Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in ...

The mathematics underpinning the modern method of elliptic curve cryptography originated with Renaissance architect Filippo Brunelleschi ...

This is the geometry we learned in school. The angles of a triangle add up to 180 degrees, and the area of a circle is πr 2. The simplest example of a flat three-dimensional shape is ordinary infinite ...

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 ...

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 ...

In an attempt to answer age-old questions about how basic musical elements work together, Dmitri Tymoczko has journeyed far into the land of topology and non-Euclidean geometry, and has returned with ...