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The pedal curve of a rectangular hyperbola with the pedal point at the focus is a circle (left figure; Hilbert and Cohn-Vossen 1999, p. 26). The pedal curve of a rectangular ...

If M^n is a finite simplicial complex of dimension n>=5 that has the homotopy type of the sphere S^n and is locally piecewise linearly homeomorphic to the Euclidean space ...

A straight line is tangent to a given curve f(x) at a point x_0 on the curve if the line passes through the point (x_0,f(x_0)) on the curve and has slope f^'(x_0), where ...

The theory of point sets and sequences having a uniform distribution. Uniform distribution theory is important in modeling and simulation, and especially in so-called Monte ...

The angle of incidence of a ray to a surface is measured as the difference in angle between the ray and the normal vector of the surface at the point of intersection.

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.