Link Archive

How many ways are there of writing some natural number $n$ as the sum of two squares?

$𝑛=𝑝^2+𝑞^2$

I don’t want an answer for some particular $n$ . I don’t even want a general formula. I just want to know… on average.

To commemorate Pi Day on March 14th, we have put together this Virtual Special Issue of articles on the topic of Pi, from the Mathematical Association of America’s four publications.

People have been figuring ways to compute π for ages, and most of them were very very tedious and time-consuming. Archimedes figured it out to 3 decimal places. 750 years later, we managed to get 4 digits. Another 900 years passed, and we got to 16. In the late 1800s, hapless William Shanks busted his buns for 15 years to compute π to 707 places using John Machin's formula (seen in the app, above). In a stroke of bad luck, however, he blew it 527 digits in, so the remainder of the estimate is incorrect. [Nooooooo...!] Fortunately, no one was willing to spend the time to double-check his work, and he died in the blissful happiness of a job well-done.

Installation of mkcert on CentOS and Fedora is similar to Ubuntu/Debian installation. You only need to install nss-tools tools first.

The web is moving to HTTPS, preventing network attackers from observing or injecting page contents. But HTTPS needs TLS certificates, and while deployment is increasingly a solved issue thanks to the ACME protocol and Let's Encrypt, development still mostly ends up happening over HTTP because no one can get an universally valid certificate for localhost.

The world's first linear algebra book with fully interactive figures.

These pages are a collection of facts (identities, approximations, inequalities, relations, ...) about matrices and matters relating to them.It is collected in this form for the convenience of anyone who wants a quick desktop reference.

As for her mom's signature dumpling recipe, for which the animated short is named? Shi says that her family likes to keep it old-school. "She won't use a food processor or a meat grinder for the pork filling," Shi says. "She'll use an old-school cleaver and just chop everything, throw in chives and garlic, mince everything together, and chop for ten minutes."

Having a file structure full of various file types you want to sync only files of one type into a new location.

rsync -rv --include '*/' --include '*.js' --exclude '*' --prune-empty-dirs Source/ Target/

This will generate the same structure found in Source into Target but only including the JavaScript(.js) files.

${var%Pattern}

Remove from \$var the shortest part of \$Pattern that matches the back end of \$var.

This page explains the design and implementation of operations on big (modular) integers, used for RSA and generic elliptic curve computations.

This article walks through the components of a modern LZ compressor. It's amazing how rich and deep the compression field is. If you enjoy algorithms and data structures, there are not too many better places to play. I hope you enjoy reading it as much as I enjoyed writing it!

By the end, we will have a compressor that can beat gzip while decompressing at almost the same speed — in less than 1000 lines. You can find the source for the article at https://github.com/glinscott/linzip2.

The Apollo Guidance Computer (AGC) provided guidance, navigation and control onboard the Apollo flights to the Moon. This historic computer was one of the first to use integrated circuits, containing just two types of ICs: a 3-input NOR gate for the logic circuitry and a sense amplifier IC for the memory. It also used numerous analog circuits built from discrete components using unusual cordwood construction.

magine that you have attached a pencil to a pendulum so that it brushes across a piece of paper as the pendulum swings back and forth. When the pendulum finishes swinging you will end up with a single straight line drawn on your paper – very dull indeed! Now imagine further that you somehow manage to connect a second pendulum to your pencil which oscillates at right angles to the first. The resulting drawing might look something like the image below. If your imagination fails you (or if my explanation isn’t up to the job) then you can see a video of the set up I am trying to describe by clicking here.

Strange Attractors are plots of relatively simple formulas. They are created by repeating (or iterating) a formula over and over again and using the results at each iteration to plot a point. The result of each iteration is fed back into the equation. After millions of points have been plotted fractal structures appear. The repeated points fall within a basin of attraction (they are attracted to the points that make up these shapes).

 

But the fix is easy and there’s no addons required.

1. Navigate to about:config (in Firefox’s URL bar)
2. Change the value of the following two properties to 0:
   • mousewheel.with_control.action
   • mousewheel.with_meta.action

 

In firefox 63 the autoplay preferences are reorganised in preparation for this feature shipping out of the box in one of the upcoming versions. in about:config you can set media.autoplay.default to 1 in order to block automatic playback on all pages or set it to 2 to decide on a per domain basis.

Observers of yesterday’s lunar eclipse were blessed with the first known sighting of a meteorite impact during such an event.

Every molecule of water on the Earth and inside you or any other living thing has existed for billions of years. After it came to Earth, that water has been cycling through rocks, air, animals, plants, and back again. Each molecule has been on an incredible voyage before coming to you. At some point, the water inside you would have been inside dinosaurs, bacteria, the oceans, storm clouds, the polar ice caps, and much more.

The Intel 80386 is the next step in the evolution of the processor series that started with the Intel 8086 (which was itself inspired by the Intel 8080, which was in turn inspired by the Intel 8008). Even at this early stage, it had a long history, which helps to explain many of its strange corners.

As with all the processor retrospective series, I'm going to focus on how Windows NT used the Intel 80386 in user mode because the original audience for all of these discussions was user-mode developers trying to get up to speed debugging their programs. Normally, this means that I omit instructions that you are unlikely to see in compiler-generated code. However, I'll set aside a day to cover some of the legacy instructions that are functional but not used in practice.

Nancy by Olivia Jaimes for January 20, 2019 https://www.gocomics.com/nancy 

10 PRINT is a book about a one-line Commodore 64 BASIC program, published in November 2012. Book purchases support the nonprofit organizations The Electronic Literature Organization (to which all royalties are being donated) and The MIT Press, the book's publisher.