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 ...

The course presents a rigorous treatment of the foundations of Euclidean and non-Euclidean geometries. The discovery of non-Euclidean geometry in the first half of the 19th century shattered the ...

WILLIAM MEADE WATERS, JR., Separation in Euclidean space: an intuitive introduction for informal geometry, The Arithmetic Teacher, Vol. 21, No. 5 (MAY 1974), pp. 458-461 ...

A team of artists and mathematicians has just created a non-Euclidean virtual-reality universe where the usual rules of geometry and physics don't apply.

Abstract This survey highlights some foundational history and some interesting recent discoveries in elementary geometry that deserve to be better known, such as the hierarchies of axiom systems, ...