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 ...

This is a preview. Log in through your library . Abstract We give a geometric proof of the Berger Holonomy Theorem. The proof uses Euclidean submanifold geometry of orbits and gives a link between ...

In 1847, an eccentric British mathematician named Oliver Byrne released a new edition of Euclid’s famous mathematical treatise, The Elements of Geometry. Byrne added a rather longwinded but ultimately ...

The theorems of Hadamard and of Poincaré–Miranda give sufficient conditions for the existence of at least one zero for some continuous mappings from a Euclidean space into itself. The note gives ...

The earliest known evidence for the Pythagorean Theorem comes from an ancient clay tablet called, “IM 67118.” This tablet uses the theorem to determine the length of a diagonal within a rectangle, and ...