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 ...

Discover how science can tell us what to value and why moral judgments aren't objectively true, despite popular belief. Values are a certain kind of fact. They are facts about the well-being of ...

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 ...

Mathematics Magazine presents articles and notes on undergraduate mathematical topics in a lively expository style that appeals to students and faculty throughout the undergraduate years. The journal ...

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 ...

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 ...

Description: Incidence geometry in planes and space, separation in planes and space, angular measure, neutral geometry, history of the parallel postulate, Euclidean geometry of the plane and space, ...

Hyperbolic geometry originated in the 19th century, when mathematicians questioned the necessity of the parallel postulate in Euclidean geometry and discovered the hyperbolic plane ℍ², which satisfied ...