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If a line L is the Simson line of a point P on the circumcircle of a triangle, then P is called the pole of L (Honsberger 1995, p. 128).

The tangent indicatrix of a curve of constant precession is a spherical helix. The equation of a spherical helix on a sphere with radius r making an angle theta with the ...

A plot of a function expressed in spherical coordinates, with radius r as a function of angles theta and phi. Polar plots can be drawn using SphericalPlot3D[r, {phi, phimin, ...

A spheroidal section is the curve formed by the intersection of a plane with a spheroid. A spheroidal section is either a circle (for planes parallel to an equator, i.e., ...

If, in a plane or spherical convex polygon ABCDEFG, all of whose sides AB, BC, CD, ..., FG (with the exception of AG) have fixed lengths, one simultaneously increases ...

The exploration of three-dimensional space from two-dimensional sections of projections of solid bodies.

A surface in 3-space can be parameterized by two variables (or coordinates) u and v such that x = x(u,v) (1) y = y(u,v) (2) z = z(u,v). (3) If a surface is parameterized as ...

Informally, a symplectic map is a map which preserves the sum of areas projected onto the set of (p_i,q_i) planes. It is the generalization of an area-preserving map. ...

An inscribed angle in a semicircle is a right angle.

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...