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If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.
Spherical triangles into which a sphere is divided by the planes of symmetry of a uniform polyhedron.
A cyclide formed by inversion of a standard torus when inversion sphere is tangent to the torus.
A parabolic cyclide formed by inversion of a horn torus when the inversion sphere is tangent to the torus.
A parabolic cyclide formed by inversion of a ring torus when the inversion sphere is tangent to the torus.
A parabolic cyclide formed by inversion of a spindle torus when the inversion sphere is tangent to the torus.
The parallel curves for (outward) offset k of an ellipse with semi-axis lengths a and b are given by x_p = (a+(bk)/(sqrt(a^2sin^2t+b^2cos^2t)))cost (1) y_p = ...
A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...
The term "twisted sphere" is used to mean either a projective plane (Henle 1994, p. 110) or the corkscrew surface obtained by extending a sphere along a diameter and then ...
There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...
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