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The line segment connecting opposite polyhedron vertices (i.e., two polyhedron vertices which do not share a common face) in a parallelepiped or other similar solid. Also ...

A roulette is a curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of ...

The Pasch graph is the Levi graph of the Pasch configuration. The Pasch graph is edge-transitive but not vertex-transitive, but fails to be semisymmetric since it is not ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

Given collinear points W, X, Y, and Z, Y and Z are harmonic conjugates with respect to W and X if (|WY|)/(|YX|)=(|WZ|)/(|XZ|). (1) W and X are also harmonic conjugates with ...

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 ...

int_a^b(del f)·ds=f(b)-f(a), where del is the gradient, and the integral is a line integral. It is this relationship which makes the definition of a scalar potential function ...

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

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 ...