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The Tschirnhausen cubic is a plane curve given by the polar equation r=asec^3(1/3theta). (1) Letting theta=3tan^(-1)t gives the parametric equations x = a(1-3t^2) (2) y = ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The two-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the line ...

Underdamped simple harmonic motion is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0 (1) in which beta^2-4omega_0^2<0. (2) Since we have ...

A Vandermonde matrix is a type of matrix that arises in the polynomial least squares fitting, Lagrange interpolating polynomials (Hoffman and Kunze p. 114), and the ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

The "witch of Agnesi" is a curve studied by Maria Agnesi in 1748 in her book Instituzioni analitiche ad uso della gioventù italiana (the first surviving mathematical work ...

The nth root (or "nth radical") of a quantity z is a value r such that z=r^n, and therefore is the inverse function to the taking of a power. The nth root is denoted ...

The van Aubel line is the line in the plane of a reference triangle that connects the orthocenter H and symmedian point K, and symmedian point of the orthic triangle. The ...

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, ...

The Chebyshev polynomials of the first kind are a set of orthogonal polynomials defined as the solutions to the Chebyshev differential equation and denoted T_n(x). They are ...