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Let a particle travel a distance s(t) as a function of time t (here, s can be thought of as the arc length of the curve traced out by the particle). The speed (the scalar ...

The minimal polynomial of an algebraic number zeta is the unique irreducible monic polynomial of smallest degree p(x) with rational coefficients such that p(zeta)=0 and whose ...

The conjecture that the number of alternating sign matrices "bordered" by +1s A_n is explicitly given by the formula A_n=product_(j=0)^(n-1)((3j+1)!)/((n+j)!). This ...

The antipedal triangle DeltaA^'B^'C^' of a reference triangle DeltaABC with respect to a given point P is the triangle of which DeltaABC is the pedal triangle with respect to ...

The Archimedean duals are the 13 duals of the 13 Archimedean solids, sometimes called the Catalan solids. They are summarized in the following table and illustrated below ...

The Barth sextic is a sextic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 65. The surface was ...

The biggest little polygon with n sides is the convex plane n-gon of unit polygon diameter having largest possible area. Reinhardt (1922) showed that for n odd, the regular ...

Given a general quadrilateral with sides of lengths a, b, c, and d, the area is given by K = 1/4sqrt(4p^2q^2-(b^2+d^2-a^2-c^2)^2) (1) = (2) (Coolidge 1939; Ivanov 1960; Beyer ...

The "Cartesian ovals," sometimes also known as the Cartesian curve or oval of Descartes, are the quartic curve consisting of two ovals. They were first studied by Descartes ...

"Casting out nines" is an elementary check of a multiplication which makes use of the congruence 10^n=1 (mod 9). Let decimal numbers be written a=a_n...a_2a_1a_0, ...