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An initial point that provides safe convergence of Newton's method (Smale 1981; Petković et al. 1997, p. 1).

Lee (1944) defines an authalic map projection to be one in which at any point the scales in two orthogonal directions are inversely proportional.

A basepoint is the beginning and ending point of a loop. The fundamental group of a topological space is always with respect to a particular choice of basepoint.

Two curves which, at any point, have a common principal normal vector are called Bertrand curves. The product of the torsions of Bertrand curves is a constant.

If P(x) is an irreducible cubic polynomial all of whose roots are real, then to obtain them by radicals, you must take roots of nonreal numbers at some point.

The radial curve of the catenary x = t (1) y = cosht (2) with radiant point (x_0,y_0) is given by x_r = x_0-coshtsinht (3) y_r = y_0+cosht. (4)

The pedal curve of the cissoid, when the pedal point is on the axis beyond the asymptote at a distance from the cusp which is four times that of the asymptote is a cardioid.

Given a point lattice, a cluster is a group of filled cells which are all connected to their neighbors vertically or horizontally.

The four medians of a tetrahedron concur in a point which divides each tetrahedron median in the ratio 1:3, the longer segment being on the side of the vertex of the ...

The cubic groups are the point groups T_h and O_h together with their pure rotation subgroups T_d, T, and O (Cotton 1990, pp. 433-434).