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The area Delta (sometimes also denoted sigma) of a triangle DeltaABC with side lengths a, b, c and corresponding angles A, B, and C is given by Delta = 1/2bcsinA (1) = ...

The straight line on which all points at infinity lie. The line at infinity is central line L_6 (Kimberling 1998, p. 150), and has trilinear equation aalpha+bbeta+cgamma=0, ...

The diagonal triangle of a complete quadrangle is the triangle formed by its three diagonal points. If the quadrangle is a cyclic quadrilateral, then the circle is the polar ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the B- and C-excircles (with centers J_B and J_C, respectively). Of these, three correspond to the ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the incircle (with center I) and the A-excircle (with center J_A). Of these, three correspond to the ...

The Stammler triangle is the triangle formed by the centers of the Stammler circles. It is an equilateral triangle. It circumscribes the circumcircle and homothetic to the ...

A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...

The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

By analogy with the outer Napoleon triangle, consider the external erection of three squares on the sides of a triangle DeltaABC. These centers form a triangle DeltaO_AO_BO_C ...

An independent vertex set of a graph G is a subset of the vertices such that no two vertices in the subset represent an edge of G. The figure above shows independent sets ...