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The n-hypersphere (often simply called the n-sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) ...

Given three coins of possibly different sizes which are arranged so that each is tangent to the other two, find the coin which is tangent to the other three coins. The ...

Möbius tetrahedra, also called Möbius tetrads (Baker 1922, pp. 61-62) are a pair of tetrahedra, each of which has all the vertices lying on the faces of the other: in other ...

Let three isoscelizers I_(AC)I_(AB), I_(BA)I_(BC), and I_(CA)I_(CB) be constructed on a triangle DeltaABC, one for each side. This makes all of the inner triangles similar to ...

The regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral ...

An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is ...

The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. ...

A connex is a geometric form introduced by Clebsch (1872) that included as special cases the curve considered as a point locus and the curve considered as a line envelope ...

The normal vector, often simply called the "normal," to a surface is a vector which is perpendicular to the surface at a given point. When normals are considered on closed ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...