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The illusion due to psychologist Edward Bradford Titchener that a circle surrounded by other circles will appear smaller if the surrounding circles are enlarged. This effect ...

A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and ...

The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

Let x and y be vectors. Then the triangle inequality is given by |x|-|y|<=|x+y|<=|x|+|y|. (1) Equivalently, for complex numbers z_1 and z_2, ...

The total power of a triangle is defined by P=1/2(a_1^2+a_2^2+a_3^2), (1) where a_i are the side lengths, and the "partial power" is defined by p_1=1/2(a_2^2+a_3^2-a_1^2). ...

A spherical harmonic of the form sin(mphi)P_m^m(costheta) or cos(mphi)P_m^m(costheta).

Let a spherical triangle have sides of length a, b, and c, and semiperimeter s. Then the spherical excess E is given by

The associated Legendre polynomials P_l^m(x) and P_l^(-m)(x) generalize the Legendre polynomials P_l(x) and are solutions to the associated Legendre differential equation, ...

A cylindrical segment, sometimes also called a truncated cylinder, is the solid cut from a circular cylinder by two (or more) planes. If there are two cutting planes, one ...

The centroid is center of mass of a two-dimensional planar lamina or a three-dimensional solid. The mass of a lamina with surface density function sigma(x,y) is ...