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Find a way to stack a square of cannonballs laid out on the ground into a square pyramid (i.e., find a square number which is also square pyramidal). This corresponds to ...

The curve given by the polar equation r=a(1-costheta), (1) sometimes also written r=2b(1-costheta), (2) where b=a/2. The cardioid has Cartesian equation ...

Cartesian coordinates are rectilinear two- or three-dimensional coordinates (and therefore a special case of curvilinear coordinates) which are also called rectangular ...

A circumconic is a conic section that passes through the vertices of a triangle (Kimberling 1998, p. 235). Every circumconic has a trilinear equation of the form ...

The complete elliptic integral of the first kind K(k), illustrated above as a function of the elliptic modulus k, is defined by K(k) = F(1/2pi,k) (1) = ...

A cubic curve is an algebraic curve of curve order 3. An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in ...

The curl of a vector field, denoted curl(F) or del xF (the notation used in this work), is defined as the vector field having magnitude equal to the maximum "circulation" at ...

Erfc is the complementary error function, commonly denoted erfc(z), is an entire function defined by erfc(z) = 1-erf(z) (1) = 2/(sqrt(pi))int_z^inftye^(-t^2)dt. (2) It is ...

The Gegenbauer polynomials C_n^((lambda))(x) are solutions to the Gegenbauer differential equation for integer n. They are generalizations of the associated Legendre ...

The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, ...