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Guilloché patterns are spirograph-like curves that frame a curve within an inner and outer envelope curve. They are used on banknotes, securities, and passports worldwide for ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

The Lotka-Volterra equations describe an ecological predator-prey (or parasite-host) model which assumes that, for a set of fixed positive constants A (the growth rate of ...

The geodesic on an oblate spheroid can be computed analytically, although the resulting expression is much more unwieldy than for a simple sphere. A spheroid with equatorial ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...

A secant line, also simply called a secant, is a line passing through two points of a curve. As the two points are brought together (or, more precisely, as one is brought ...

The 27 real or imaginary lines which lie on the general cubic surface and the 45 triple tangent planes to the surface. All are related to the 28 bitangents of the general ...

A piecewise polynomial function that can have a locally very simple form, yet at the same time be globally flexible and smooth. Splines are very useful for modeling arbitrary ...

In the early 1960s, B. Birch and H. P. F. Swinnerton-Dyer conjectured that if a given elliptic curve has an infinite number of solutions, then the associated L-series has ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...