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A conic projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cone with apex A which tangent to the ...

The triangle bounded by the polars of the vertices of a triangle DeltaABC with respect to a conic is called its polar triangle. The following table summarizes polar triangles ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

A transformation T (a.k.a., map, function) over a domain D takes the elements X in D to elements Y in T(D), where the range (a.k.a., image) of T is defined as ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

The triangulation point Y of a reference triangle DeltaABC for which triangles DeltaBYC, DeltaCYA, and DeltaAYB have congruent incircles. It is a special case of an Elkies ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...

Geometry which depends only on the first four of Euclid's postulates and not on the parallel postulate. Euclid himself used only the first four postulates for the first 28 ...

A curve which is invariant under inversion. Examples include the cardioid, cartesian ovals, Cassini ovals, Limaçon, strophoid, and Maclaurin trisectrix.

Let M be the midpoint of the arc AMB. Pick C at random and pick D such that MD_|_AC (where _|_ denotes perpendicular). Then AD=DC+BC.