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A solid of revolution is a solid enclosing the surface of revolution obtained by rotating a 1-dimensional curve, line, etc. about an axis. A portion of a solid of revolution ...

Sangaku problems, often written "san gaku," are geometric problems of the type found on devotional mathematical wooden tablets ("sangaku") which were hung under the roofs of ...

An infinite sequence of circles such that every four consecutive circles are mutually tangent, and the circles' radii ..., R_(-n), ..., R_(-1), R_0, R_1, R_2, R_3, R_4, ..., ...

Any one of the eight Apollonius circles of three given circles is tangent to a circle H known as a Hart circle, as are the other three Apollonius circles having (1) like ...

The radius rho of the midsphere of a polyhedron, also called the interradius. Let P be a point on the original polyhedron and P^' the corresponding point P on the dual. Then ...

In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a ...

While early soccer balls were constructed in a number of ways, a fairly stadard 32-panel ball was designed by Danish national team goalkeeer Eigil Nielsen in 1962. This was ...

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

A 4-sphere has positive curvature, with R^2=x^2+y^2+z^2+w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)+2w=0. (2) Since r=xx^^+yy^^+zz^^ (3) dw = -(xdx+ydy+zdz)/w (4) = ...

The bend of a circle C mutually tangent to three other circles is defined as the signed curvature of C. If the contacts are all external, the signs of the bends of all four ...