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# How to Use the SCP Command to Securely Transfer Files

SCP (Secure Copy) is a command-line utility that allows you to copy files from one computer to another over a secure, encrypted connection. It uses the SSH protocol to provide a secure connection to the remote system.

With the scp command you can copy files or directories in the following ways:

1. From your local system to a remote system
2. From a remote system to your local system
3. Between two remote systems, while sending the commands from your local system.

The SCP command-line utility is available in most Linux distributions.

In this tutorial we’ll cover how to use the scp command in various scenarios to securely transfer files from one computer to another, using practical examples. We’ll also show you some of the most frequent options that you can use with the scp command to customize your file transfers.

SCP is usually used to refer to both SCP (the command-line utility, developed by the OpenSSH Project), as well as Secure Copy Protocol, which is the protocol used by the utility.

SCP is based on the Secure Shell (SSH) protocol, and it comes with a similar set of options, and is provided in most SSH implementations.

It uses credentials (such as passwords or SSH keys) for authentication, and it secures your transfers by encrypting both passwords and the transferred data, so your contents should be impervious to snooping.

A related protocol is SFTP (Secure File Transfer Protocol), however SCP does not have some of the capabilities that SFTP does, such as resuming broken transfers or remote file manipulation, like deletion.

SCP is similar to rsync, but unlike rsync, scp can only copy files and cannot sync directories.

## Before You Begin

### Requirements

1. To be able to transfer files from/to remote hosts via scp, you need the user’s authentication credentials – such as user/password or SSH keys.
2. To be able to transfer files between systems you must have at least read permissions on the source file and write permissions on the destination system.

### Useful Info

By default, scp operates on port 22 unless you change it using a command-line option.

You can use SCP with Linux, Mac, and Windows.
SCP should already be installed on Linux and Mac, however on Windows you have to install it – if you’re on Windows please see the section below on installing SCP on Windows.

When transferring large files, you’ll probably have to wait some time for the transfers to finish. For various reasons, you may not want to have to keep the command line open for hours. A solution here is running the scp command inside a terminal multiplexer such as screen or tmux, which allow you to leave commands running even if you log off.

## SCP Command Syntax

The basic syntax of the SCP command is the following.

scp [OPTIONS] [[[email protected]]SOURCE_HOST:]file1 [[[email protected]]DESTINATION_HOST:]file2

Let’s break down and explain what the above expression means:

[OPTIONS]: Options alter scp’s behavior, such as changing the encryption cipher, ssh_config location, identity file location, limit bandwidth, change SSH port, recursive copy, and others.

You can check all available options by running man scp in the command line or read the scp man page online.

[[[email protected]]SOURCE_HOST:]file1: This is the source file, the file to be copied.

If you’re copying from your local machine then you should just specify the relative (~/file1) or absolute path (/home/edxd/file1).

If the source file is located on a remote system, then you’ll have to specify the user and host ([email protected]_source_ip) followed by the colon (:) separator, and then the file’s absolute or relative path.

For example: [email protected]:/var/www/file1.txt

[[[email protected]]DESTINATION_HOST:]file2: This is the destination file, where the file is going to be copied.

If you’re copying to a remote host, it should include the user and host specification [email protected]_destination_ip:/path/to/file2.

If you’re copying from a remote host to your machine, absolute or relative path where you want the file copied, such as just /path/to/file2.

There are a few ways you can handle the remote user and host specifications.

You can use:

1. an IP address: [email protected]
2. a domain name: [email protected]
3. a host defined in the /etc/hosts file
4. a host defined in ~/.ssh/config (or %userprofile%\.ssh\config on Windows, usually C:\Users\your_user\.ssh\config)

## Copy Files and Directories Between Two Hosts With the SCP Command

### 1. Copy a Local File to a Remote Host Using SCP Command

It’s one of the most straightforward SCP commands you can carry out. We’re copying a single file (example.txt) from our computer to our remote host, which has .

To copy a local file to a remote host run a command like:

scp /path/to/example.txt [email protected]:/remote/path

Let’s quickly explain the above command.

/path/to/example.txt is the path to the file you want to copy from your local computer, remote_user is the user on the remote server, 121.134.21.14 is the IP of the remote host.

Next, comes a colon : after which you can specify the path where you want the file to be copied (/remote/path/). The copied file will retain it’s original name.

Here is a video to illustrate how this works. I’ll run the following command:

scp example.txt [email protected]:/home/stelixd

In the video below, on the left, we have a terminal on our local computer, and on the right we have the terminal of an Ubuntu remote server.

1. SCP Command - Copy a file from your local computer to a remote host

If you are connecting to your remote host for the first time, you will see the prompt Are you sure you want to continue connecting (Yes/no)?.

Assuming you trust the remote server, type Yes, press Enter, and fill in the user password (if you’re not using SSH keys).

When we execute the ls command on the remote server, you can see the example.txt was successfully copied.

You can also specify a new name for the file (/remote/path/file1_new_name):

scp /path/to/file1 [email protected]:/remote/path/file1_new_name

#### Copy Multiple Local Files to a Remote Host

You can also copy multiple local files on our remote host in a single command. In my case I’ll transfer movie1.mp4, movie2.mp4, movie3.mp4, and movie4.mp4.

To transfer multiple local files with scp just include all of them in the command, separated by a space:

scp movie1.mp4 movie2.mp4 movie3.mp4 movie4.mp4 [email protected]:/home/stelixd

### 2. Copy a Remote File to Your Local Machine Using SCP Command

To copy a remote file to your local machine using the scp command, just use the remote location as the source file, and the local location as the destination:

scp [email protected]:/home/stelixd/example.txt example.txt

#### Copy Multiple Remote Files to Your Local Machine

To copy multiple remote files to our local machine, use the following syntax:

scp [email protected]_destination:/some/remote/directory/\{file1,file2,file 3\} /some/local/directory

Where [email protected]_destination is your remote host details, /some/remote/directory/ is a directory on your remote host, and \{file1,file2,file3\} are the files we want to transfer, separated by a comma, in escaped (\) curly braces {}.

Escaping is a method that allows us to tell a computer to do something special with the text we supply or to ignore the special function of a character. To tell the computer that it should expect an escape character we use a special escape marker, we usually make use of the backslash \, such as we have done with the curly braces (\{, \}).

Here is an example of me transferring 3 empty files from a remote server to a local computer:

scp mrtest:/home/edxd/\{file1,file2,file3\} /home/stelixd/
Output
file1 100% 5120KB 2.5MB/s 00:01
file2 100% 11MB 8.1MB/s 00:01
file3 100% 8192KB 8.0MB/s 00:00

### 3. Copy a File between Two Remote Hosts Using the SCP Command

With the scp command you can copy files from a remote host directly to another remote host, all without having to SSH into any of them.

You’ll just send the command from a third machine, such as your local computer. The following command will copy file1 between two remote machines:

scp [email protected]_host_1:/var/www/file1 [email protected]_host_2:/var/www/file2

Video Demo
Here is an example where I copy a file between two remote hosts with scp:

scp [email protected]:/home/edxd/my_file [email protected]:/home/stelixd
5. SCP Command - Copy Files Across Remote Hosts

Important: In some cases scp hangs, and doesn’t prompt you for both passwords so it can proceed with the transfer, and I’m not yet sure the reason for this.

One solution for this is setting up SSH-key based authentication between the computer issuing the command, and both the remote hosts.

#### Copy Files Between Two Remote Hosts That Are Not in The Same Network

Usually you can transfer files between remote machines with the scp command because they are on the same network, with routers between them that route the traffic.

But there are instances where you need to transfer files between remote machines that aren’t on the same network, because there are no routers between them, however you can connect to both of them from your computer.

With the scp command you have an option to transfer files through the third machine sending the command, such as your local computer. You can do this with the -3 option.

The following command will copy files from two machines through the machine that is sending the command.

scp -3 [email protected]_host_1:/var/www/file1 [email protected]_host_2:/var/www/file2

Video Demo

An example of the above command.

scp -3 [email protected]:/home/edxd/my_file [email protected]:/home/stelixd
5. SCP Command - Copy Files Across Remote Hosts (Route)

### 5. Copy Files with Certain Extensions With the SCP Command

To copy files of a specific type using the scp command you can run a command such as:

scp [email protected]_host:'/directory/*.{html,php}' /destination/folder

Important Note: Please note the pair of single quotes ', along with the * wildcard, and curly braces with comma separated extensions. This will cause the shell to turn the expression into:

scp [email protected]_host:/directory/*.html [email protected]_host:/directory/*.php /destination/folder

### 6. Copy a Directory Recursively With the SCP Command

To copy a directory along with all its contents, we will include the -r (recursive) parameter in our SCP command. This command will copy a directory and all its contents:

scp -r transfer_folder [email protected]_host:/remote/path/

Let’s copy the transfer_folder directory on our local computer to our remote host.

scp -r transfer_folder [email protected]:/home/stelixd

Video Demo

3. SCP Command - Copy a Directory Recursively

## SCP Options

You can easily view the scp command’s options in your command-line by running man scp. We’ll explore a few of these options here.

### SCP Verbose Mode (-v, -vv, -vvv)

By enabling verbose mode with the scp command, you can see debug information for SCP – essentially you’re seeing everything happening behind the scenes.

The more -v you use, the more verbose the output will be. The maximum number of -v is 3.

Video Demo

For our example we’ll copy a few files movie1.mp4, movie2.mp4, movie3.mp4 and movie4.mp4 using -v.

4. SCP Command - Copy Files Verbose Mode

### Transfer and Compress Files on The Fly (-C)

If you are copying a large file or multiple files over a slow network, you can use the -C parameter, which will enable scp to compress the files before transferring them over the internet.

That may also save on your bandwidth if bandwidth is an issue. On reasonably fast connections, this might just slow things down, however.

Note: We have included the -v (verbose) parameter in the command below to see what is happening behind the scenes.

scp -vC example_file [email protected]:/home/stelixd

Video Demo

6. SCP Command - Compress and Copy Files

### Limit Bandwidth Usage (-l)

When you’re copying a file from your local computer to a remote host, think of it as an upload process. Now, if the upload bandwidth used by the SCP command is high, it might impact the network or other processes and devices also uploading data.

Luckily, we can use the -l parameter and specify the bandwidth used by the SCP command in Kilobits/sec (kbps).

Important: Even though we specify the transfer rate in Kilobits/sec (kbps), the transfer rate will be displayed in Kilobytes/sec (KB/s). A Kilobyte is made up of 8 Kilobits. So when we specify, say scp -l 1600, we’re saying we want a transfer rate of 1600 Kilobits, which in KB/s means 1600 / 8 = 200 KB/s. As another example, if you want to limit transfer to 300 KB/s, you multiply 300 * 8 = 2400 Kilobits. So we run scp -l 2400.

In the command below, we will set our SCP transfer bandwidth to 800 Kb/s (800 * 8 = 6400 Kilobits/sec).

scp -l 6400 example_file [email protected]:/home/stelixd
7. SCP Command - Limit Bandwidth Usage

### Specify Port Number (-P)

By default, SSH uses port 22.

For security reasons and other related measures, some people prefer changing this default port and configuring a custom port to work with the SSh service. You will need to specify the custom SSH port in your SCP command using the -P parameter in such a situation.

We haven’t configured any custom port in our case, and we will just enter port 22.

scp -P 22 example_file [email protected]:/home/stelixd
8. SCP Command - Specify Port Number

### Set a Different Cipher (-c)

To copy files securely over a network, scp uses the AES encryption algorithm. To specify a different algorithm, use the -c parameter. For this example, we will use the aes128-ctr cipher. Some ciphers are more secure and others are faster than others.

Note: This -c parameter is a lowercase character, unlike our -C (uppercase) used for file compression.

scp -c aes128-ctr example_file [email protected]:/home/stelixd
9. SCP Command - Set a Different Cipher

### Force SCP to Use IPv4 or IPv6 Addresses (-4 / -6)

You can specify whether the scp command should use IPv4 or IPv6, with the -4 and -6 options.

To use IPv4:

scp -4 /path/to/file1 [email protected]_host:/remote/path/

To use IPv6:

scp -6 /path/to/file1 [email protected]:/remote/path/

### Automate File Transfers Using a SCP Shell Script

If you have files or directories that you copy regularly, you can create a simple bash script and save the time of writing those long commands on the terminal.

There are various ways you can write scripts to use the SCP command.

In this example I’ll create a simple script that requests a target file or directory that I manually input, then it loops through some destinations in a file (that I’ve set beforehand), and transfers the file I entered to those destinations.

I created a file called destination_address.txt in the /tmp directory. This text file will hold the [email protected]_address:/destination of our remote host. In this case, I want to transfer files to my remote server, in the ~/remote_transfers folder.

[email protected]:~/remote_transfers/

Now let’s create our bash script:

echo "=================="
echo "Running SCP Script"
echo "=================="
echo -e "Enter the path to the file you wish to copy:\c"

for dest in cat /tmp/destination_address.txt; do
scp -r $file${dest}

done

We will save our script as scp_script.sh. To make the script executable, remember to run the command chmod +x scp_script.sh.

To run it I’ll run:

sudo bash scp_script.sh
10. SCP Command - Automate File Transfers Using a SCP Shell Script

### SSH Key (Identity File) Path (-i) with the SCP Command

If you have configured SSH key-based authentication, you can use the -i option and specify the path to the identity file.

Identity files come in different formats, depending on your setup and environment. For example .pub is the file format used by SSH, .pem can be used for AWS when you created your key-pair.

The following command connects to a remote host using an SSH Key.

scp -i /path/to/ssh_key.pub /path/to/local_file [email protected]_host:path/to/remote/file

### Using Multiple SCP Command Options

You can use multiple options in the same command. Some flags can be combined. If you check man scp you should see the scp command’s full syntax, which should give you a good idea on what flags you can combine:

scp [-346BCpqrTv] [-c cipher] [-F ssh_config] [-i identity_file] [-J destination] [-l limit] [-o ssh_option] [-P port] [-S program] source ... target

### Preserve File Modification/Access Times and Modes With the SCP Command (-p)

To preserve modification times, access times, and modes with the scp command you can use the -p flag:

scp -p /path/to/example.txt [email protected]:/remote/path

### How to Resume Interrupted SCP File Transfers

SCP does not understand range-request or partial transfer, such as HTTP does. As such, scp implementations, such as our command-line utility can’t resume interrupted downloads.

However, there are simple ways to resume interrupted scp transfers, by using other utilities that have this capability.

A very easy and straightforward way of resuming aborted downloads is using the sftp interactive commands reput and reget.

#### Resume Interrupted File Transfers with SFTP Reget or Reput

SFTP (SSH File Transfer Protocol) is a related secure transfer protocol, which is used to access, manage and transfer files using SSH.

To read more on sftp and its’ options you can run man sftp or read the sftp manual page online.

It works a little different than the scp command, as it offers an option to run interactive commands after connecting to a remote server.

1. reget: resumes downloads
2. reput: resumes upload

In the following example we start downloading a 700 mebgabyte file called bytexd.txt from a remote server, that we interrupt by pressing Ctrl + C, when it’s at 9%:

scp [email protected]_host:/remote/directory/bytexd.txt bytexd.txt
Output
bytexd.txt 9% 65MB 3.1MB/s 03:34 ETA

To continue the download we’ll have to connect to the remote host using sftp:

sftp [email protected]_host

You will have to authenticate, such as you would with scp or ssh.

When you’re logged in with sftp you’ll notice your prompt has changed into:

sftp>

Now we can run interactive commands.

You can also run commands such as cd and ls to navigate and find your files. Read more on all available interactive commands in the man page.

To resume the download, we’ll run the reget interactive command, followed by the file path on the remote directory:

sftp> reget /remote/directory/bytexd.com
Output
Resuming /remote/directory/bytexd.txt to bytexd.txt
/remote/directory/bytexd.txt 10% 73MB 771.1KB/s 13:53 ETA

## Installing SCP (Optional)

On Linux and Mac, scp is usually already installed, and on Windows you’ll most likely have to install it yourself.

### Install SCP on Linux

Installing scp will different, depending on your distro.

#### Install SCP on Debian-based Distros

To install scp on Debian-based distros (such as Debian, Ubuntu, Linux Mint, and others) run:

sudo apt install openssh-client

#### Install SCP on RHEL-based Distros

To install scp on RHEL-based distros (such as CentOS, Fedora, Rocky Linux, AlmaLinux, and others) run:

sudo dnf install openssh-clients

### Install SCP on Windows

SCP doesn’t come installed on Windows so we’ll have to install it ourselves. We’ll cover two common ways. There are probably more out there, but these two are popular and tested.

#### pscp (Putty) – Windows SCP via Command-line

PSCP (PuTTY Secure Copy) is similar to scp and comes bundled with PuTTY, probably the most used SSH client for Windows. It is free and open-source.

You can download and install Putty from the developer’s (Simon Tatham) website, if you don’t have it already.

You can also download and install pscp.exe separately, if you prefer.

After installing it, open a new command shell (like cmd.exe) and run:

pscp

You should see something like:

PuTTY Secure Copy client
Release 0.74
Usage: pscp [options] [[email protected]]host:source target
pscp [options] source [source...] [[email protected]]host:target
pscp [options] -ls [[email protected]]host:filespec
Options:
-V        print version information and exit
-pgpfp    print PGP key fingerprints and exit
-p        preserve file attributes
-q        quiet, don't show statistics
-r        copy directories recursively
-v        show verbose messages
-P port   connect to specified port
-l user   connect with specified username
-1 -2     force use of particular SSH protocol version
-4 -6     force use of IPv4 or IPv6
-C        enable compression
-i key    private key file for user authentication
-noagent  disable use of Pageant
-agent    enable use of Pageant
-hostkey aa:bb:cc:...
manually specify a host key (may be repeated)
-batch    disable all interactive prompts
-no-sanitise-stderr  don't strip control chars from standard error
-proxycmd command
use 'command' as local proxy
-unsafe   allow server-side wildcards (DANGEROUS)
-sftp     force use of SFTP protocol
-scp      force use of SCP protocol
-sshlog file
-sshrawlog file
log protocol details to a file

File path notation is different for Windows that for Linux. With pscp you must specify the file paths appropriately for each operating system.

#### Copy Files from Windows to Linux with PSCP

To copy files from Windows to Linux, using pscp you can run something like:

pscp c:\path\to\file [email protected]_host:/path/to/file

#### Copy Files from Linux to Windows with PSCP

To copy files from Linux to Windows using pscp:

pscp [email protected]_host:/path/to/file c:\path\to\file

#### WinSCP – GUI Version of SCP

WinSCP is a very popular GUI (graphical user interface) software, for Windows, that allows copying files between local and remote hosts, and supports the following file transfer protocols – SCP, FTP, FTPS, SFTP, WebDAV and S3.

It’s very straightforward and easy to use. To install it follow the instructions in the install guide , and you can read about its features and other useful information in the Documentation.

Many Windows users prefer WinSCP since it mainly offers a graphical user interface and offers functionalities such as:

1. Drag & Drop: Simply using the interface to drag/drop files to copy them from the local to the remote system, and vice versa.
2. Synchronizing: Which synchronizes content of a local directory onto the remote directory, vice versa, or even full sync which means that any modification made on either system, it will be applied to the other system.
3. Resuming Transfers
4. .. many more that you can find in the WinSCP Docs

## Conclusion

This post has given you a detailed guide on using the scp command to transfer files securely, and how to use some of the most common options. To easily see all the scp command options, along with their explanations, you can run the man scp command in your command-line, or you can read them online.

If you have any questions or requests, then feel free to let us know in the comments section and we’ll get back to you as soon as we can.

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danny
1 year ago

what console do you use?

## Bash Case Statement

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# Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.

I’m stuck at this question. Can someone please help me?

Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.

Let $x$ be the element of $G$ which has order 2. Let $y$ be an arbitrary element of $G$. We have to prove that $x \cdot y = y \cdot x$.

Since $x$ has order $2$, $$x^2 = e$$
That is,
$$x^{-1}=x$$

I don’t really know how to proceed. I’ve tried a number of things, but none of them seem to work.

#### Solutions Collecting From Web of "Prove that if a group contains exactly one element of order 2, then that element is in the center of the group."

Consider the element $z =y^{-1}xy$, we have: $z^2 = (y^{-1}xy)^2 = (y^{-1}xy)(y^{-1}xy) = e$. So: $z = x$, and $y^{-1}xy = x$. So: $xy = yx$. So: $x$ is in the center of $G$.

More generally, if a group$~G$ contains exactly one element$~x$ having any given property that can be expressed in the language of group theory (in particular without mentioning any specific element of$~G$, other than the identity element$~e$), then $x$ is in the center of$~G$. Namely, any automorphism of$~G$ must send $x$ to an element with the same property, which means it has to fix$~x$. In particular this is the case for inner automorphisms (conjugation by some element of$~G$), and this implies that $x$ is in the centre of$~G$.

Every element of a conjugacy class has the same order. Since there is only one element of order 2 that element forms a singleton conjugacy class. An element has a singleton conjugacy class iff it is in the center.

These are basic observations once you get to the class equation.

Hint:
$$y y^{-1} = e \implies yxxy^{-1} = e \implies yxy^{-1} yxy^{-1} = e \implies \left( yxy^{-1} \right)^2 = e \overset{*}{\implies} yxy^{-1} = x$$

Now the real question is why do we have the implication denoted by $\overset{*}{\implies}$?

If a group contain exacly one element of order 2.then it has exactly one sub group order 2.so it must be normal .so for any Y belongs to G yxy^-1 should be in x .and it shoud be x so from that we say that X must be in centre of G

format: plain


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## Algebra 1: Common Core (15th Edition)

h=$\frac{3V}{\pi r^{2}}$
The first thing you want to do is multiply each side of the equation by 3. This gives: 3V =$\pi r^{2}$h Next, divide each side by $\pi r^{2}$ to get h by itself, giving you the answer: h=$\frac{3V}{\pi r^{2}}$


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# Torque on a charged ring

I have been studying electromagnetic induction. As I understand, a magnetic field will exert a force on a moving charge. What I would like to know is whether a changing magnetic field will exert a force on a stationary charge?

For example, consider a charged ring that is placed in a magnetic field. I know that if a current was flowing through this ring, the torque exerted by a magnetic field would be given by $I(\hat{A} \times \hat B)$. Where I is the current flowing in the circuit, $A$ is the area of the coil and $B$ is the magnetic field.

As I understand, a current is just a flow of charge, or in other words, changing charge. Thus, a changing magnetic field should exert a torque on a stationary charge. Is this right?

## bumped to the homepage by Community♦13 hours ago

This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.

• That's how an induction motor works, isn't it? – CuriousOne May 12 '16 at 7:57
• @CuriousOne Isn't the torque in an induction motor developed due to a changing CURRENT rather than a changing magnetic field? – Gummy bears May 12 '16 at 8:34
• You can't get a current without a changing magnetic field, unless you have a superconductor. – CuriousOne May 12 '16 at 9:18

Yes, it is right :)
A changing magnetic field is equivalent to an electrical field. That's what Maxwells equations say.
So a static charge will feel a force, and a collection of charges might feel a torque.

But actually, as pointed out by Feynman (this some decades old, but I have not heard, that it's deprecated), there are two conceptually different mechanisms, the connection of which we do not understand yet - it seems a coincidence.
I mean, the force $F_L$ of a magnetic field on a moving charge, and the force from a changing magnetic field on a static charge. Both lead to the rule, that the emf is equal to the derivative of the magnetic flux. But it seems, there are two distinct reasons for this rule, not obviously derivable one from the other.

• It's surely not coincidence, but one can make the argument that classical field theory can't make causative statements about matter. One will probably have to look at quantum field theory (or even one level deeper) for that. – CuriousOne May 12 '16 at 9:27
• So is there a formula for force/torque on a collection of charges due to a changing magnetic field? – Gummy bears May 12 '16 at 11:53
• well, not one formula, you need to know the properties of the field $B(t)$ and your charges (the positions). Then, yes, en.wikipedia.org/wiki/Maxwell's_equations ;) - just calculate the resulting E-field, and the force is straightforward $E\cdot q$ – Ilja May 12 '16 at 12:06


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## Hydrogen HUMMER for the Governor—But It’s ICE

##### 22 October 2004

California Gov. Schwarzenegger opened a hydrogen fueling station at LAX (Los Angeles International Airport) on Friday, rolling into the station in a prototype H2ICE Hummer prototype—the H2H—loaned by GM.

The H2H is an internal combustion engine (ICE) HUMMER H2 SUT (Sport Utility Truck) converted to burn gaseous hydrogen fuel. The truck uses a supercharged version of the truck’s original Vortec 6000 (6.0-liter V-8).

“The H2H was created for two purposes,” said Elizabeth Lowery, GM vice president, Environment & Energy. “It brings focus and attention to the journey to a hydrogen economy, and it will provide GM with key learnings on hydrogen storage, hydrogen delivery systems, and hydrogen refueling infrastructure development.”

Even as an avowed non-production prototype, this is a bit of a major departure for GM, which has been one of the automakers the most insistent on hydrogen fuel cell vehicles as the future. As a result, the automaker has never publicly emphasized an H2ICE prototype, preferring instead to seed the growing number of hydrogen trials around the globe with fuel cell vehicles such as its HydroGen3.

By contrast, Ford, which also has a robust hydrogen fuel cell program, of late has been putting emphasis on its prototype H2ICE vehicles as a way to gain more experience with hydrogen—exactly the reasoning GM outlined above. (Earlier posts here, here, and here.)

As an aside, the H2H also provides an example of a big truck that doesn’t depend on oil and is more friendly (leaving the source of the hydrogen out of the discussion of perception) to the environment. Of course, if that was the only concern, they could just trot out a biodiesel version.

GM produced the H2H in conjunction with its partner Quantum Technologies, a leader in hydrogen fuel systems and storage for both ICE and fuel cell vehicles.

In March 2004, California’s South Coast Air Quality Management District (AQMD) awarded a $2.3 million contract to Quantum to convert a fleet of 30 Toyota Priuses to hydrogen-burning hybrids. For that project, Quantum is developing the complete OEM-level hydrogen internal combustion engine fuel system, including both the injection system and hydrogen storage system. Included in the fuel systems will be the company’s patented fuel injectors, fuel rails, electronic control system and software, hydrogen storage and a customized turbocharger. Presumably, Quantum did not need to play such a complete role in the converison of H2 to H2H. It will be interesting to see if GM follows up with any other H2ICE prototypes. If they do, then it may be an indication that they are beginning to hedge their fuel cell bet, at least in terms of how soon they can build the FCV market. (Thanks to Autoblog for the tip on the Gov.) ### Comments Californian Dream? Gov Schwarzenegger must have grown up in one of those homes where, if something is good for you, a whole lot of something must be really good for you. Is a six liter V8 behemoth really the right tool to promote environmental responsibility? Or is it simply the right toy to appeal to Californian voters? Clean Hummers for everyone! Now how am I going to vent my Hummer-envy ?! There's nothing left to be morally superior about! You bast*rds! What are we waiting for oil to go to$5.a gal. or the last drop of oil to be used. Hydrogen is the way to go. It's totally renewable for ever and nomore dangerous then LNG.The government should require all gas stations to install hydrogen refueling pumps over the next few years so that what ever type of hydrogen powered cars are made they will be ready.The oil companies will convert to hydrogen production using solar or wind power and it could be pumped through pipes like natural gas is today. JAG

What are we waiting for oil to go to \$5.a gal. or the last drop of oil to be used. Hydrogen is the way to go. It's totally renewable for ever and nomore dangerous then LNG.The government should require all gas stations to install hydrogen refueling pumps over the next few years so that what ever type of hydrogen powered cars are made they will be ready.The oil companies will convert to hydrogen production using solar or wind power and it could be pumped through pipes like natural gas is today. JAG

I see it as people don't often like to see too quick of any kind of change if their already willing to let the Oil and Gas companies gouge at their pocket books. Hydrogen is easily noted as the best alternatve from Oil and Gas. ICE's that convert Hydrogen to Water are seemingly very Pro-enviromental. With GM's plans to start introducing H2ICE cars within the next 9 to 10 years, sure it seems like thats a step forward, but to the common, we feel its a lifetime away and we stay clear of the idea of change because we feel it's not upon us and their is no need to be pushy. What I'm actually tying to say here is that, if people in general are still willing to put up with the ever growing High Cost of maintaining todays Vehical models, then the Top Priority of change isn't going to be to hasty and the huge companies of todays leading Fuel providers will attempt to take and endulge in every last penny it can get from US citizens.

Hey guess what:

Now if you are a sports car enthusiast, Mazda is coming out with a Gas/Hydrogen hybrid RX-7. They promise all the performance of current Rotary Rockets. So now you can ZOOM ZOOM and be ecologically correct -(:->

Cherrio

GM (as much as I hate to say this) is on the right track. As far as I can see, from years of environmental study and activisim, the companies who stand to lose the most are the oil companies who have the capital and infrastructure to complete the problem of delivering this fuel source to the world. They own the land that the gas stations sit on, the transportation equipment, they have people who work in R&D! They are the ones who can decide the speed at wich the enevitable conversion will happen. I will do what I can to lobby my lawmakers to make this easy for the (evil) oil companies to correct the petro-chemical mess they have made and I am willing to forgive any one who will take active steps to correct a mistake.

The comments to this entry are closed.


text:
## Prime Determines Divisors

Round 19

#### Statement

Find the smallest positive integer $N$ which is a multiple of $11$ and is such that $N^2$ has exactly $9$ divisors.

Time Remaining:
0%

#### Problem Status

 Points: 500 Solved by: 80 Success Rate 57%

### Score:

#### Friends' Standings

Rank Name A B C D E F G H


text:
# sksurv.linear_model.IPCRidge#

class sksurv.linear_model.IPCRidge(alpha=1.0, fit_intercept=True, normalize='deprecated', copy_X=True, max_iter=None, tol=0.001, solver='auto')[source]#

Accelerated failure time model with inverse probability of censoring weights.

This model assumes a regression model of the form

$\log y = \beta_0 + \mathbf{X} \beta + \epsilon$

L2-shrinkage is applied to the coefficients $$\beta$$ and each sample is weighted by the inverse probability of censoring to account for right censoring (under the assumption that censoring is independent of the features, i.e., random censoring).

See 1 for further description.

Parameters

alpha (float, optional, default: 1.0) – Small positive values of alpha improve the conditioning of the problem and reduce the variance of the estimates.

coef_#

Weight vector.

Type

ndarray, shape = (n_features,)

n_features_in_#

Number of features seen during fit.

Type

int

feature_names_in_#

Names of features seen during fit. Defined only when X has feature names that are all strings.

Type

ndarray of shape (n_features_in_,)

References

1

W. Stute, “Consistent estimation under random censorship when covariables are present”, Journal of Multivariate Analysis, vol. 45, no. 1, pp. 89-103, 1993. doi:10.1006/jmva.1993.1028.

__init__(alpha=1.0, fit_intercept=True, normalize='deprecated', copy_X=True, max_iter=None, tol=0.001, solver='auto')[source]#

Methods

 __init__([alpha, fit_intercept, normalize, ...]) fit(X, y) Build an accelerated failure time model. get_params([deep]) Get parameters for this estimator. Predict using the linear accelerated failure time model. score(X, y[, sample_weight]) Return the coefficient of determination of the prediction. set_params(**params) Set the parameters of this estimator.
fit(X, y)[source]#

Build an accelerated failure time model.

Parameters
• X (array-like, shape = (n_samples, n_features)) – Data matrix.

• y (structured array, shape = (n_samples,)) – A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.

Return type

self

get_params(deep=True)#

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

predict(X)[source]#

Predict using the linear accelerated failure time model.

Parameters

X ({array-like, sparse matrix}, shape = (n_samples, n_features)) – Samples.

Returns

C – Returns predicted values on original scale (NOT log scale).

Return type

array, shape = (n_samples,)

score(X, y, sample_weight=None)[source]#

Return the coefficient of determination of the prediction.

The coefficient of determination $$R^2$$ is defined as $$(1 - \frac{u}{v})$$, where $$u$$ is the residual sum of squares ((y_true - y_pred)** 2).sum() and $$v$$ is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a $$R^2$$ score of 0.0.

Parameters
• X (array-like of shape (n_samples, n_features)) – Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

• y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True values for X.

• sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns

score$$R^2$$ of self.predict(X) wrt. y.

Return type

float

Notes

The $$R^2$$ score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score(). This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params)#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance


text:
# Infinite Union!

Algebra Level 4

$\left[\dfrac 12,1\right]\cup \left[\dfrac 14,\dfrac 12 \right]\cup \left[\dfrac 18,\dfrac 14\right]\cup \cdots=X$
Then which of the options describe the set $$X$$?

Clarification: All sets on the left are of the form $$\left[\dfrac 1{2^{n+1}},\dfrac 1{2^n}\right]$$ for some integer $$n$$.

Inspiration

×


text:
# Total length of ellipse

1. Jun 12, 2005

### ktpr2

I'm asked to show that the total length of the ellipse
x = a sin x
y = b cos x, a>b>0 is

$$L = 4a \int_{1}^{pi/2} \sqrt{1-e^2sin^2x} dx$$
where e is the eccentricity of the ellipse (e = c/a, where c = $$\sqrt{a^2-b^2}$$

I've tried a whole bunch of algebraic and trignometric manipulation but I'm getting the feeling I'm overlooking something. How would you approach this problem? I've tried working backwards and eventually got something of the form:

$$L = \int_{1}^{pi/2} \sqrt{2b^2cos^2x+c^2cos^2x-b^2(cos 2x)} dx$$

but i figured I should post here for ideas as well.

2. Jun 12, 2005

### dextercioby

HINT:The total length is 4 times the arc in the first quadrant.Choose the wise parametrization and use the definition of the eccentricity (the modulus of the elliptic integral).

Daniel.

3. Jun 12, 2005

### BobG

This can be a challenging problem. Checking out how http://home.att.net/~numericana/answer/ellipse.htm#elliptic [Broken] have solved this might give you some ideas on how to approach it.

Last edited by a moderator: May 2, 2017
4. Jun 12, 2005

### dextercioby

There's no big deal,Bob

$$L_{\mbox{ellipse}}=4L_{\mbox{arc in the first quadrant}}$$ (1)

Parametrization (polar elliptical)

$$\left\{\begin{array}{c}x(\phi)=a\cos\phi \\ y(\phi)=b\sin\phi \end{array} \right$$ (2)

$$\left\{\begin{array}{c} (dx)^{2}(\phi)=a^{2}\sin^{2}\phi \ (d\phi)^{2}\\ (dy)^{2}(\phi)=b^{2}\cos^{2}\phi \ (d\phi) ^{2}\end{array} \right$$ (3)

$$L_{\mbox{arc in the first quadrant}} =\int \sqrt{(dx)^{2}+(dy)^{2}} =\int_{0}^{\frac{\pi}{2}} \sqrt{a^{2}\sin^{2}\phi+b^{2}\cos^{2}\phi} \ d\phi$$ (4)

Now i'll leave it to the OP to finish it.

Daniel.

P.S.His answer is wrong.

5. Jun 13, 2005

### ktpr2

wow. that was down and funky. I figured it out in four lines after an embarrassing number of scrap sheets before. Thanks people.

I'll give several hints to those with the same question in the future:

The integral is from 0 to 2pi originally, but you can cut it down to 0 to pi/2 and multiply by four. recall that c^2is really just 1 - b^2/a^2 and when at the end of a deserted road, question if you can multiply by 1 expressed in a twisty way.

6. May 25, 2010

### peeyush_ali

the length of any geometrical arc is given by [ intg of ( (dx .dx +dy.dy)^1/2 ) ] within proper limits... that is according to "pythogorean theorem"..

on simplifying the above thing we get... intg [(1+(dy/dx)^2)^1/2) ].dx

Now, comming to the problem i.e., length of an ellipse, calculate (dy/dx) from the standard equation in terms of "x" and put it in the above integral and solve thus obtained integral within proper limits....thas alll........... :)

if u do tht u will get approx L= pi[ 3(a+b)- {(3a+b)(a+3b)}^1/2 ]

7. May 29, 2010

### peeyush_ali

By "within limits" i mean the limits of corresponding variable by which the integrand is multiplied i.e. the factor by which the integrand is multiplied which is a differential magnitude.... ( eg., limits of "x" if the integrand is multiplied by "dx" and limits of "theta" if the integrand is multiplied by "d(theta)" )


text:
• Corpus ID: 119126467

# Local properties of the random Delaunay triangulation model and topological 2D gravity

@article{Charbonnier2017LocalPO,
title={Local properties of the random Delaunay triangulation model and topological 2D gravity},
author={S'everin Charbonnier and Franccois David and Bertrand Eynard},
journal={arXiv: Mathematical Physics},
year={2017}
}
• Published 10 January 2017
• Mathematics
• arXiv: Mathematical Physics
Delaunay triangulations provide a bijection between a set of $N+3$ points in the complex plane, and the set of triangulations with given circumcircle intersection angles. The uniform Lebesgue measure on these angles translates into a K\"ahler measure for Delaunay triangulations, or equivalently on the moduli space $\mathcal M_{0,N+3}$ of genus zero Riemann surfaces with $N+3$ marked points. We study the properties of this measure. First we relate it to the topological Weil-Petersson symplectic…
2 Citations

## Figures from this paper

Irreducible Metric Maps and Weil–Petersson Volumes
• T. Budd
• Art
Communications in Mathematical Physics
• 2022
<jats:p>We consider maps on a surface of genus <jats:italic>g</jats:italic> with all vertices of degree at least three and positive real lengths assigned to the edges. In particular, we study the
Liouville theory and random maps
This thesis explore several aspects of random maps through the study of three models. First, we examine the properties of a measure defined on the set of planar Delaunay triangulations with n

## References

SHOWING 1-10 OF 35 REFERENCES
Planar maps, circle patterns and 2D gravity
• Mathematics
• 2013
Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a
The Brownian map is the scaling limit of uniform random plane quadrangulations
We prove that uniform random quadrangulations of the sphere with n faces, endowed with the usual graph distance and renormalized by n−1/4, converge as n → ∞ in distribution for the Gromov–Hausdorff
The decorated Teichmüller space of punctured surfaces
A principal ℝ+5-bundle over the usual Teichmüller space of ans times punctured surface is introduced. The bundle is mapping class group equivariant and admits an invariant foliation. Several
Large Strebel Graphs and (3,2) Liouville CFT
• Mathematics
• 2017
Abstract2D quantum gravity is the idea that a set of discretized surfaces (called map, a graph on a surface), equipped with a graph measure, converges in the large size limit (large number of faces)
Uniqueness and universality of the Brownian map
We consider a random planar map Mn which is uniformly distributed over the class of all rooted q-angulations with n faces. We let mn be the vertex set of Mn, which is equipped with the graph distance
Liouville Quantum Gravity on the Riemann Sphere
• Mathematics
• 2014
In this paper, we rigorously construct Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov. We establish some of its fundamental properties like
Sur l'entropie des surfaces aléatoires
We prove, and generalize to the case of surfaces with arbitrary genus, a conjecture by Knizhnik, Polyakov and Zamolodchikov for the value of the susceptibility exponent γ of a random surface as a


text:
# How do you simplify a^10*a^2*a^-6 and write it using only positive exponents?

${a}^{10} + {a}^{2} + {a}^{-} 6 = {a}^{10 + 2 - 6} = {a}^{6}$


text:
• The object started from rest, reached a maximum velocity of $$20 \, \mathrm{m/s}$$ and then returned to rest
• The object started from rest and covered a total distance of $$20 \, \mathrm{m}$$ in $$4 \, \mathrm{s}$$
• The object's final displacement was $$40 \, \mathrm{m}$$: $$20 \, \mathrm{m}$$ in the first $$2 \, \mathrm{s}$$ and $$20 \, \mathrm{m}$$ in the next $$2 \, \mathrm{s}$$
• The object reached a displacement of $$20 \, \mathrm{m}$$ in $$2 \, \mathrm{s}$$ and then came back to the original point, with a final displacement of $$0 \, \mathrm{m}$$


text:
# Ohm's law

 Page 1 / 1

## Introduction

The study of electrical circuits is essential to understand the technology that uses electricity in the real-world. This includes electricity being used for the operation of electronic devices like computers.

## Experiment : ohm's law

Aim:

In this experiment we will look at the relationship between the current going through a resistor and the potential difference (voltage) across the same resistor.

Method:

1. Set up the circuit according to the circuit diagram, starting with just one cell.
2. Draw the following table in your lab book.
 Voltage, $V$ (V) Current, $I$ (A) 1,5 3,0 4,5 6,0
3. Get your teacher to check the circuit before turning the power on.
4. Measure the current.
5. Add one more 1,5 V cell to the circuit and measure the current again.
6. Repeat until you have four cells and you have completed your table.
7. Draw a graph of voltage versus current.

Results:

1. Does your experimental results verify Ohm's Law? Explain.
2. How would you go about finding the resistance of an unknown resistor using only a power supply, a voltmeter and a known resistor ${R}_{0}$ ?

## Activity : ohm's law

If you do not have access to the equipment necessary for the Ohm's Law experiment, you can do this activity.

 Voltage, $V$ (V) Current, $I$ (A) 3,0 0,4 6,0 0,8 9,0 1,2 12,0 1,6
1. Plot a graph of voltage (on the $x$ -axis) and current (on the $y$ -axis).

Conclusions:

1. What type of graph do you obtain (straight line, parabola, other curve)
2. Calculate the gradient of the graph.
3. Do your experimental results verify Ohm's Law? Explain.
4. How would you go about finding the resistance of an unknown resistor using only a power supply, a voltmeter and a known resistor ${R}_{0}$ ?

An important relationship between the current, voltage and resistance in a circuit was discovered by Georg Simon Ohm and is called Ohm's Law .

Ohm's Law

The amount of electric current through a metal conductor, at a constant temperature, in a circuit is proportional to the voltage across the conductor. Mathematically, Ohm's Law is written:

$V=R·I.$

Ohm's Law tells us that if a conductor is at a constant temperature, the current flowing through the conductor is proportional to the voltage across it. This means that if we plot voltage on the $x$ -axis of a graph and current on the $y$ -axis of the graph, we will get a straight-line. The gradient of the straight-line graph is related to the resistance of the conductor.

## Ohmic and non-ohmic conductors

As you have seen, there is a mention of constant temperature when we talk about Ohm's Law. This is because the resistance of some conductors changes as their temperature changes. These types of conductors are called non-ohmic conductors, because they do not obey Ohm's Law. As can be expected, the conductors that obey Ohm's Law are called ohmic conductors. A light bulb is a common example of a non-ohmic conductor. Nichrome wire is an ohmic conductor.

In a light bulb, the resistance of the filament wire will increase dramatically as it warms from room temperature to operating temperature. If we increase the supply voltage in a real lamp circuit, the resulting increase in current causes the filament to increase in temperature, which increases its resistance. This effectively limits the increase in current. In this case, voltage and current do not obey Ohm's Law.

The phenomenon of resistance changing with variations in temperature is one shared by almost all metals, of which most wires are made. For most applications, these changes in resistance are small enough to be ignored. In the application of metal lamp filaments, which increase a lot in temperature (up to about 1000 ${}^{\circ }$ C, and starting from room temperature) the change is quite large.

In general non-ohmic conductors have plots of voltage against current that are curved, indicating that the resistance is not constant over all values of voltage and current.

## Experiment : ohmic and non-ohmic conductors

Repeat the experiment as decribed in the previous section. In this case use a light bulb as a resistor. Compare your results to the ohmic resistor.

## Using ohm's law

We are now ready to see how Ohm's Law is used to analyse circuits.

Consider the circuit with an ohmic resistor, $R$ . If the resistor has a resistance of 5  $\Omega$ and voltage across the resistor is 5 V, then we can use Ohm's law to calculate the current flowing through the resistor.

Ohm's law is:

$V=R·I$

which can be rearranged to:

$I=\frac{V}{R}$

The current flowing through the resistor is:

$\begin{array}{ccc}\hfill I& =& \frac{V}{R}\hfill \\ & =& \frac{5\phantom{\rule{0.277778em}{0ex}}\mathrm{V}}{5\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\Omega }\hfill \\ & =& 1\phantom{\rule{0.277778em}{0ex}}\mathrm{A}\hfill \end{array}$

The resistance of the above resistor is 10  $\Omega$ and the current going through the resistor is 4 A. What is the potential difference (voltage) across the resistor?

1. It is an Ohm's Law problem. So we use the equation:

$V=R·I$
2. $\begin{array}{ccc}\hfill V& =& R·I\hfill \\ & =& \left(10\right)\left(4\right)\hfill \\ & =& 40\phantom{\rule{3.33333pt}{0ex}}V\hfill \end{array}$
3. The voltage across the resistor is 40 V.

## Ohm's law

1. Calculate the resistance of a resistor that has a potential difference of 8 V across it when a current of 2 A flows through it.
2. What current will flow through a resistor of 6  $\Omega$ when there is a potential difference of 18 V across its ends?
3. What is the voltage across a 10  $\Omega$ resistor when a current of 1,5 A flows though it?

#### Questions & Answers

which gas is ideal gas
how to calculate emf when you are given two circuits with different external resistance, current but no internal resistance?
you have to find the current of whole both circuits nd add em...
Amanzialwandle
calculate the distance between two charge +4nc and -3nc if electrostatic is 0.005N
use the coulombs law equation where there is F u substite by 0.005 then u cross multiple
Neldo
what is atomic
what is charge
motheo
why do we need to add oil to an engine
Kamohelo
we need to add all to an engine 2 lubricate the bearings and the shops to avoid friction that will lead to overheating and knocking
Easyas
charge is a unit of matter that expresses the extent to which it has more or less electrons than protons
Easyas
how to calculate the distance between Q1 and point P if you are given distance between point P and Q2
how do we calculate the magnitude of the force between two objects
we use Newtons law ...fnet=ma
Fikile
how do you calculate the enery change in enthalpy reaction, can someone explain it to me guys
∆H(enthalpy change)= Hproducts- Hreactants.... use this formula, H stands for enthalpy which is regarded as energy
Andiswa
atomic model john dalton
Hlw,, I want to join.
crippah
what is a normal force
normal force is the line that is perpendicular to the surface
Thabo
normal force is the force exerted to an object by the surface , perpendicular to the surface
Fhatani
I want to join
Londiwe
better explanation of FARADAY'S LAW OF INDUCTION
Kgaugelo
what is the formular of energy
E=f\q
Wonder
E=hf
Mondli
doesnt it like depend on the type of energy
Benjamin
what does (1s2 2s2 and 2p6) mean?
That is Albau Diagram I guess!! it represent number of electrons in each energy orbit!! the numbers 1s, 2s&2p, 3s and so on represent energy orbit and then the other numbers after s & p represent number of electrons
Andiswa
That is SP notation
Kgaugelo
What are the differences between pd and emf?
How to calculate magnitude of Friction force
in Newton
Obakeng
yeh
Obakeng
in newton
Fikile
Onother Question?
crippah
yes bruh
Fikile
First of all in wat Grade ae u..?
crippah
grde 11
Fikile
Oka nd hw is the properties of a substance afected by the intermoleculaer forces...
crippah
hi guys I m in grade 11 I need help with electrostatics
Serati
what is newton
look for the x components n y components then after y add the x components separate n y separate then u use the Pythagoras theorem 2 find the resultand
Thank you very much
Luvuyo
how do I find 🔍 the critical angle
Ntandokazi
angle of incident and angle of reflection must always approach normal line thats where u will see 90° which is critical point
Tumelo


text:
# Practical ceramics

1. Jan 7, 2005

### jimbot

The space shuttle had thousands of tiles that were close to the ultimate insulators. Has anyone gotten to the point where they're not $1000s a pound yet? I was wondering if anyone has created a thermos bottle that you could put in a microwave for a reasonable price. Why can't they spin off something useful from all those$ they spent on the shuttle?

2. Jan 7, 2005

### Gokul43201

Staff Emeritus
I can't see what's so useful about a thermos that can be put in a microwave. A good thermos shouldn't need to be put in a microwave, and if you want to heat up your coffee anyway, why carry it in a thermos ? Or maybe I'm just used to getting hot (albeit lousy) coffee from the vending machine.

I think I'm missing the point here...I don't see the relevance of the ceramic tiles.


text:
## Barn door tracker?

Tell us about those other projects you are working on.
maceemiller
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### Re: Barn door tracker?

Star Dad wrote:
Tue Jan 21, 2020 6:15 pm
SkyHiker wrote:
Tue Jan 21, 2020 3:22 am
I recommend using a small stepper motor and an Arduino. With digital control you can avoid having to use circularly curved screws which simplifies the mechanics. I have built three kinds one of which was dual-axis and autoguided for a 10" Dob. Look on the AF, user Camelhat.
Please take this with the humor I mean to convey. Only a true geek would say that using an Arduino , a stepper motor, and software can "avoid having to use circularly curved screws ". The screw that took all of 5 minutes to bend to its proper shape. ROFL! I LOVE it SkyHiker!
If I'm honest, i dont get what humour you are trying to convey?

I am slowly learning from this thread and looking forward to it clicking in my head.
ARock
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maceemiller wrote:
Tue Jan 21, 2020 8:35 pm
I am slowly learning from this thread and looking forward to it clicking in my head.

I started with Arduino and Steppers for astronomy as well. Some links that I bookmarked...

1. Stepper motor basics from the Arduino forums.
https://forum.arduino.cc/index.php?topic=284828.0

2. In addition to an Arduino and a Stepper motor you need a "driver chip". There are many, and you need to pick one which works with the stepper you choose. But here is a good example of how to connect a particular one, the DRV8825
https://www.pololu.com/product/2133
You can get the driver chips with pins soldered on ebay for very cheap.

3. A stepper driver board for the DRV8825. This is a board to connect the driver chip DRV8825 above and the arduino without any soldering. Different driver chips have different such boards. It does not allow you to change microstepping mode on the fly.
https://www.ebay.com/itm/42-CH-Stepper- ... 2159700787

4. If you want to add a stepper motor to EQ your mount and add guiding to it, here is a good example. It will work even if you dont do guiding (the default is tracking). You need to change a few numbers to adapt the code for your particular mount.
https://forum.arduino.cc/index.php?topic=245679.0
AR
Scopes: Zhumell Z8, Meade Adventure 80mm, Bushnell 1300x100 Goto Mak.
Mount: ES EXOS Nano EQ Mount, DIY Arduino+Stepper RA drive.
AP: 50mm guidescope, AR0130 based guidecam, Canon T3i, UHC filter.
EPs: ES82 18,11,6.7mm, Zhumell 30,9mm FJ Ortho 9mm, assorted plossls, Meade 2x S-F Barlow, DGM NPB filter.
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#### TSS Photo of the Day

ARock wrote:
Tue Jan 21, 2020 10:01 pm
maceemiller wrote:
Tue Jan 21, 2020 8:35 pm
I am slowly learning from this thread and looking forward to it clicking in my head.

I started with Arduino and Steppers for astronomy as well. Some links that I bookmarked...

1. Stepper motor basics from the Arduino forums.
https://forum.arduino.cc/index.php?topic=284828.0

2. In addition to an Arduino and a Stepper motor you need a "driver chip". There are many, and you need to pick one which works with the stepper you choose. But here is a good example of how to connect a particular one, the DRV8825
https://www.pololu.com/product/2133
You can get the driver chips with pins soldered on ebay for very cheap.

3. A stepper driver board for the DRV8825. This is a board to connect the driver chip DRV8825 above and the arduino without any soldering. Different driver chips have different such boards. It does not allow you to change microstepping mode on the fly.
https://www.ebay.com/itm/42-CH-Stepper- ... 2159700787

4. If you want to add a stepper motor to EQ your mount and add guiding to it, here is a good example. It will work even if you dont do guiding (the default is tracking). You need to change a few numbers to adapt the code for your particular mount.
https://forum.arduino.cc/index.php?topic=245679.0
Thankyou. Wow, my heads gone at the mo....so much to try and digest.
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Star Dad wrote:
Tue Jan 21, 2020 6:15 pm
SkyHiker wrote:
Tue Jan 21, 2020 3:22 am
I recommend using a small stepper motor and an Arduino. With digital control you can avoid having to use circularly curved screws which simplifies the mechanics. I have built three kinds one of which was dual-axis and autoguided for a 10" Dob. Look on the AF, user Camelhat.
Please take this with the humor I mean to convey. Only a true geek would say that using an Arduino , a stepper motor, and software can "avoid having to use circularly curved screws ". The screw that took all of 5 minutes to bend to its proper shape. ROFL! I LOVE it SkyHiker!
Of course it's easy to bend a screw but a bent screw cannot be turned while a straight one can. So a straight screw gives you more design options. Instead of having to drive a cog wheel around the screw you can turn the screw itself, which involves fewer moving parts to deal with.

In my design all that I used was a $3 mass produced microstepper with internal gears that is sold with a controller board. The motor axle was pushed into a blob of epoxy putty on the screw, that's all, a T nut for the screw, no other parts needed. A stepper has the advantage of being very precise and easy to program for those who are familiar with programming. ... Henk. Telescopes: 6" Mak-Newt (Comet Hunter), ES ED127CF, ES ED80, Zhumell Z12, Coulter Odyssey 10, AT6RC, Venture RX-7, Celestron Skymaster 20x80, Mounts and tripod: Losmandy G11S, AVX, LXD55, Tiltall, Cameras: Fuji X-a1, Canon SX40, Xt, XSi, T6, ELPH 100HS, DIY: Dob and camera barndoor trackers, afocal adapter, Dob with foldable base and Az/Alt setting circles, Accessories: SSAG, Plossls, Barlows, Telrad, laser collimators (Seben LK1, Z12, Howie Glatter), Cheshire, 2 Orion RACIs 8x50, Software: DSS, ImageMagick, PHD, Nebulosity, Photo Gallery, Gimp, CHDK SkyHiker Saturn Ambassador Articles: 0 Posts: 351 Joined: Sat May 11, 2019 8:40 pm Location: Santa Barbara, CA Has thanked: 481 times Been thanked: 554 times I started with a stepper driver library from some Arduino site but I found out later that this generic library was not good. Always follow the stepper motor manufacturer's pulse scheme, that works best. Also, program against a time line to avoid numerical errors. The one disadvantage of a straight screw is that you have to start from a predetermined initial position because that's what the math is based on but it's not much of an issue really. Here's a bunch of 5 stepper motors plus controller boards for a whole$12 on Amazon, https://www.amazon.com/HiLetgo-ULN2003- ... 5286&psc=1 . It runs on 5V from the Arduino, no other power needed. For development it all runs off your laptop's USB port.
... Henk. Telescopes: 6" Mak-Newt (Comet Hunter), ES ED127CF, ES ED80, Zhumell Z12, Coulter Odyssey 10, AT6RC, Venture RX-7, Celestron Skymaster 20x80, Mounts and tripod: Losmandy G11S, AVX, LXD55, Tiltall, Cameras: Fuji X-a1, Canon SX40, Xt, XSi, T6, ELPH 100HS, DIY: Dob and camera barndoor trackers, afocal adapter, Dob with foldable base and Az/Alt setting circles, Accessories: SSAG, Plossls, Barlows, Telrad, laser collimators (Seben LK1, Z12, Howie Glatter), Cheshire, 2 Orion RACIs 8x50, Software: DSS, ImageMagick, PHD, Nebulosity, Photo Gallery, Gimp, CHDK
Star Dad
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maceemiller wrote:
Tue Jan 21, 2020 8:35 pm
Star Dad wrote:
Tue Jan 21, 2020 6:15 pm
SkyHiker wrote:
Tue Jan 21, 2020 3:22 am
I recommend using a small stepper motor and an Arduino. With digital control you can avoid having to use circularly curved screws which simplifies the mechanics. I have built three kinds one of which was dual-axis and autoguided for a 10" Dob. Look on the AF, user Camelhat.
Please take this with the humor I mean to convey. Only a true geek would say that using an Arduino , a stepper motor, and software can "avoid having to use circularly curved screws ". The screw that took all of 5 minutes to bend to its proper shape. ROFL! I LOVE it SkyHiker!
If I'm honest, i dont get what humour you are trying to convey?

I am slowly learning from this thread and looking forward to it clicking in my head.
Just to be clear - I am smiling at SkyHikers solution. I too have a tendency to take tech to it's highest form to solve a simple problem. I actually admire him for the Arduino/stepper motor solution. Only wish I had thought of it. I have an Arduino sitting on my desk right now - and I'm trying to come up with a problem in need of an arduino solution.

And SkyHiker is right - I have two gears - one on the motor and one that rotates around a brass threaded rod four times slower than the motor. I was surprised that there were no glitches because of the bending of the rod - ie the gears rotated smoothly despite the threads being compressed on one side and expanded on the other. As the gears rotate the threaded rod slowly pushes open the hinge.
"To be good is not enough when you dream of being great"

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#### TSS Photo of the Day

So, got some materials ready to start building but a little confused as to what motor to buy. Any recommendations on a cheap motor to work with the drive bolt?
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#### TSS Photo of the Day

Hi all. So while I'm waiting to see what motor I should use I've been getting on with my trap

I've NO skills when it comes to woodwork (I'm a landscaper/bricklayer.....i prefer dirt and cement) yet I'm happy where I'm at in this build....
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#### TSS Photo of the Day

One tip that was told to me today was, after the rod is bent, run a nut up and down the thread a few times.....

I didnt quite understand at the time as to why yet I get it now.....

When the rod is bent it slightly compresses the threads on the inside curve and stretches the threads on the outside curve. Running a nut up and down a few times "realigns" the threads making the movement smoother.

I did this and found about 10 threads binded a little halfway on the rod....now its smooth as silk which, hopefully will make the gear turn without any resistance
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maceemiller wrote:
Mon Jan 27, 2020 6:14 pm
Hi all. So while I'm waiting to see what motor I should use I've been getting on with my trap

I've NO skills when it comes to woodwork (I'm a landscaper/bricklayer.....i prefer dirt and cement) yet I'm happy where I'm at in this build....
I am working on this build and another similar to it which can be found at https://www.thingiverse.com/thing:2377686

I have all the pieces made and/or purchased and am now ready to assemble.

But, I Have hit a snag. The person who posted this build gives the following code for the arduino nano.

Arduino code.

#include<AccelStepper.h>
#define HALFSTEP 8
#define motorPin1 3 // IN1 on the ULN2003 driver 1
#define motorPin2 4 // IN2 on the ULN2003 driver 1
#define motorPin3 5 // IN3 on the ULN2003 driver 1
#define motorPin4 6 // IN4 on the ULN2003 driver 1

AccelStepper stepper1(HALFSTEP, motorPin1, motorPin3, motorPin2, motorPin4);

int buttonmode = 2;
boolean Motortoggle = 0;
const int SwitchPin = 12; // the number of the pushbutton pin
const int ledPin = 13; // the number of the LED pin
// variables will change:
int Switchstate = 0; // variable for reading the pushbutton status

void setup() {
Serial.begin(9600);

stepper1.setMaxSpeed(261.41);
stepper1.setAcceleration(50.0);
stepper1.setSpeed(261.41);
//stepper1.moveTo(20000);
// initialize the LED pin as an output:
pinMode(SwitchPin, INPUT_PULLUP);
pinMode(ledPin, OUTPUT);
// initialize the pushbutton pin as an input:
digitalWrite(SwitchPin, HIGH);
}

void loop() {
// read the state of the switch value:
Switchstate = digitalRead(SwitchPin);
if (Switchstate == LOW) {
stepper1.runSpeed();
digitalWrite(ledPin, HIGH);
} else {
stepper1.stop();
digitalWrite(ledPin, LOW);
}
}

Unfortunately, I do not know how to load the code onto the nano. I have installed marlin code onto an arduino board before, but can't figure this out at all!!

Hope somebody can help me.
ARock
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Follow the instructions here

https://www.arduino.cc/en/Guide/ArduinoNano

I use the Arduino Desktop IDE, this means downloading and installing it. The link for it is in the page above.
Try the blink example as described above, before you try your own code file. The page includes instructions on what to do if your nano is old and needs an old bootloader.
AR
Scopes: Zhumell Z8, Meade Adventure 80mm, Bushnell 1300x100 Goto Mak.
Mount: ES EXOS Nano EQ Mount, DIY Arduino+Stepper RA drive.
AP: 50mm guidescope, AR0130 based guidecam, Canon T3i, UHC filter.
EPs: ES82 18,11,6.7mm, Zhumell 30,9mm FJ Ortho 9mm, assorted plossls, Meade 2x S-F Barlow, DGM NPB filter.
Binos: Celestron Skymaster 15x70 (Albott tripod/monopod), Nikon Naturalist 7x35.
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When I paste the above code into the arduino IDE window and upload it, I get the following messages:

Sketch uses 6696 bytes (21%) of program storage space. Maximum is 30720 bytes.
Global variables use 278 bytes (13%) of dynamic memory, leaving 1770 bytes for local variables. Maximum is 2048 bytes.
Invalid library found in C:\Users\Vern\Documents\Arduino\libraries\sketch_jan27a: no headers files (.h) found in C:\Users\Vern\Documents\Arduino\libraries\sketch_jan27a
Invalid library found in C:\Users\Vern\Documents\Arduino\libraries\sketch_jan27a: no headers files (.h) found in C:\Users\Vern\Documents\Arduino\libraries\sketch_jan27a

Can sombody please tell me what this means and how to correct the problem?

Thanks.
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Most likely you need the AccelStepper library which is not included by default. So you need to install it.
Try Tools->Manage Libraries, search for AccelStepper click on the item and install it.
If you have any problems try the AccelStepper website
http://www.airspayce.com/mikem/arduino/AccelStepper/
They have a google group to ask questions linked on that page.
AR
Scopes: Zhumell Z8, Meade Adventure 80mm, Bushnell 1300x100 Goto Mak.
Mount: ES EXOS Nano EQ Mount, DIY Arduino+Stepper RA drive.
AP: 50mm guidescope, AR0130 based guidecam, Canon T3i, UHC filter.
EPs: ES82 18,11,6.7mm, Zhumell 30,9mm FJ Ortho 9mm, assorted plossls, Meade 2x S-F Barlow, DGM NPB filter.
Binos: Celestron Skymaster 15x70 (Albott tripod/monopod), Nikon Naturalist 7x35.
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#### TSS Photo of the Day

Hi all.

So, continuing with my DIY barn door I've stripped down an old printer I had. Seems i have 2 motors, a load of cogs (gears) and a belt....

....this will take some time to figure out but slowly I'm getting there....
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#### TSS Photo of the Day

Sorry to double post yet is there a calculation on how gears work to either slow down or speed up? I'm guessing it depends on the motors RPM in the first place....
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ARock wrote:
Sat Feb 01, 2020 5:05 am
Most likely you need the AccelStepper library which is not included by default. So you need to install it.
Try Tools->Manage Libraries, search for AccelStepper click on the item and install it.
If you have any problems try the AccelStepper website
http://www.airspayce.com/mikem/arduino/AccelStepper/
They have a google group to ask questions linked on that page.
The AccelStepper library is installed
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I have found the problem. I was burning a file called star_tracker, but kept getting a message bout missing headers in a file called sketch_jan27a. There was an error in that file so I copied and pasted the correct code there and copiled again.

Thanks to everyone for the help.
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#### TSS Photo of the Day

vpres wrote:
Sat Feb 01, 2020 8:34 pm
I have found the problem. I was burning a file called star_tracker, but kept getting a message bout missing headers in a file called sketch_jan27a. There was an error in that file so I copied and pasted the correct code there and copiled again.

Thanks to everyone for the help.
I'm sorry but I have no idea what you mean
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#### TSS Photo of the Day

Hi all.

So, I've just bought a motor speed controller unit and it works perfectly to control the stepper motor i salvaged out of an old HP printer....

Now this is a dumb question and one I believe I know the answer to but I have to ask.....

....whilst running the unit via the 9v battery, every now and again the motor slowed, ever so slightly then sped back up.

I know it's a tiny battery and I know it's not brand new....I wouldn't use a battery like this anyway for powering my trap yet am I better using a 9v plugged in power supply to receive a more constant voltage?
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I would say yes to that. I actually used a plug on the wires to the electronic case so that I could switch from battery to ac/DC converter. That way I can have both.
"To be good is not enough when you dream of being great"

Orion 203mm/f4.9/1000mm, converted TASCO 114mm/f9/1000mm to steam punk, Meade 114mm/f9/1000, Coronado PST, Orion EQ-G, Ioptron Mini-Tower and iEQ30, Canon 70D, ASI120MM,ASI294MC


text:
# Customize page numbering so all pages are equally formatted in book class

The title says it all. A friend is working on her thesis and we cannot figure out how to ensure that the page numbering is equally formatted on all the pages that display page numbers.

Default positioning has the page numbers altering left and right on even and odd pages, and at the bottom of the first page of every chapter.

Ideally she wants the the page numbers on every page printed on the top right corner of her book with no special formatting added for the first page of a chapter.

Any experience with this kind of customization?

Edit:

An MWE was requested and is therefore supplied.

\documentclass{book}
\begin{document}
\chapter{foo}
Special chapter title page. Page number positioned at bottom of page

\pagebreak
Normal body text. Page number positioned at top left corner of page.
\end{document}

-
Perhaps all you need to do is turn off two-sided mode? If you have "twoside" set as a document option (on the \documentclass line), just take it out. If it's not that simple please post a MWE. –  Thruston May 10 '13 at 14:13
Are you stuck with the book class? If not try changing to \documentclass{report} and then put \pagestyle{headings} right after the \begin{document}. –  Thruston May 10 '13 at 15:39

To get all pages formatted with a page number in the center of the footer is quite simple with fancyhdr.

# MWE 1

\documentclass{book}
\usepackage{fancyhdr}
\pagestyle{fancy}
\cfoot{\thepage}
\begin{document}
\chapter{foo}
Special chapter title page. Page number positioned at bottom of page.

\pagebreak
Normal body text. Page number positioned at bottom of page again.
\end{document}

If you want all pages to have the number in the upper right, it's a tiny bit more complicated but still quite doable, see Section 7 of the fancyhdr manual.

# MWE 2

\documentclass{book}
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyfoot[C]{}

\fancypagestyle{plain}{%
\fancyhf{}


text:
# Thread: Trig Identity

1. ## Trig Identity

So Im trying to prove the following inequality 8cos3θ6cosθ=1.
Ive tried a lot of different things, using substitutions for cos3θ, 2cosθ, pretty much everything and I cant seem to prove it.
Any help would be appreciated.
Thanks

2. ## Re: Trig Identity

That is neither an inequality nor an identity. WolframAlpha

Now, if you want to know for what values of $\theta$ you have $8\cos(3\theta) - 6\cos \theta = 1$, that is solvable, but not easy. You wind up with a cubic polynomial, which is solvable, but extremely difficult. Solution


text:
Topic: Conferences

Otto Muskens 30 September 2012

“Predator” conferences and open-access publishers

Tags: , , ,
Posted in Conferences, Getting published, Miscellaneous

This week I received the following email stating “The purpose of this letter is to formally invite you, on behalf of the Organizing Committee, to be the speaker at the upcoming “2nd International Conference on Nanotek and Expo” (Nanotek-2012).” This sounds very much like a desirable invited talk in my area of expertise, nanotechnology. The website of the organizer, OMICS looks good and the organization seems associated with a list of proper scientists as keynote speakers and members.

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Ruud Wijdeven 14 September 2012

Biomeeter: find your way in the world of conferences

Posted in Conferences, Research and education

Presenting your data at conferences is key for doing good science. However, finding the right conference can be as challenging as the actual experiments. Especially when you work interdisciplinary there is a lack of overview of what is organized and where. We scientists mostly rely on the occasional mail from our supervisor for our meeting ideas. Or on the few meeting posters that litter the hallway, who looks at them anyway.

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Frerik van Beijnum 26 July 2012

Effectiveness of large scale conferences

Tags: , ,
Posted in Conferences, Speaking in public

Last May I visited the first large scale international conference (CLEO) during my PhD. I was shocked about the enormous contrast with smaller scale (more specialized) conferences. In this post, I will discuss some of the advantages and disadvantages that struck me during this conference.

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# How do you find the two arcs to make a path between two points and two tangents?

Say I have two points $$A$$ and $$B$$ in an $$(x,y)$$ plane and tangents of the points which are normalised vectors $$\mathrm{dir} A$$ $$\mathrm{dir} B$$, how do you find a path made of two arcs that join them together?

Here is a visual of what I mean. Since the images are not clear, the grey vectors from the two tangents are equal in magnitude but the magnitude is unknown.

Note: I am looking for perfect arcs not cubic bezier curves.

• assuming the directions are normalized, in order to find the segments that act as guides you need to solve $|(A+a \times dirA)-(B-b \times dirB)|=a+b$, where a is the length of the segment that starts from A and b is the length of the segments that ends in B (there could be two solutions, but if the initial directions are oriented along the path like you show in the picture you should exclude the negative solution) Apr 13 '20 at 8:01

Geogebra drawing

Say that you have a line $$a$$ defined by two points, $$A$$ and $$A'$$, and a line $$b$$ defined by points $$B$$ and $$B'$$. In my Geogebra drawing you can adjust directions of lines $$a,b$$ by moving points $$A'$$ and $$B'$$. You want to create a smooth curve APB made of two circular arcs, $$AP$$ and $$PB$$, so that arc $$AP$$ is tangent to line $$a$$ at point $$A$$ and arc $$PB$$ is tangent to line $$b$$ at point $$B$$.

First of all, if nothing else is given, there are infinitely many solutions. I will show that exactly one solution can be obtianed by fixing point $$D$$ on line $$a$$ so that line $$DPE$$ is tangent to both arcs at point $$P$$.

Introduce $$F=a\cap b$$. I will discuss only one case

• when point $$F$$ exists ($$a \not\parallel b$$)
• point $$D$$ is between $$F$$ and $$A$$
• point $$E$$ is between $$F$$ and $$B$$

Other cases can be discussed in a similar way.

The followin lengths and angle are known:

$$p=FA, q=FB, x=FD, \alpha=\angle AFB$$

The only problem is to calculate $$y=FE$$. Note that:

$$DE=DP+EP=DA+EB=(FA-FD)+(FB-FE)=p-x+q-y$$

On the other side:

$$DE^2=FD^2+FE^2-2FD\cdot FE \cos\angle AFB\tag{1}$$

or:

$$(p-x+q-y)^2=x^2+y^2-2xy\cos\alpha$$

$$p^2+q^2-2px+2pq-2py-2xq+2xy-2qy=-2xy\cos\alpha$$

$$p^2+q^2-2px+2pq-2xq=2py-2xy+2qy-2xy\cos\alpha$$

$$(p+q)^2-2x(p+q)=2y(p+q-x(1+\cos\alpha))$$

$$FE=y=\frac{p+q}{2}\ \frac{p+q-2x}{p+q-x(1+\cos\alpha)}$$

Now that you have point $$E$$, finding point P is easy (because $$DP=DA,EP=EB$$).

Center of arc AP can be found by intersecting line perpendicular to $$DP$$ at $$P$$ and bisector of angle $$PDA$$. In a similar way you can find the center of arc $$BP$$ (construction not shown).

You can play with my Geogebra drawing by moving lines $$a$$ and $$b$$ and adjusting position of point $$D$$. Basically, you can play with blue dots.

Other cases, for example, when $$A$$ is between $$F$$ and $$D$$ are also interesting. I'll leave detailed analysis up to you:

EDIT:

In the meantime WDUK added another condition:

$$AD=DP=PE=BE=z$$

In this case, by applying cosine theorem (1) to triangle $$FDE$$ we get the following equation:

$$(p-z)^2+(q-z)^2-2(p-z)(q-z)\cos\alpha=(2z)^2$$

The solutions are:

$$z_1=\frac{-p-q+(p+q)\cos\alpha+\sqrt{3p^2+2pq+3q^2-8pq\cos\alpha+(p-q)^2\cos^2\alpha}}{2(1+\cos\alpha)}$$

$$z_2=-\frac{p+q-(p+q)\cos\alpha+\sqrt{3p^2+2pq+3q^2-8pq\cos\alpha+(p-q)^2\cos^2\alpha}}{2(1+\cos\alpha)}$$

...and therefore we have two possible solutions, $$APB$$ and $$AQB$$:

Geogebra

EDIT 2:

Another example:

$$FA=p,\ FB=q,\ AD=DP=PE=BE=z$$

In this case, by applying cosine theorem (1) to triangle $$FDE$$ we get the following equation:

$$(p+z)^2+(q-z)^2-2(p+z)(q-z)\cos\alpha=(2z)^2$$

The positive solution of this quadratic equation is:

$$z=\frac{-p+q+(-p+q)\cos\alpha-\sqrt{3p^2-2pq+3q^2-8pq\cos\alpha+(p+q)^2\cos^2\alpha}}{2(-1+\cos\alpha)}$$

This defines positions of points $$D$$ and $$E$$. The rest of the construction is trivial.

• You mention the following lengths are known x = FD but you never showed how to calculate the position of D. Since from what i gather you find D from knowing where P is tangent to the two arcs, but we don't know the two arcs yet either. I should mention (don't know if this simplifies the math) but from my original image, AD and BE are to be assumed equal in magnitude which gives a constraint to guarantee only one solution.
– WDUK
Apr 16 '20 at 19:42
• @WDUK You are changing the description of the problem a LOT! You should have mentioned that DP should be equal to PE. I had to limit the number of solutions somehow and I did that by choosing point D arbitrarily. You are talking about a completely different problem now. Apr 16 '20 at 19:57
• I thought the images made it clear the grey vectors from the tangents were equal in magnitude. Which was why they were drawn in. Maybe i should've made it more clear in the images.
– WDUK
Apr 16 '20 at 20:11
• @WDUK It just looks so. If it's not mentioned, it cannot be guessed. I'll try to provide a new answer. Apr 16 '20 at 20:12
• I've noticed, all your tangents are counter pointing to each other. So they don't form one continuous path from A to B (or B to A). Instead they point in a direction that would lead to a meeting point at the middle of the two arcs (P or Q). For example your tangents match the top right example in my question but your solution does not follow the directions, its only finding arcs that match tangents. You can't reach B via AQB since the tangent points the wrong way (you would be going the wrong way around blue arc). You can't reach B from P since A's direction is the other way. Make sense?
– WDUK
Apr 16 '20 at 21:35


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# IIT JEE divisible determinants

Video transcript
So in problem 44, once again we have the exact same setup that we had in problems 42 and 43. But now they're asking us the number of A in T sub p such that the determinant of A is not divisible by p. Well, we've already done some work in problem 43 in figuring out some set of the members that are divisible by p. So why don't we just figure out the total number of members of T sub p, and then subtract the total members whose determinants are divisible by p, and then we'll get this answer right over here. So what's the total members in T sub p? Well, for a, I have p possible choices, right? If I'm picking between-- up to p minus 1, but I'm including 0, there's actually p possible choices. So I have p possible choices for a, p possible choices for b by the same logic, and p possible choices for c. So I have p to the third possibilities. So there are a total of p to the third members in T sub p. Now, what did the last problem tell us? This was number 43. It told us the members-- maybe I should write it this way. The number of members, numbers of A's, such that the trace of A-- this was the language I used in the last video or the last problem-- such that the trace of A not divisible by p, but the determinant of A is. And we got the answer as p minus 1 squared. Now, if you remember that problem, and even just to do that problem, when we thought about this statement, such that the trace of A is not divisible by p, we figured out that this was exactly equal to saying that A does not equal 0. So one way to view the result of problem 43 is if you assume that A is not equal to 0, there are p minus 1 squared members of T sub p where the determinant is divisible by p. So we're starting to count some of the A's whose determinant is divisible by p. But these are the only-- the matrix A's whose a entry is not equal to 0. So if we want to count all of them, we have to also count the ones where a does equal 0, so where a does equal 0. So let's think about that case. We can figure out how many matrices there are where a does equal 0, and the determinant of A is divisible by p. Add it to that. Then we have the total number of A's whose determinants are divisible by p. And we could subtract that from the total number of possibilities, and hopefully, we'll get one of the answers up here. So let's think a little bit about what will the determinant look like over here? So in this situation, the determinant of our matrix will be-- it's a squared. It's a times a minus b times c, a squared minus bc. Now, we're assuming that a is equal to 0. If a is equal to 0, it's equal to negative bc. And we need to think about how is this going to be a multiple, or how is this going to be divisible by p? So this has got to be equal to some multiple of p. So the first thing, just think about b's and the c's. They are both non-negative. So this value right here cannot be negative. So if you put a negative sign there, it cannot be positive. So it can't be any positive multiples of p. It could be 0. So we could have negative bc. We could have negative bc is equal to 0, which is equivalent to saying that bc is equal to 0. That's one possibility, where it equals 0 times p. That's still a multiple. Or maybe it could be negative. Maybe we could have negative bc is equal to negative 1 times p. But when you think about it here, if this was true, that would mean that bc is equal to p, so b or c would be factors of p. Now, we know that p is a prime number. Its factors are only 1 and p. b and c-- I mean, one of these guys could be 1, but then the other guy would have to be p. They can't be p. They only get as high as p minus 1. This is not an option. So the only possibility, if a is equal to 0, for the determinant of capital A to still be divisible by p, is for bc to be equal to 0. So let's think about how many possibilities there are over here. So let's think about all of the combinations. So there's the one situation, where b and c are equal to 0. b and c is equal to 0. Now let's think about the other ones. There's one where b is equal to 0 and c isn't. bc will still equal 0 in this situation. So how many possibilities are there? How many possibilities are there for this? Well, b is equal to 0. C over here can be any value, although we've already considered the case where c is equal to 0. So it could be any value so that we don't double count, any value where c does not equal 0. So it could be 1 through p minus 1. Or another way to think about it, there's p minus 1 possibilities. Now let's think about c is equal to 0 and b isn't. Well, exact same logic. Once again, we don't want to double count that they're both being equal to 0. So let me write it. And c isn't-- well, we're saying it isn't 0, so we are actually already putting that constraint there. So it has p minus 1 possibilities. So how many total possibilities do we have where the determinant of A is equal to 0 and a is equal to 0? So we have one here. We have one possibility here, then p minus 1 and p minus 1. So our total possibilities are p minus 1 plus p minus 1 plus 1, which is 2p minus 2 plus 1, which is 2p minus 1. 2p minus 1 incremental possibilities when a is equal to 0 for the determinant of A to be divisible by p. So that's what we just got in this video. In the last video, we had p minus 1 squared possibility when a does not equal 0. So if we want the total number of A's, where the determinant of A is divisible by 0, we can add the number that we got in the last video to the number we just got. So let's do that. So if I were to rewrite this over here, this is equal to p squared minus 2p plus 1. And then I want to add this 2p minus 1 here, so plus 2p minus 1. And what do I get? These cancel out. These cancel with that. And these guys cancel out. So there's a total of p squared possible A's where the determinant of A is divisible by p. Now, we're very close, but this isn't what they're asking. They want the total members where the determinant of A is not divisible by p. So all we have to do here is take our total membership, which is p to the third, and subtract from that the members whose determinants are divisible by p. And we just figured that out. We subtract p squared. And now we'll get the number of A's where determinant of A not divisible by p. Now let's see if that's one of the choices, and it is. D, p cubed minus p squared.


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[–] 0 points1 point  (1 child)

Let's say the data looked like:

in first 10,000,000 digits of pi...
0: ********** 999440
1: ********** 999333
2: **********1000306
3: ******************** 1999965
4: ********** 1001093
5: ********** 1000466
6: 3
7: ********** 1000206
8: ********** 999814
9: ********** 1000040

...would anyone claim that pi was normal?

[–] 1 point2 points  (0 children)

Absolutely!! Switch it around on you: I'm thinking of a number whose decimal expansion is 0.000000.... at least as far as the 10-gazillionth digit. Do you believe it is an integer? Similarly I am thinking of a sequence 1,1/2,1/4,... and so on up to the billionth term. Does it converge?

Absent some formal proof one way or the other the first N digits tell you NOTHING about the long term behavior. So you have to take empirical data with a big bowl of salt when talking about infinities. The instances that obey the behavior established at the front of the sequence are (without further restriction) a measure zero subset of all the possible ways to complete the sequence. Since in this case the measure zero set is the non-normals, you expect all numbers to be normal.

[EDIT] One could define some notion of "\epsilon-super-normal" where not only is the number normal, but all finite digit approximations pass a statistical test of normality up to some variance \epsilon. [/EDIT]

[EDIT2] For some interesting examples of false conclusions from the first few members of a sequence. Now in this case few means <50, but the best part of mathematics is we know that somewhere out there are deceptive pattern with millions or billions of deceptive terms. www.tmrfindia.org/sutra/v2i12.pdf[/EDIT]


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