The parallel postulate was Euclid's famous, and sometimes infamous, fifth postulate. Euclid's five postulates, or axioms, as they are sometimes called, appear in his masterpiece the Elements, one of the most influential mathematics books ever written....

Ever since the time of Euclid, mathematicians have felt that Euclid's fifth postulate, which lets only one straight line be drawn through a given point parallel to a given line, was a somewhat unnatural addition to the other, more intuitively...

In geometry, the parallel postulate, also called Euclid's fifth postulate since it is the fifth postulate in Euclid's Elements, is a distinctive axiom in what is now called Euclidean geometry. It states...

INTRODUCTION A recent article A Glance at Hyperbolic Geometry Provides a Challenge to Students' Intuition by Eric Milou [3 ], indicated that an attractive junior-level geometry course can involve studying the BeltramiPoincare (BP) model (also known as the upper half-plane model) of hyperbolic...

INTRODUCTION Common sense says that energy efficiency gains will reduce energy demand below where it otherwise would be. So evident is this that most countries' energy policies--not to mention oil industry forecasts and many academic writings--take it as a cornerstone fact. In...