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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 = ...

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

The difference between the measured or inferred value of a quantity x_0 and its actual value x, given by Deltax=x_0-x (sometimes with the absolute value taken) is called the ...

Inference of the truth of an unknown result obtained by noting its similarity to a result already known to be true. In the hands of a skilled mathematician, analogy can be a ...

An azimuthal projection which is neither equal-area nor conformal. Let phi_1 and lambda_0 be the latitude and longitude of the center of the projection, then the ...

Ballantine's series is the series for pi given by pi=864sum_(n=0)^infty((n!)^24^n)/((2n+1)!325^(n+1)) +1824sum_(n=0)^infty((n!)^24^n)/((2n+1)!3250^(n+1))-20cot^(-1)239 ...

Let the nth composition of a function f(x) be denoted f^((n))(x), such that f^((0))(x)=x and f^((1))(x)=f(x). Denote the composition of f and g by f degreesg(x)=f(g(x)), and ...

The number of single operations (of addition, subtraction, and multiplication) required to complete an algorithm.

A map projection defined by x = sin^(-1)[cosphisin(lambda-lambda_0)] (1) y = tan^(-1)[(tanphi)/(cos(lambda-lambda_0))]. (2) The inverse formulas are phi = sin^(-1)(sinDcosx) ...

Special cases of general formulas due to Bessel. J_0(sqrt(z^2-y^2))=1/piint_0^pie^(ycostheta)cos(zsintheta)dtheta, where J_0(z) is a Bessel function of the first kind. Now, ...