"The efficiency gap": understanding the math behind a crucial Supreme Court gerrymandering case

Last October, the Supreme Court heard argument in Gill v. Whitford, a Wisconsin gerrymandering case that has far-reaching implications for the November midterms in 2018; the court is expected to rule next June. Read the rest

Max Brückner’s polyhedral models

The German geometer Max Brückner was fascinated by polyhedra, and he wrote about them in depth in his 1900 work Polygons and Polyhedra: Theory and History.

Over at the Internet Archive, they've scanned the book, and if you flip to the end -- beginning at page 243 -- there's a real visual treat: Several pages of Brückner's line drawings of polyhedra, followed by photos of his collection of 3D polyhedral objects.

The Public Domain Review recently unearthed these, and now I want some of these pages blown up to poster-size for my walls! (You can seem more of these screenshots over at the Public Domain Review's post.) Read the rest

Watch a mathematician explore non-euclidian geometry with a VR headset

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

José Bernabé's organic geometry

Graphic designer José Bernabé explores a lot of wonderful concepts as part of his work, including this standalone project titled Organic Geometry. Note: if you click this link to see more, there's a supremely annoying autoplaying song embedded. Read the rest

Video of cube passing through hole in equally sized cube

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.

From Wikipedia:

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.

Image: Wikipedia/Acf6 Read the rest

iRuler is a website that turns your screen into an inaccurate ruler

iRuler.net detects the dimensions and resolution of your display and then displays a rule upon it. In the photo above, I've placed a real ruler on the screen (above) to verify the accuracy of the iRuler (below). Good enough for me! Read the rest

Watch mesmerizing forms complement the music of Symmetry

Symmetry is a single by Max Cooper and Tom Hodge from Max's EP Emergence. Designer Kevin McGloughlin created a stunning video of teal and copper concentric circles morphing and meshing in surprising and hypnotic ways. Read the rest

How Eratosthenes calculated the circumference of the Earth in 200 BC

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.

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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The baffling topology of the burrito method for covering your duvet

Inhabitat's video explaining the "burrito" method for getting a duvet into its cover is both excruciatingly slow in places, and also fantastically baffling: how the actual fuck does this topological exercise work? (via Kottke) Read the rest

Fix your floppy pizza slice with Gaussian curvature

It turns out that folding a pizza slice lengthwise to improve its rigidity is a great example of the "Remarkable Theorem" by Gauss. Cliff Stoll explains. Read the rest

Site finds the "visual center" of your images

Visual Center is a website that takes an image and attempts to find its compositional center point. It works well with designy images that have an obvious geometry to them and well-defined shapes to find and center — think logotype surrounded by whitespace. I'm not having a lot of success with photographs, though. [via] Read the rest

What's the best way to distribute numbers on the faces of a D120?

Exotic polyhedron purveyor Dice Lab's crowning randomizer is its monstrous, $12 120-sided die. Read the rest

How to draw Islamic geometric patterns

Over at the Root Simple website, Mr. Homegrown wrote about the fun he's been having learning how to draw Islamic geometric patterns from this book by Eric Broug.

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..

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Watch this elegant dance of triangles by animator René Jodoin (1966)

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.

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The geometric horror game Euclidean is Lovecraft levels of scary

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

The geometry of fireworks

“Enjoy the parabolic envelopes that form while those bright, sparkling, parabolic curves are etched into the sky tonight.”

3D printed dress made from 2,279 triangles and 3,316 hinges

Designer Jessica Rosenkrantz writes, "I made this 3D printed dress and the MoMA just acquired it. This video, filmed at Shapeways factory showing the printing and depowdering of the dress (there's also this one, documenting the dress's sounds and movements). Read the rest

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