Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in two-dimensional (2D) and three-dimensional (3D) settings. The rules of Euclidean ...

Euclidean geometry is a mathematical well-known system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic discussion of geometry. It has been ...

We’ve all learned “parallel lines never intersect” in high school geometry. But what your teachers failed to explain is that “parallel lines never intersect” is only true in Euclidean geometry, which ...

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 ...

Bernhard Riemann was a man with a hypothesis. He was confident that it was true, probably. But he didn’t prove it. And attempts over the last century and a half by others to prove it have failed. A ...

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 ...

Everyone learns the number one rule about triangles in high school: the angles of a triangle add up to 180 degrees. But did you know that sometimes they don't? Triangles are much more interesting than ...

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 ...