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Roots of Unity

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

An illustration from Oliver Byrne's 1847 edition of Euclid's Elements. Image: Public domain, via Wikimedia Commons.

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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Roots of Unity

Felix Klein on Mathematical Progress

I just finished reading a set of lectures the great mathematician Felix Klein delivered at the 1893 World’s Columbian Exposition in Chicago. The lectures are now in the public domain, and you can download them for free here. (Unfortunately, not all the mathematical notation survived digitization, so a good amount of creative interpretation—also known as [...]

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