The geometry we learn in school, the so-called Euclidean geometry, is more than 2,000 years old. About two centuries ago, the Russian mathematician Lobachewsky established a new kind of geometry for ...

Geometry may be one of the oldest branches of mathematics, but it’s much more than a theoretical subject. It’s part of our everyday lives, says Professor Jennifer Taback, and key to understanding many ...

THE two books under notice together constitute an excellent introduction to non-Euclidean geometry in all its aspects. The lectures of F. Klein now appear in print for the first time under the ...

The course presents a rigorous treatment of the foundations of Euclidean and non-Euclidean geometries. The discovery of non-Euclidean geometry in the first half of the 19th century shattered the ...

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 ...

Virtual reality can take you to some far-out places — mountaintops, distant cities and even fantastical game worlds. A team of artists and mathematicians is now adding to that list: universes where ...

THE philosopher Kant declared that Euclidean geometry was inherent in the human mind and expressed the truth about space. We now recognize that non-Euclidean geometry is equally valid as an abstract ...