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Posts Tagged "mathematics and the arts"

Roots of Unity

Some Infinities Are Bigger than Other Infinities, and Some Are Just the Same Size

How to count potatoes by pairing them with numbers. Image: Yen Duong.

Warning: contains minor spoilers for The Fault in Our Stars. I recently read The Fault in Our Stars by John Green, now a major motion picture that has led to theft in Amsterdam and a shortage of dry eyes in movie theaters around the world. One of the ideas that resonates with Hazel, the 16-year-old narrator [...]

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Roots of Unity

Nothing Is More Fun than a Hypercube of Monkeys

More Fun than a Hypercube of Monkeys, a sculpture by Henry Segerman and Will Segerman. The monkeys do not all look like they are the same size, but that is due to the stereographic projection technique used to visualize a 4-dimensional object in 3-d. (Similarly, if one part of a 3-d object is closer to a surface than another part, it will appear larger when projected to that surface.) Image: Henry Segerman and Will Segerman.

Monkeys! Mathematical groups! 4-dimensional geometry! Together at last! This sculpture, called More Fun than a Hypercube of Monkeys, answers an open question: has the quaternion group ever appeared as the symmetry group of an object? Thanks to mathematician Henry Segerman and mathemusician Vi Hart, the answer is now yes. Their very readable paper about the sculpture [...]

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Roots of Unity

Measure Yourself by the Standard of the Capybara

Are you more or less of a fish than this capybara? Image: VigilancePrime, via Wikimedia Commons.

We all know a lot of measurements about ourselves. You are some number of feet or meters tall. You weigh some number of pounds, kilograms, or stone. Your BMI is some number of kilograms per square meter, even though humans are not two-dimensional. You have some number of milligrams of cholesterol in each deciliter of [...]

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Roots of Unity

Knotted Needles Make Knitted Knots

A knitted (5,15) torus link. Image: sarah-marie belcastro.

Step aside, infinity scarves, you aren’t infinite at all. The (5,3) torus knot cowl is where it’s at. For me, one of the highlights of January’s Joint Mathematics Meetings was the mathematical fiber arts session. You can view a slide show I put together from the session here. During the session, co-organizer sarah-marie belcastro gave a [...]

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Roots of Unity

Has Anyone Ever Flipped Heads 76 Times in a Row?

What are the odds? Image: Evelyn Lamb

Tom Stoppard’s absurdist play Rosencrantz and Guildenstern Are Dead begins with one of them, Guildenstern (or is it Rosencrantz?), flipping coins. “Heads,” Rosencrantz says, and takes the coin. Guildenstern flips again. “Heads,” Rosencrantz says, and takes the coin. Another flip. “Heads.” Again, “Heads.” Soon we find out that Guildenstern has flipped 76 coins, and all [...]

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Roots of Unity

These Hypocycloids Will Make You Happy

A 2-cusped hypocycloid rolling inside a 3-cusped hypocycloid rolling inside a 4-cusped hypocycloid... Image: Greg Egan. Used with permission.

Unless you’re holding a baby or a scalpel, drop everything and read this blog post about hypocycloids by John Baez. (And if you’re holding a scalpel, please put away whatever device you’re reading this on and pay attention to your surgery!) In addition to a lovely exposition by Baez, the post features some gorgeous animations [...]

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Roots of Unity

Counterexamples in Origami

Ain't she a beaut? Image: Evelyn Lamb.

Surfaces are complicated. Triangles are simple. That’s an idea behind some methods of creating computer graphics and some advanced mathematics. If we have a surface, we can take a bunch of points on the surface and connect them into triangles to obtain an approximation of the surface. That’s all well and good, but how reliable [...]

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Roots of Unity

A Cuddly, Crocheted Klein Quartic Curve

A cuddly Klein quartic. Image copyright Daina Taimina. Used with permission.

Last week, mathematician and artist Daina Taimina shared her latest creation on Twitter. It’s a model of a surface called the Klein quartic. Isn’t it cute? So what is it? The Klein quartic surface is a 2-dimensional object with 3 holes that has a lot of symmetries. In fact, it has as many symmetries as [...]

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Roots of Unity

Zombie Fever: A Mathematician Studies a Pop Culture Epidemic

Helpful information for surviving the zombie apocalypse. Image: Todd Hryck, via flickr.

Zombies. They’re everywhere. My dentist and his assistant spent my last visit and chatting about The Walking Dead while drilling into my head, and it seems like every reasonably large town hosts a zombie run. Science education is getting in on the trend, too. Colleges have classes about zombies, AMC (the network that broadcasts The [...]

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Roots of Unity

Carnival of Mathematics #103

Image: David Simmonds, via flickr.

Welcome to the 103rd Carnival of Mathematics! The number 103 is prime, and it’s the “older” twin of a pair of twin primes as well—or is it the “younger” twin because it comes later? Regardless, 101 and 103 are twin primes. According to Tanya Khovanova’s site Number Gossip, 103 is not only prime and happy [...]

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