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Five point geometry is a finite geometry subject to the following three axioms: 1. there exist exactly five points, 2. each two distinct points have exactly one line on both ...

Three point geometry is a finite geometry subject to the following four axioms: 1. There exist exactly three points. 2. Two distinct points are on exactly one line. 3. Not ...

An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformations (such as rotation, reflection, inversion, or more ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

The figure determined by four lines, no three of which are concurrent, and their six points of intersection (Johnson 1929, pp. 61-62). Note that this figure is different from ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

The cross number of a zero-system sigma={g_1,g_2,...,g_n} of G is defined as K(sigma)=sum_(i=1)^n1/(|g_i|) The cross number of a group G has two different definitions. 1. ...

In a monoid or multiplicative group where the operation is a product ·, the multiplicative inverse of any element g is the element g^(-1) such that g·g^(-1)=g^(-1)·g=1, with ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...