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A fiber bundle (also called simply a bundle) with fiber F is a map f:E->B where E is called the total space of the fiber bundle and B the base space of the fiber bundle. The ...

Keller conjectured that tiling an n-dimensional space with n-dimensional hypercubes of equal size yields an arrangement in which at least two hypercubes have an entire ...

Hadamard matrices H_n can be constructed using finite field GF(p^m) when p=4l-1 and m is odd. Pick a representation r relatively prime to p. Then by coloring white ...

The numbers of positive definite n×n matrices of given types are summarized in the following table. For example, the three positive eigenvalues 2×2 (0,1)-matrices are [1 0; 0 ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

Dürer's solid, also known as the truncated triangular trapezohedron, is the 8-faced solid depicted in an engraving entitled Melencolia I by Albrecht Dürer (The British ...

The hypercube is a generalization of a 3-cube to n dimensions, also called an n-cube or measure polytope. It is a regular polytope with mutually perpendicular sides, and is ...

Pre-Algebra

The great truncated icosidodecahedron, also called the great quasitruncated icosidodecahedron, is the uniform polyhedron with Maeder index 68 (Maeder 1997), Wenninger index ...

Given a circle C with center O and radius k, then two points P and Q are inverse with respect to C if OP·OQ=k^2. If P describes a curve C_1, then Q describes a curve C_2 ...