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 ...

INDIA: Euclid’s Postulates serves as the foundation of modern Geometry. Talking about Geometry, it is the branch of mathematics concerned with the properties and relationships of points, lines, angles ...

This is a git repository of the source files for the book The Elements of non-Euclidean Geometry by Coolidge, Julian Lowell. This book is in the Public Domain, see ...

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 ...

This Paper addresses the limitations of classical machine learning approaches primarily developed for data lying in Euclidean space. Modern machine learning increasingly encounters richly structured ...

MR. FRANKLAND (NATURE, September 7) has raised the old problem of Bertrand's proof of the parallel-axiom by a consideration of infinite areas. This is perhaps the most subtle and the most specious of ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don’t apply: angles of a triangle add up to less than 180 degrees and Euclid’s parallel postulate, ...