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If 1<=b<a and (a,b)=1 (i.e., a and b are relatively prime), then a^n-b^n has at least one primitive prime factor with the following two possible exceptions: 1. 2^6-1^6. 2. ...

An amazing pandigital approximation to e that is correct to 18457734525360901453873570 decimal digits is given by (1+9^(-4^(7·6)))^(3^(2^(85))), (1) found by R. Sabey in 2004 ...

All triangles are bicentric, i.e., possess both an incircle and a circumcircle. This is not necessarily the case for polygons with four or more sides. The inradius r and ...

While the above figure appears to be a sequence of nested squares, it actually consists of a single square spiral.

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 ...

A diagonal of a square matrix which is traversed in the "southeast" direction. "The" diagonal (or "main diagonal," or "principal diagonal," or "leading diagonal") of an n×n ...

The diameter of a circle is the distance from a point on the circle to a point pi radians away, and is the maximum distance from one point on a circle to another. The ...

An equilateral polyhedron is a polyhedron whose edges are all of equal length. Platonic solids, Archimedean solids, canonical antiprisms, and canonical prisms, Johnson ...

A line segment connecting nonadjacent polyhedron vertices sharing a common face in a parallelepiped or other similar solid.

A smooth curve which corresponds to the limiting case of a histogram computed for a frequency distribution of a continuous distribution as the number of data points becomes ...