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The Euclidean plane parametrized by coordinates, so that each point is located based on its position with respect to two perpendicular lines, called coordinate axes. They are ...

For any system that seeks to minimize a function, only seven different local forms of catastrophe "typically" occur for four or fewer variables: 1. Fold catastrophe, 2. Cusp ...

Given A = |a_(11)-x a_(12) ... a_(1m); a_(21) a_(22)-x ... a_(2m); | | ... |; a_(m1) a_(m2) ... a_(mm)-x| (1) = x^m+c_(m-1)x^(m-1)+...+c_0, (2) then ...

The Christoffel symbols are tensor-like objects derived from a Riemannian metric g. They are used to study the geometry of the metric and appear, for example, in the geodesic ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

A central circle is a circle with trilinear equation (lalpha+mbeta+ngamma)(aalpha+bbeta+cgamma)+k(abetagamma+bgammaalpha+calphabeta)=0 such that l:m:n is a triangle center ...

In the figure above with tangent line PT and secant line PA, (PA)/(PT)=(PT)/(PB) (1) (Jurgensen et al. 1963, p. 346). The line tangent to a circle of radius a centered at ...

The circum-medial triangle DeltaA^'B^'C^' is the circumcevian triangle of a reference triangle DeltaABC with respect to the triangle centroid G of DeltaABC (Kimberling 1998, ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

Consider a combination lock consisting of n buttons that can be pressed in any combination (including multiple buttons at once), but in such a way that each number is pressed ...