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A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

A lucky number of Euler is a number p such that the prime-generating polynomial n^2-n+p is prime for n=1, 2, ..., p-1. Such numbers are related to the imaginary quadratic ...

A formula relating the number of polyhedron vertices V, faces F, and polyhedron edges E of a simply connected (i.e., genus 0) polyhedron (or polygon). It was discovered ...

The turning of an object or coordinate system by an angle about a fixed point. A rotation is an orientation-preserving orthogonal transformation. Euler's rotation theorem ...

The Tixier point X_(476) is the reflection of the focus of the Kiepert parabola (X_(110)) in the Euler line. It has equivalent trilinear center functions X_(476) = ...

Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then the Selberg zeta function is defined as ...

The geometric mean is smaller than the arithmetic mean, (product_(i=1)^Nn_i)^(1/N)<=(sum_(i=1)^(N)n_i)/N, with equality in the cases (1) N=1 or (2) n_i=n_j for all i,j.

If r experiments are performed with n_i possible outcomes for each experiment i=1,2,...,r, then there are a total of product_(i=1)^(r)n_i possible outcomes.

For a positive integer n, (2pi)^((n-1)/2)n^(1/2-nz)Gamma(nz)=product_(k=0)^(n-1)Gamma(z+k/n),

The statistical index P_G=[product((p_n)/(p_0))^(v_0)]^(1/Sigmav_0), where p_n is the price per unit in period n, q_n is the quantity produced in period n, and v_n=p_nq_n the ...