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Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

The point at which the three lines connecting the vertices of two perspective triangles concur, sometimes also called the perspective center, homology center, or pole. In the ...

The line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspective axis or homology ...

The Euler-Mascheroni constant gamma, sometimes also called 'Euler's constant' or 'the Euler constant' (but not to be confused with the constant e=2.718281...) is defined as ...

A square number, also called a perfect square, is a figurate number of the form S_n=n^2, where n is an integer. The square numbers for n=0, 1, ... are 0, 1, 4, 9, 16, 25, 36, ...

Archimedes' spiral is an Archimedean spiral with polar equation r=atheta. (1) This spiral was studied by Conon, and later by Archimedes in On Spirals about 225 BC. Archimedes ...

Define a Bouniakowsky polynomial as an irreducible polynomial f(x) with integer coefficients, degree >1, and GCD(f(1),f(2),...)=1. The Bouniakowsky conjecture states that ...

Bürmann's theorem deals with the expansion of functions in powers of another function. Let phi(z) be a function of z which is analytic in a closed region S, of which a is an ...

In 1638, Fermat proposed that every positive integer is a sum of at most three triangular numbers, four square numbers, five pentagonal numbers, and n n-polygonal numbers. ...