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An axiomatic theory (such as a geometry) is said to be complete if each valid statement in the theory is capable of being proven true or false.

The five of Hilbert's axioms which concern geometric equivalence.

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

A countable set is a set that is either finite or denumerable. However, some authors (e.g., Ciesielski 1997, p. 64) use the definition "equipollent to the finite ordinals," ...

A fractal curve of infinite length which bounds an area twice that of the original square.

The rotation vector of the trihedron of a curve with curvature kappa!=0 when a point moves along a curve with unit speed. It is given by D=tauT+kappaB, (1) where tau is the ...

A set of points which do not lie on any of a certain class of hyperplanes.

In two dimensions, the curve known as an "egg' is an oval with one end more pointed than the other.

Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...