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A number taken to the power 3 is said to be cubed, so x^3 is called "x cubed." This terminology derives from the fact that the volume of a cube of edge length x is given by ...

The cuboctahedral graph is an Archimedean quartic symmetric graph on 12 nodes and 24 edges that is the skeleton of the cuboctahedron, as well as the uniform ...

Does there exist an algorithm for deciding whether or not a specific mathematical assertion does or does not have a proof? The decision problem is also known as the ...

Given binomial coefficient (N; k), write N-k+i=a_ib_i, for 1<=i<=k, where b_i contains only those prime factors >k. Then the number of i for which b_i=1 (i.e., for which all ...

A curve which can be turned continuously inside an equilateral triangle. There are an infinite number of delta curves, but the simplest are the circle and lens-shaped ...

Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

Consider the length of the diagonal of a unit square as approximated by piecewise linear steps that may only be taken in the right and up directions. Obviously, the length so ...

The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

A.k.a. the pigeonhole principle. Given n boxes and m>n objects, at least one box must contain more than one object. This statement has important applications in number theory ...

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...