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The most common statement known as Steiner's theorem (Casey 1893, p. 329) states that the Pascal lines of the hexagons 123456, 143652, and 163254 formed by interchanging the ...

The second de Villiers point is the perspector of the reference triangle and the excenter analog of the BCI triangle, which is Kimberling center X_(1128) has triangle center ...

If a univariate real function f(x) has a single critical point and that point is a local maximum, then f(x) has its global maximum there (Wagon 1991, p. 87). The test breaks ...

The limaçon is a polar curve of the form r=b+acostheta (1) also called the limaçon of Pascal. It was first investigated by Dürer, who gave a method for drawing it in ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

The correspondence which relates the Hanoi graph to the isomorphic graph of the odd binomial coefficients in Pascal's triangle, where the adjacencies are determined by ...

In Euclidean space R^3, the curve that minimizes the distance between two points is clearly a straight line segment. This can be shown mathematically as follows using ...

In the case of a general surface, the distance between two points measured along the surface is known as a geodesic. For example, the shortest distance between two points on ...

In finding the average area A^__R of a triangle chosen from a closed, bounded, convex region R of the plane, then A^__(T(R))=A^__R, for T any nonsingular affine ...

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 ...