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Roots of Unity

Lambert on Love and Hate in Geometry

Johann Heinrich Lambert. Image: public domain, via Wikimedia Commons.

The history of hyperbolic geometry is filled with hyperbolic quotes, and I came across a beautiful one earlier this semester in my math history class. Johann Heinrich Lambert, a Swiss mathematician who lived from 1728-1777, was trying to prove the parallel postulate and thereby establish beyond a shadow of a doubt the truth of Euclidean [...]

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Roots of Unity

Hyperbolic Quotes about Hyperbolic Geometry

This Hungarian postage stamp does not portray János Bolyai. For more information about finding the "real face of János Bolyai," click the picture to read Tamás Dénes's article on the subject.

“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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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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