If you have two cubes of equal size, it's possible to cut a hole in one cube that's large enough for the other cube to pass through it.
In geometry, Prince Rupert's cube (named after Prince Rupert of the Rhine) is the largest cube that can pass through a hole cut through a unit cube, i.e. through a cube whose sides have length 1, without splitting the cube into two pieces. Its side length is approximately 6% larger than that of the unit cube through which it passes. The problem of finding the largest square that lies entirely within a unit cube is closely related, and has the same solution.
The original proposition posed by Prince Rupert of the Rhine was that a cube could be passed through a hole made in another cube of the same size without splitting the cube into two pieces.
High school teacher Joe Howard made another excellent math video. This time, he shows how Eratosthenes calculated the circumference of the Earth in 200 BC.
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In one of the dopest displays of critical thinking in history, Erotosthenes estimated the circumference of the Earth. All he had was a pole, the sun, knowledge of a famous well in Egypt, and potentially money to pay someone to walk the distance between two cities. This story demonstrates the beauty of trigonometry.
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It’s a book of step by step drawing instructions. All you need is a ruler, compass, pencil and pen. While the geometry behind theses patterns is enormously sophisticated, actually drawing out the shapes is surprisingly easy and relaxing. It’s also a fun and painless lesson in geometry, especially for those of us not inclined towards math..
From 1966, René Jodoin's beautiful minimalist animation of a geometric ballet, "Notes on a Triangle." Jodoin, who died earlier this year, was founder of the National Film Board of Canada's animation studio. "Note on a Triangle" was only one of several films meant as an introduction to geometric forms. See more here.
Tentacles made of cubes reach for you from within the watery abyss. "You're not supposed to be here," an unseen being informs you as you descend into the first level of the game Euclidean. Deep sea creatures made of shapes swarm, pulse and strain around you—and soon, they notice you. "Everything here will kill you," the voice intones a few moments later. Read the rest
Let the People Draw the Lines Act, a bill introduced by Alan Lowenthal (D-CA), would appoint panels of independent experts to adjust electoral district boundaries in an attempt to remove the "safe seats" created through gerrymandering, by which electoral districts are torturously redrawn to include as many voters likely to keep the incumbent in and to exclude everyone else. As Wonkblog explains, the bill is a long-shot, but it's also a shining example of the kind of legislation that fights corruption and creates a climate of real representative democracy. The fact that this bill is wildly unlikely to pass doesn't make it laughable: it makes Congress irredeemable. Read the rest
Vi Hart, the Internet's favorite manic vlogging mathematician, has released a new video in which she teams up with math artists Andrea Hawksley and Gwen Fisher, and Gwen's sister Ruth of Sweets by Ruth. The four of them bake satisfyingly precise and geometric gingerbread polygons, then build up a variety of astounding three dimensional forms by piecing them together with icing. The video is both hunger-inspiring and brain-inspiring, and is likely to be the best thing you watch this week.