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A magic tesseract is a four-dimensional generalization of the two-dimensional magic square and the three-dimensional magic cube. A magic tesseract has magic constant ...

An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...

A snake is an Eulerian path in the d-hypercube that has no chords (i.e., any hypercube edge joining snake vertices is a snake edge). Klee (1970) asked for the maximum length ...

An E_8 polytope is a polytope having the symmetry of the exceptional simple Lie groups E_8 of dimension 248. There are 255 uniform polytopes with E_8 symmetry in 8 ...

The one-dimensional wave equation is given by (partial^2psi)/(partialx^2)=1/(v^2)(partial^2psi)/(partialt^2). (1) In order to specify a wave, the equation is subject to ...

A path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. A lattice path is therefore a sequence of points P_0, P_1, ...

Any method which solves a problem by generating suitable random numbers and observing that fraction of the numbers obeying some property or properties. The method is useful ...

The Ouchi illusion, illustrated above, is an illusion named after its inventor, Japanese artist Hajime Ouchi. In this illusion, the central disk seems to float above the ...

A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional ...

There are several meanings of the word content in mathematics. The content of a polytope or other n-dimensional object is its generalized volume (i.e., its "hypervolume"). ...