THIS work will be found really valuable by all students of geometry, especially by those who know little or nothing of the non-Euclidean theories. First of all we have a discussion of the elementary ...

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 ...

This is a preview. Log in through your library . Journal Information PNAS is the world's most-cited multidisciplinary scientific serial. It publishes high-impact research reports, commentaries, ...

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 shortest distance between two points is a straight line. This is one of the basic principles of Euclidean geometry. But we live on a spherical Earth, so we cannot travel the straight line path ...