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A pentagon is a five-sided polygon. Several special types of pentagons are illustrated above. In particular, a pentagon with vertices equally spaced around a circle and with ...

A sequence {a_i} is said to be periodic with period p with if it satisfies a_i=a_(i+np) for n=1, 2, .... For example, {1,2,1,2,1,2,1,2,1,2,1,2,1,2,...} is a periodic sequence ...

All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

When |x|<1/2, (1-x)^(-a)_2F_1(a,b;c;-x/(1-x))=_2F_1(a,c-b;c;x).

An adjoint curve which bears a special relation to the base curve.

Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

The study of harmonic functions (also called potential functions).

An algebra in which the associator (x,x,x)=0. The subalgebra generated by one element is associative.

The derivative of the power x^n is given by d/(dx)(x^n)=nx^(n-1).

A ring for which the product of any pair of ideals is zero only if one of the two ideals is zero. All simple rings are prime.