IN a recent number of NATURE (June 30) there appeared a review of a book by G. Mannoury on the philosophy of mathematics, and the reviewer emphasised a statement of the author to the effect that the ...

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 ...

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 ...

This originally appeared in the July/August issue of Discover magazine as "Your Hyperbolic Mind." Support our science journalism by becoming a subscriber. The human brain is both a marvel and a ...