hours are for the overtime?

Question 36

At what rate percent  will N520.00 yield a simple interest of N39.00 in three years

Question 37

If the ratio  x : y = 3 : 5 and y : z = 4 : 7, find the ratio x: y : z

Question 38

The Venn diagram shows the choice of food of a number of visitors to a canteenthere were 35 visitors in all, find the value of x

Question 39

The Venn diagram shows the choice of food of a number of visitors to a canteen. How many people took at least two kinds of food?

Question 40

$\triangle PQR$ is a equilateral triangle with sides $2\sqrt{3}cm$ calculate its height

Question 41

Which of the following is a factor of $2-x-{{x}^{2}}$


text:
# Will split question feature be useful?

I often encounter situation when a new user is posting several absolutely non correlated questions as a single quetion. As the result we get a bunch of non-enlightening answers which are very short since they try to cover all the OP's question. Even more one can answer only a part of this questions but do not do this, because he is supposed to completely answer the whole list of OP's question. I suggest to request this feature, and what is more I think it will be useful for all SE sites.

• Who will own these new questions? The mod / high rep user performing the split, or the original poster? Presumably, the poster. Then it's a fundamental change of the way SE operates: someone will be able to create a question and assign its ownership to me. I do not like this.
– user53153
Dec 25 '12 at 1:54
• When someone posts several question in one, I tell him/her not to. Dec 25 '12 at 6:54
• And what ususaly that people do? Dec 25 '12 at 10:13
• Dec 25 '12 at 17:43
• Sorry, Norbert, I haven't been able to keep track of what people do when I ask them not to post multiple questions in one. Sometimes, they get multiple answers before they can even read my comment, which sort of makes my comment moot. By the way, if you want to be sure I read something addressed to me, you have to put @Gerry in it. Dec 26 '12 at 7:15
• @GerryMyerson Thank you, I see people not enthusiastic about my idea. Dec 26 '12 at 8:12
• @user53153 These new questions could be owned by the Community user. meta.math.stackexchange.com/users/-1/community Feb 15 '16 at 14:17

No, I don't think this is useful.

I think a better response to such questions is to leave a comment suggesting that the questions be posted separately, and that the current question be deleted. You can punctuate this with a downvote and/or a vote to close.

It is better for the asker to do the work of splitting the question. If someone else does it, errors could be introduced or necessary context omitted.

• Asker won't do the splitting, because in most cases author of such questions are newbies that will visit this site only once. Jan 27 '13 at 18:31
• Well then, they won't get an answer, and their question will probably be closed, and that's just too bad. If someone else is interested in one of the questions, they can ask it themselves. Jan 27 '13 at 18:57
• Then what is the purpose to leave such a trash on site, if you are sure that it will be closed/non-answered/downvoted ? Jan 28 '13 at 10:34
• @Norbert It does not have to stay on the site. Closed questions can be deleted with 3 votes to delete. Unanswered questions with $\le 0$ votes are automatically deleted after a year.
– user53153
Jan 28 '13 at 17:08
• @Norbert And unanswered questions with $<0$ votes are deleted after only a month. Source
– user53153
Jan 28 '13 at 20:10


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# Hooghoudt

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### Spacing drainage pipes to reduce groundwater mounding

The yellow box represents the recommended hydraulic conductivity of bioretention filter media

In most LID underdrain applications, lateral drains should be spaced between 5 - 6 m apart.

This recommendation is supported by an analysis of Hooghoudt's equation [1][2][3] in relation to loamy or clayey native soils, where Kmedia>>Ksoil, finds the first term of the numerator negligible, so that the original equation$Drain\ spacing=\sqrt{\frac{8K_{soil}H\left(D_{i}-D_{d}\right)\left(D_{d}-D_{w}\right)+4K_{soil}\left(D_{d}-D_{w}\right)^{2}}{q}}$ may be simplified to$Drain\ spacing=\sqrt{\frac{4K_{media}\left(D_{d}-D_{w}\right)^{2}}{q}}$

Where:

• Kmedia is expressed in m/day
• Dd is the depth to the drain pipe (m)
• Dw is the minimum acceptable depth to the water table during infiltration event
• q is the inflow volume expressed as a depth over the entire surface (m)
1. H.P.Ritzema, 1994, Subsurface flow to drains. Chapter 8 in: H.P.Ritzema (ed.), Drainage Principles and Applications, Publ. 16, pp. 236-304, International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. ISBN 90-70754-33-9
2. W.H. van der Molen en J.Wesseling, 1991. A solution in closed form and a series solution to replace the tables for the thickness of the equivalent layer in Hooghoudt's drain spacing equation. Agricultural Water Management 19, pp.1-16
3. van Beers, W.F.J. 1976, COMPUTING DRAIN SPACINGS: A generalized method with special reference to sensitivity analysis and geo-hydrological investigations, International Institute for Land Reclamation and Improvement (ILRI) Wageningen, The Netherlands


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What are Rational and Irrational Numbers?

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In daily life, we tend to think of numbers as perfectly rounded and workable quantities, but do you know that some numbers are not of this kind? Let’s explore what rational and irrational numbers are in this article.

Rational Numbers

In the last paragraph, we mentioned numbers that are perfectly expressible. They are called rational numbers and can be expressed as fractions of two integers. For example, all integers on the real number line are rational numbers, as any integer n is n / 1. If you go down the decimal places, all numbers you’ll find are rational numbers. That’s because they are still expressible as a specific integer divided by a certain power of 10. For example, the floating point number 3.1415926535 is rational because one can express it as 31415926535 / 10.

The world of rational numbers doesn’t only include integers and decimals with a finite number of places. In fact, some rational numbers have an infinite number of decimal places. Take 1/3 for an example. The answer is 0.333333……, and this series of numbers continue forever. Even though you cannot express it exactly in the base of decimal, you can always turn to fractions and mention that it’s 1/3. Therefore, it is a rational number as well. As a result, numbers with repeating decimal places, no matter where the cycle starts, are always rational numbers.

Irrational Numbers

Rational numbers are all that you, your computer, a supercomputer, or anything in the observable universe can imagine. However, the vast majority of numbers are not in this category. They are irrational numbers, which are those that cannot be expressed as fractions of integers. This may seem weird, as you may think you can find a fraction with the precise value of the number in question as you approach that number. But the truth is, some numbers are proven to be inexpressible with the ratios of integers. Therefore, any way to store them in computer memory will result in approximations instead of exact values.

In fact, there is no way to precisely define the value of irrational numbers unless they are the result of an algebraic expression or geometric definition. For example, π is the circumference of a circle divided by its diameter, and √ 2 is the side length of a square of area 2 and also the answer to the equation x2 = 2. In fact, most well-defined irrational numbers are mathematical constants or the result of multiplying them by some rational number. That’s because most of the numbers between those constants are not useful, and thus are not worth defining (and may not have an exact definition).

In the previous paragraphs, we mentioned that it’s proven that some numbers are irrational. Well, here is one of the famous ones, proving that √ 2 is irrational. Suppose that √ 2 can be expressed as p / q in which p and q are coprime (i.e., whose GCD is 1).

$\sqrt 2 = p/q$ $\sqrt 2 q = p$ $2q^2 = p^2$

Since q is an integer, 2p2 is divisible by 2. Thus, we can substitute p as 2x, so p2 = 2x2. Then, we can work down the fact and prove that q is divisible by 2 as well:

$2q^2 = (2x)^2$ $2q^2 = 4x^2$ $q^2 = 2x^2$

Thus, we can infer that q is divisible by 2 as well. Since p and q now have a common factor of 2, it cannot exist in its simplified form. Every fraction (x / y) can be simplified into one where x and y are coprime. Therefore, those two numbers that can make √ 2 rational does not exist, and √ 2 is therefore, irrational.

Conclusion

In this article, we’ve introduced rational and irrational numbers, how to define them, and how to know if a certain number is rational. Remember that, although the concept of irrational numbers may seem a bit complicated, they exist as provable facts. If we’ve missed anything we should have mentioned, please leave those points in the comments below.