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An (n-1)-dimensional face of an n-dimensional polytope. A procedure for generating facets is known as faceting.

In a given acute triangle DeltaABC, locate a point whose distances from A, B, and C have the smallest possible sum. The solution is the point from which each side subtends an ...

When a point P moves along a line through the circumcenter of a given triangle Delta, the pedal circle of P with respect to Delta passes through a fixed point (the Griffiths ...

The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

The isogonal transform of a geometric object is the object obtained by collectively taking the isogonal conjugates of all its points.

The isotomic transform of a geometric object is the object obtained by collectively taking the isotomic conjugates of all its points.

A leg of a triangle is one of its sides. For a right triangle, the term "leg" generally refers to a side other than the one opposite the right angle (which is termed the ...

Lemoine-Brocard geometry is that part of triangle geometry concerned with the Brocard points, Brocard triangles, etc. and with symmedians and symmedian points.

Lemoine geometry is that part of triangle geometry concerned with symmedians and symmedian points.

A Monge patch is a patch x:U->R^3 of the form x(u,v)=(u,v,h(u,v)), (1) where U is an open set in R^2 and h:U->R is a differentiable function. The coefficients of the first ...