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Let lambda be the longitude, lambda_0 the reference longitude, phi the latitude, phi_0 the reference latitude, and phi_1 and phi_2 the standard parallels. Then the ...

The Lemoine hexagon is a cyclic hexagon with vertices given by the six concyclic intersections of the parallels of a reference triangle through its symmedian point K. The ...

The Lemoine ellipse is an inconic (that is always an ellipse) that has inconic parameters x:y:z=(2(b^2+c^2)-a^2)/(bc):(2(a^2+c^2)-b^2)/(ac): (2(a^2+b^2)-c^2)/(ab). (1) The ...

The Longuet-Higgins circle is the radical circle of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c, c+a, and a+b. Its ...

The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function alpha_(1151)=2cosA+sinA (1) corresponding ...

Let x=(x_1,x_2,...,x_n) and y=(y_1,y_2,...,y_n) be nonincreasing sequences of real numbers. Then x majorizes y if, for each k=1, 2, ..., n, sum_(i=1)^kx_i>=sum_(i=1)^ky_i, ...

The mid-arc triangle is the triangle DeltaA^'B^'C^' whose vertices consist of the intersections of the internal angle bisectors with the incircle, where the points of ...

The Moses-Longuet-Higgins circle is the radical circle of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c-a, c+a-b, and ...

The orthic inconic of a triangle is the inconic with inconic parameters x:y:z=cosA:cosB:cosC. (1) It has trilinear equation ...

Let A^' be the outermost vertex of the regular pentagon erected outward on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...