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The trilinear coordinates alpha:beta:gamma of a point P relative to a reference triangle are proportional to the directed distances a^':b^':c^' from P to the side lines of ...

A term for number theory.

Abstractly, a spatial configuration F is said to possess rotational symmetry if F remains invariant under the group C=C(F). Here, C(F) denotes the group of rotations of F and ...

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...

The tangent plane to a surface at a point p is the tangent space at p (after translating to the origin). The elements of the tangent space are called tangent vectors, and ...

A map projection. The inverse equations for phi are computed by iteration. Let the angle of the projection plane be theta_b. Define a={0 for theta_b=1/2pi; ...

In general, the catacaustics of the astroid are complicated curves. For an astroid with parametric equations x = cos^3t (1) y = sin^3t, (2) the catacaustic for a radiant ...

For the cardioid given parametrically as x = a(1+cost)cost (1) y = a(1+cost)sint, (2) the negative pedal curve with respect to the pedal point (x_0,y_0)=(0,0) is the circle ...

For the parametric representation x = (2t^2)/(1+t^2) (1) y = (2t^3)/(1+t^2), (2) the catacaustic of this curve from the radiant point (8a,0) is given by x = ...