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.

It may contain inaccuracies due to the limitations of machine translation. A dialogue on how questioning a 2,000-year-old truth gave birth to a new geometry that reshaped mathematics and our ...

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 ...

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 ...

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 ...

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, ...

“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 ...