finite geometry

Noun

finite geometry (countable and uncountable, plural finite geometries)

1. Any geometric system that has only a finite number of points.
   • 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...1980, Judson Chambers Webb, Mechanism, Mentalism and Metamathematics: An Essay on Finitism, Springer, page 39
   • 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.1999, S. Ball, “Polynomials in Finite Geometries”, in J. D. Lamb, D. A. Preece, editors, Surveys in Combinatorics, 1999, Cambridge University Press, page 17
2. (uncountable) The branch of geometry that concerns geometric systems with only a finite number of points.
   • The coordinates of geometry were as incompatible with representation theory as were the splitting fields of representation theory with finite geometry.1983, Robert A. Liebler, “Combinatorial Representation Theory and Translation Planes”, in Norman L. Johnson, Michael J. Kallaher, Calvin T. Long, editors, Finite Geometries: Proceedings of a...
   • 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.1996, Dieter Jungnickel, “Maximal Sets of Mutually Orthogonal Latin Squares”, in S. Cohen, H. Niederreiter, editors, Finite Fields and Applications: Proceedings of the 3rd International Conference...