Meaning of finite geometry | Babel Free

Definitions

1. Any geometric system that has only a finite number of points.
   countable, uncountable
2. The branch of geometry that concerns geometric systems with only a finite number of points.
   uncountable

Examples

“But the work of von Staudt, Fano, and Veblen led even to the construction of finite geometries having only finitely many points and lines. Originally having only incidence relations, these finite geometries have been extensively developed through the introduction of suitable axioms of order and congruence by Järnefelt and Kustaanheimo, who have proposed their use in physics to solve certain paradoxes due apparently to the use of continuous variables.”

“A method of using polynomials to describe objects in finite geometries is outlined and the problems where this method has led to a solution are surveyed.”

“Finite geometries, such as Euclidean and projective geometries, are powerful mathematical tools for constructing error-control codes.”

“The coordinates of geometry were as incompatible with representation theory as were the splitting fields of representation theory with finite geometry.”

“We give a survey on a topic in Finite Geometry which has generated considerable interest in the literature: the construction of maximal sets of mutually orthogonal Latin squares (MOLS) or, equivalently, of maximal nets.”

“Finite geometry is a broad area of research, but much of it is not Euclidean in flavour and no theory seems to match that of oriented matroids in establishing combinatorial Euclidean geometry.”

CEFR level