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Given a triangle DeltaABC, construct the contact triangle DeltaDEF. Then the Nobbs points are the intersections of the corresponding sides of triangles DeltaABC and DeltaDEF, ...

The insphere of a solid is a sphere that is tangent to all faces of the solid. An insphere does not always exist, but when it does, its radius r is called the inradius and ...

A subset S subset R^n is said to be pseudo-convex at a point x in S if the associated pseudo-tangent cone P_S(x) to S at x contains S-{x}, i.e., if S-{x} subset P_S(x). Any ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. For M in R^3, the second fundamental form is the symmetric bilinear form on the tangent ...

Given a triangle DeltaABC with inner and outer Soddy centers S and S^', respectively, the inner Soddy triangle DeltaPQR (respectively, outer Soddy triangle DeltaP^'Q^'R^') is ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

A quadrilateral tiling is a tiling of the plane by identical quadrilaterals. Any nonself-intersecting quadrilateral (Wells 1991, p. 208) tiles the plane, as illustrated above.

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

A set of plane measure 0 that contains a circle of every radius.