This paper gives a proof that the Completeness Axiom of
Lobachevskian geometry -- as formulated in the second English translation
of David Hilbert's Foundations of Geometry (tenth German
edition)--is a theorem in the ...
A systematic and rigorous derivation of the Boolean functions that represent the three operations of the ring of integers in the 1-2-4-5 code is developed from their corresponding tables. The same is done for numerical c ...
This paper presents an extension of Hubert's incidence axioms to n dimensions and uses these and his order axioms to prove several theorems. We prove extensions of Pasch's Axiom, the Crossbar Theorem, and Desargues' Theo ...
Among the geometries with n points on every line (with n
an integer greater than one), those in which there are no parallels
and those in which the axiom of parallels holds have been discussed
(as finite projective an ...
A technique of differentiation with respect to the distance to
the boundary of an outer parallel-body is applied to known measures of
sets of p-dimensional linear spaces which intersect a general convex
body in n-dime ...
A theory of straight line triangulations of points in the plane is developed. A basic transformation is presented, and it is shown that any triangulation may be transformed into any other triangulation which has the same ...
