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In the case of a general surface, the distance between two points measured along the surface is known as a geodesic. For example, the shortest distance between two points on ...

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 ...

The mean triangle area of a triangle picked inside a regular n-gon of unit area is A^__n=(9cos^2omega+52cosomega+44)/(36n^2sin^2omega), (1) where omega=2pi/n (Alikoski 1939; ...

A polyhedron compound is an arrangement of a number of interpenetrating polyhedra, either all the same or of several distinct types, usually having visually attractive ...

There are four fully supported stellations of the rhombic dodecahedron including as usual the original solid in the count (Wells 1991; Webb). The three nontrivial ones ...

Let the inner and outer Soddy triangles of a reference triangle DeltaABC be denoted DeltaPQR and DeltaP^'Q^'R^', respectively. Similarly, let the tangential triangles of ...

A semicubical parabola is a curve of the form y=+/-ax^(3/2) (1) (i.e., it is half a cubic, and hence has power 3/2). It has parametric equations x = t^2 (2) y = at^3, (3) and ...

A curve which may pass through any region of three-dimensional space, as contrasted to a plane curve which must lie in a single plane. Von Staudt (1847) classified space ...

A projection of the Veronese surface into three dimensions (which must contain singularities) is called a Steiner surface. A classification of Steiner surfaces allowing ...

A map projection obtained by projecting points P on the surface of sphere from the sphere's north pole N to point P^' in a plane tangent to the south pole S (Coxeter 1969, p. ...