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