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Trigonometric functions of npi/9 radians for n an integer not divisible by 3 (e.g., 40 degrees and 80 degrees) cannot be expressed in terms of sums, products, and finite root ...

There exist points A^', B^', and C^' on segments BC, CA, and AB of a triangle, respectively, such that A^'C+CB^'=B^'A+AC^'=C^'B+BA^' (1) and the lines AA^', BB^', CC^' ...

A vector Laplacian can be defined for a vector A by del ^2A=del (del ·A)-del x(del xA), (1) where the notation ✡ is sometimes used to distinguish the vector Laplacian from ...

The surface area of a spherical segment. Call the radius of the sphere R, the upper and lower radii b and a, respectively, and the height of the spherical segment h. The zone ...

Fermat's last theorem is a theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

A Heronian triangle is a triangle having rational side lengths and rational area. The triangles are so named because such triangles are related to Heron's formula ...

The number 163 is very important in number theory, since d=163 is the largest number such that the imaginary quadratic field Q(sqrt(-d)) has class number h(-d)=1. It also ...

An alpha value is a number 0<=alpha<=1 such that P(z>=z_(observed))<=alpha is considered "significant," where P is a P-value.

The angular distance traveled around a circle is the number of radians the path subtends, theta=l/(2pir)2pi=l/r.