In a delightful short video, Klara Sjöberg demonstrates the extreme and alarming freakout that you can trigger in a mechanical calculator by trying to divide a number by zero; in a followup, Lynn Grant tweets "That is why the old Friden calculators had a 'Divide Stop' key."
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Clever and wonderfully-presented: The Incredible Palindromic Hat-Trick. You may be unimpressed if you feed it small numbers. Feed it big ones! Read the rest

Rather than attempt to describe this, I'll just quote the artist verbatim:

This is the first million integers, represented as binary vectors indicating their prime factors, and laid out using the UMAP dimensionality reduction algorithm by Leland Mcinnes. Each integer is represented in a high-dimensional space, and gets squished down to 2D so that numbers with similar prime factorisations are closer together than those with dissimilar factorisations.

A very pretty structure emerges; this might be spurious in that it captures more about the layout algorithm than any “true” structure of numbers. However, the visual effect is very appealling and requires no tricky manipulation to create.

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"Are wormholes real or are they just magic disguised as physics and maths?" *(Kurzgesagt – In a Nutshell)*

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The Fields medal, mathematic's most prized award for mathematics, was stolen from Cambridge Professor Caucher Birkar just moments after he received it.

Via the Independent:

Caucher Birkar, a Kurdish refugee from Iran, was one of four winners of the Fields Medal, often dubbed the "Nobel Prize of Mathematics", at the International Congress of Mathematics on Wednesday.

The professor put the 14-carat gold medal, worth around £3,000, in a briefcase on a table, but moments later realised it had disappeared, event organisers said.

The briefcase, which also contained his wallet and phone, was later found by security officials in a nearby pavilion, though the medal and wallet had been removed. Police reviewed security tapes and identified two potential suspects.

"The International Congress of Mathematicians is profoundly sorry about the disappearance of the briefcase belonging to mathematician Caucher Birkar, which contained his Fields Medal from the ceremony this morning," organisers said in a note.

Image via Wikipedia, Stefan Zachow of the International Mathematical Union; retouched by King of Hearts Read the rest

MIT's How to Win at Texas Hold 'Em is a CC-licensed open course taught by Will Ma in 2016 and now free to watch online; the game is the perfect combination of psych and stats, and learning to play is a great way to improve your basic reasoning skills. (*via Kottke*)
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The concept of "nothing" is easy to grasp for most humans, but the concept of zero as a number is much harder. Recent research shows that bees can be taught that zero is a number which is less than one. This nifty explainer gives an overview. Read the rest

Evil Mad Scientist Labs sell a bunch of cool open source hardware kits for making plotters -- basically, a very precise robot arm that draws with whatever pen or marker you screw into its grip. There's the Eggbot (for drawing on curved surfaces like eggs, balloons and balls), but there's also the Axidraw, which works on flat surfaces.
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Math 4 Love founder Dan Finkel writes:

You’ve been chosen as a champion to represent your wizarding house in a deadly duel against two rival magic schools. Your opponents are a powerful sorcerer who wields a wand that can turn people into fish, and a powerful enchantress who wields a wand that turns people into statues. Can you choose a wand and devise a strategy that ensures you will win the duel?

*(TEDEd)* Read the rest

The animation team from Big Hero 6 did some cool experiments for the "Into the Portal" sequence, and this week they shared one: an exploding 3D pastel fractal. Read the rest

In a paper published by the International Association for Cryptologic Research, a group of Harvard and MIT cryptographers demonstrate that even if the government were to backdoor encryption and lock up anyone who used non-backdoored systems, people could still hide undetectable, secure, private messages within the messages sent over the compromised systems.
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Multiplying large numbers before calculators led to a number of ingenious inventions to make things easier, like these Genaille-Lucas rulers demonstrated by the fine folks at DONG.

Via manufacturer Creative Crafthouse:

In the days before calculators, methods of simplifying calculations were of much interest. In 1617 Napier also published a book describing a method to multiply, divide and extract square roots using a set of bars or rods. These became known as Napier's Bones. (avail on our website)

In the late 1800s, Henri Genaille, a French civil engineer, invented an improvement to Napier's Bones that eliminates the need to handle carries from one digit position to the next. The problem was posed by Edouard Lucas and thus the alternate name of Genaille-Lucas Rulers (or Rods).

There are also sets for division. You can get your own set online or print your own from these free files.

• Genaille-Lucas Rulers (YouTube / DONG) Read the rest

YouTuber Dani Ochoa says she's a "girl with too much time on her hands," but I disagree. I think figuring out the math formula to play the *Star Wars* "Cantina Band" song with just a paper and pencil is *exactly* what she should be doing with her time.

Listen to this and compare:

(*reddit*) Read the rest

Mathematician Hannah Fry explains the "Ham Sandwich Theorem," a mathematical concept that says that even the most poorly constructed sandwich can be cut exactly in half with only one straight cut of a knife. Read the rest

Mathematician Henry Sagerman and colleagues developed a cool way to observe non-euclidian geometry from a new vantage point: inside the geometry itself via virtual reality. Read the rest

Numberpile looks at an interesting phenomenon using a common Japanese toy: a small paper balloon that can be crushed and re-inflated. What's the science behind it? Read the rest

The white circles in this gif travel in a straight line across the diameter of the black circle. In the process, they accelerate toward the center and decelerate away with the velocity of a swinging pendulum. Read the rest