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 ...

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 ...

Euclid’s parallel postulate amounts to saying that, given a line and a point, exactly one line can be drawn parallel to that line through the point. (Euclid formulates it differently.) To succeeding ...

Geometry boasts a rich and captivating history within the realm of mathematics. In its early development, it was deeply rooted in practical observation used to describe essential concepts such as ...

Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

If you enjoyed this article, I’d like to ask for your support. Scientific American has served as an advocate for science and industry for 180 years, and right now may be the most critical moment in ...

Euclid’s Elements, which presented the state of the art in geometry around 300 B.C., has been extraordinarily influential. This massive, 13-volume compendium set the standard for mathematical ...

The claim is often made that mathematical results are immutable. Once proven, they remain forever valid. But things are not so simple. There are problems at the very core of mathematics that cast a ...

“The treatise itself, therefore, contains only twenty-four pagesthe most extraordinary two dozen pages in the whole history of thought!” “How different with BolyaiJnos and Lobachvski, who claimed at ...