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 ...

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 ...

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 ...

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 ...

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 ...

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, ...

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 ...