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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 ...

The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

The intersection Ev of the Gergonne line and the Euler line. It has triangle center function alpha=(b(a-b+c)cosB+c(a+b-c)cosC-2a^2cosA)/(2a) and is Kimberling center X_(1375).

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An estimator of the actual values of population.

The concurrence S of the Euler lines E_n of the triangles DeltaXBC, DeltaXCA, DeltaXAB, and DeltaABC where X is the incenter. It has equivalent triangle center functions ...

The portion of the probability distribution which has a P-value equal to the observed P-value.

On the Clebsch diagonal cubic, all 27 of the complex lines present on a general smooth cubic surface are real. In addition, there are 10 points on the surface where three of ...