## Origin of Mysterious Portuguese Mathematical and Geographical Tiles Revealed

November 5th, 2014 | 4

A few months ago I wrote about some mystifying mathematical and geographic tiles I encountered at the National Tile Museum in Lisbon, Portugal. Their accompanying label gave no clue to who had made them or why. Several readers subsequently wrote to tell me what they knew about these tiles. Thank you to everyone who did [...]

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## Mysterious Tiles from a Time When Art and Science Were Friends

Forces in society of late have lots of us longing for the days of the Enlightenment, smallpox, powdered wigs, ridiculously uncomfortable clothing and all. It must have been nice to live in an era when science and scientists were respected, admired, and generously funded (though often by self-funded aristocrats or by royal grants gleaned from [...]

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## Glow Sticks Prove the Math Theorem behind the Famous Flatiron Building

December 11th, 2013 | 3

How many math lovers live in New York City? It’s a tough count to make, but the Museum of Mathematics made progress at its first anniversary celebration on Thursday, December 5. With a mission to illuminate the math that permeates our day-to-day lives, the Museum of Mathematics, or MoMath, wasn’t about to waste its birthday [...]

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## In Which Omar Khayyam Is Grumpy with Euclid

October 28th, 2014 | 7

My math history class is currently studying non-Euclidean geometry, which means we’ve studied quite a few “proofs” of Euclid’s fifth postulate, also known as the parallel postulate. I’ve written about this postulate before. There are many statements that are equivalent to the parallel postulate, including the fact that parallel lines in a plane are equidistant. This [...]

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## British Objects of Constant Width

July 4th, 2014 | 3

As I wrap up a trip to the UK, I reflect on the many objects of constant width I encountered here. I’ll let Numberphile tell you a little more about objects of constant width. Almost immediately after getting off the plane at Heathrow, I got some breakfast and some change in the form of metal [...]

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## What’s the Deal with Euclid’s Fourth Postulate?

April 21st, 2014 | 4

In February, I wrote about Euclid’s parallel postulate, the black sheep of the big, happy family of definitions, postulates, and axioms that make up the foundations of Euclidean geometry. I included the text of the five postulates, from Thomas Heath’s translation of Euclid’s Elements: “Let the following be postulated: 1) To draw a straight line [...]

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## The Math Wars, Lewis Carroll Style

March 4th, 2014 | 1

In 1879, Charles Dodgson, better known as Lewis Carroll, published an odd little book called Euclid and his Modern Rivals (available for free at the Internet Archive). Though it takes the form of a play, it is a defense of Euclid’s Elements as the best textbook for geometry. Carroll’s introduction lays out his purpose and why [...]

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## Chasing the Parallel Postulate

February 28th, 2014 | 8

Euclidean geometry, codified around 300 BCE by Euclid of Alexandria in one of the most influential textbooks in history, is based on 23 definitions, 5 postulates, and 5 axioms, or “common notions.” But as I mentioned in my recent post on hyperbolic geometry, one of the postulates, the parallel postulate, is not like the others. [...]

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## Hyperbolic Quotes about Hyperbolic Geometry

February 12th, 2014 | 3

“The treatise itself, therefore, contains only twenty-four pages—the most extraordinary two dozen pages in the whole history of thought!” “How different with Bolyai János and Lobachévski, who claimed at once, unflinchingly, that their discovery marked an epoch in human thought so momentous as to be unsurpassed by anything recorded in the history of philosophy or of [...]

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## Counterexamples in Origami

November 30th, 2013 | 1

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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## A Mathematical Thanksgiving Celebration

Last year, the inimitable Vi Hart made a Thanksgiving video series, describing how to imbue your holiday celebration with more mathematics. My favorite video is the one about Borromean onion rings, perhaps because I’ve been slightly obsessed with Borromean rings for a while. Borromean rings are three circles that are connected so that if you [...]

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## 10 Secret Trig Functions Your Math Teachers Never Taught You

September 12th, 2013 | 19

On Monday, the Onion reported that the “Nation’s math teachers introduce 27 new trig functions.” It’s a funny read. The gamsin, negtan, and cosvnx from the Onion article are fictional, but the piece has a kernel of truth: there are 10 secret trig functions you’ve never heard of, and they have delightful names like “haversine” [...]

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## Strumming the Lute of Pythagoras

May 29th, 2013 | 1

When I was at the Joint Math Meetings in January, the evocative name “Lute of Pythagoras” jumped out at me in a talk by Ann Hanson of Columbia College in Chicago. Hanson teaches a course, Math in Art and Nature, that satisfies the general math requirement for Columbia College but comes with a healthy helping [...]

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