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Given a general quadrilateral with sides of lengths a, b, c, and d, the area is given by K = 1/4sqrt(4p^2q^2-(b^2+d^2-a^2-c^2)^2) (1) = (2) (Coolidge 1939; Ivanov 1960; Beyer ...

Given triangle DeltaA_1A_2A_3, let the point of intersection of A_2Omega and A_3Omega^' be B_1, where Omega and Omega^' are the Brocard points, and similarly define B_2 and ...

A projection which maps a sphere (or spheroid) onto a plane. Map projections are generally classified into groups according to common properties (cylindrical vs. conical, ...

A space-filling function which maps a one-dimensional interval into a two-dimensional area. Plane-filling functions were thought to be impossible until Hilbert discovered the ...

A quadrilateral whose consecutive sides have the lengths a_1b_3, a_3b_2, a_2b_3, a_3b_1, where a_1^2+a_2^2=a_3^2 (1) and b_1^2+b_2^2=b_3^2. (2) Brahmagupta's trapezium is a ...

The circum-orthic triangle DeltaA^'B^'C^' is the circumcevian triangle of a triangle DeltaABC with respect to the orthocenter H (Kimberling 1998, p. 163). The circum-orthic ...

A cyclic pentagon is a not necessarily regular pentagon on whose polygon vertices a circle may be circumscribed. Let such a pentagon have edge lengths a_1, ..., a_5, and area ...

The solid cut from a horizontal cylinder of length L and radius R by a single plane oriented parallel to the cylinder's axis of symmetry (i.e., a portion of a horizontal ...

The inner Napoleon triangle is the triangle DeltaN_AN_BN_C formed by the centers of internally erected equilateral triangles DeltaABE_C, DeltaACE_B, and DeltaBCE_A on the ...

States that for a nondissipative Hamiltonian system, phase space density (the area between phase space contours) is constant. This requires that, given a small time increment ...