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A function y=f(x) has critical points at all points x_0 where f^'(x_0)=0 or f(x) is not differentiable. A function z=f(x,y) has critical points where the gradient del f=0 or ...

Two lines or plane congruent geometric figures which lie on top of each other are said to be coincident.

The slicing of a three-dimensional object by a plane (or more general slice).

Consider n intersecting ellipses. The maximal number of regions into which these divide the plane are N(n)=2n^2-2n+2=2(n^2-n+1), giving values for n=1, 2, ... of 2, 6, 14, ...

Given two intersecting lines, the two nonadjacent angles with the same vertex are said to be vertical angles. One can easily prove that vertical angles are congruent. Some ...

An Asian version of chess, sometimes also called Chinese Chess, that is currently played extensively in China, Taiwan, Thailand, Singapore, Vietnam, and Hong Kong. The ...

The regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral ...

The standard Lorentzian inner product on R^4 is given by -dx_0^2+dx_1^2+dx_2^2+dx_3^2, (1) i.e., for vectors v=(v_0,v_1,v_2,v_3) and w=(w_0,w_1,w_2,w_3), ...

The class of curve known as Dürer's conchoid appears in Dürer's work Instruction in Measurement with Compasses and Straight Edge (1525) and arose in investigations of ...

With n cuts of a torus of genus 1, the maximum number of pieces which can be obtained is N(n)=1/6(n^3+3n^2+8n). The first few terms are 2, 6, 13, 24, 40, 62, 91, 128, 174, ...