Geometry, the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.

Euclidean geometry is the study of plane and solid figures on the basis of axioms and theorems employed by the ancient Greek mathematician Euclid. The term refers to the plane and solid …

Euclidean geometry - Plane Geometry, Axioms, Postulates: Two triangles are said to be congruent if one can be exactly superimposed on the other by a rigid motion, and the …

Nikolay Ivanovich Lobachevsky was a Russian mathematician and founder of non-Euclidean geometry, which he developed independently of János Bolyai and Carl Gauss.

Dec 9, 2025 · Chemical bonding - Molecular Shapes, VSEPR Theory: There is a sharp distinction between ionic and covalent bonds when the geometric arrangements of atoms in compounds …

Jan 8, 2026 · Hermann Minkowski was a German mathematician who developed the geometrical theory of numbers and who made numerous contributions to number theory, mathematical …

By reducing relations difficult to state and prove geometrically to algebraic relations between coordinates (usually rectangular) of points on curves, Descartes brought about the union of …

The coordinates of a line in a congruence may be expressed as functions of two independent parameters; from this it follows that the theory of congruences is analogous to that of surfaces …

Pythagoreanism - Geometry, Mathematics, Philosophy: In geometry, the Pythagoreans cannot be credited with any proofs in the Euclidean sense.

Dec 5, 2025 · geometry, the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.