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An ordered vector basisv_1,...,v_n for a finite-dimensional vector space V defines an orientation. Another basis w_i=Av_i gives the same orientation if the matrix A has a ...

If W is a k-dimensional subspace of a vector space V with inner product <,>, then it is possible to project vectors from V to W. The most familiar projection is when W is the ...

The Voronov-Neopryatnaya-Dergachev graphs are two graphs on 372 and 972 vertices which have unit-distance embeddings with all vertices on a sphere and chromatic number 5. The ...

Let B_n(r) be the n-dimensional closed ball of radius r>1 centered at the origin. A function which is defined on B(r) is called an extension to B(r) of a function f defined ...

WireWorld is a two-dimensional four-color cellular automaton introduced by Brian Silverman in 1987. The rule for the automaton uses the cell's old value a together with the ...

A nonzero element x of a ring for which x·y=0, where y is some other nonzero element and the multiplication x·y is the multiplication of the ring. A ring with no zero ...

A kit consisting of colored rods and slotted balls that can be used to construct three-dimensional configurations. The balls into which the rods are placed resemble an ...

Trigonometry

The method of d'Alembert provides a solution to the one-dimensional wave equation (partial^2y)/(partialx^2)=1/(c^2)(partial^2y)/(partialt^2) (1) that models vibrations of a ...

A graph whose nodes are sequences of symbols from some alphabet and whose edges indicate the sequences which might overlap. The above figures show the first few n-dimensional ...