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 ...

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. If you're enjoying ...

THIS is a philosophical thesis by a writer who is really familiar with the subject of non-Euclidean geometry, and as such it is well worth reading. The first three chapters are historical; the ...

Things which are equal to the same thing are also equal to one another. If equals be added to equals, the wholes are equal. If equals be subtracted from equals, the remainders are equal.

Many ancient societies knew important mathematical facts, but only one discovered mathematics—which is not a collection of accurate rules of thumb, but a body of knowledge organized deductively, by ...

In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is rejected. The parallel postulate in Euclidean geometry states, for two ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don’t apply: angles of a triangle add up to less than 180 degrees and Euclid’s parallel postulate, ...