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The lemniscate functions arise in rectifying the arc length of the lemniscate. The lemniscate functions were first studied by Jakob Bernoulli and Giulio Fagnano. A historical ...

The inverse curve of a lemniscate in a circle centered at the origin and touching the lemniscate where it crosses the x-axis produces a rectangular hyperbola (Wells 1991).

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

The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It ...

The Lemoine cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=3, 4, 32, 56, and 1147.

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

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 Leonine triangle DeltaX_AX_BX_C (a term coined here for the first time), is the Cevian triangle of Kimberling center X_(598). It is the polar triangle of the Lemoine ...

Given the "peaks" of three equilateral triangles placed on the sides of a triangle T, construct T. The problem was proposed by Lemoine (1868) and solved for the general case ...