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For a point P inside an equilateral triangle DeltaABC, the sum of the perpendiculars p_i from P to the sides of the triangle is equal to the altitude h. This result is simply ...

If the top and bottom bases of a solid are equal in area, lie in parallel planes, and every section of the solid parallel to the bases is equal in area to that of the base, ...

The W-transform of a function f(x) is defined by the integral where Gamma[(beta_m)+s, 1-(alpha_n)-s; (alpha_p^(n+1))+s, 1-(beta_q^(m+1))-s] =Gamma[beta_1+s, ..., beta_m+s, ...

Every odd integer n is a prime or the sum of three primes. This problem is closely related to Vinogradov's theorem.

A 4-polyhex.

An operator relating the asymptotic state of a dynamical system governed by the Schrödinger equation ihd/(dt)psi(t)=Hpsi(t) to its original asymptotic state.

If two curves of the same curve genus >1 are in rational correspondence, then that correspondence is birational.

Every nonempty set of positive integers contains a smallest member.

An natural equation which expresses a curve in terms of its arc length s and tangential angle phi.

Recall the definition of the autocorrelation function C(t) of a function E(t), C(t)=int_(-infty)^inftyE^_(tau)E(t+tau)dtau. (1) Also recall that the Fourier transform of E(t) ...