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A curve named and studied by Newton in 1701 and contained in his classification of cubic curves. It had been studied earlier by L'Hospital and Huygens in 1692 (MacTutor ...

A constant-curvature surface which can be given parametrically by x = rcosphi (1) y = rsinphi (2) z = (ln[tan(1/2v)]+a(C+1)cosv)/(sqrt(C)), (3) where phi = ...

A plane shape constructed by Reinhardt (1934) that is conjectured to be the "worst" packer of all centrally-symmetric plane regions. It has a packing density of ...

The south pole is the point on a sphere with minimum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...

There are two incompatible definitions of the squircle. The first defines the squircle as the quartic plane curve which is special case of the superellipse with a=b and r=4, ...

A star polygon {p/q}, with p,q positive integers, is a figure formed by connecting with straight lines every qth point out of p regularly spaced points lying on a ...

Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to ...

The geometric centroid of the system obtained by placing a mass equal to the magnitude of the exterior angle at each vertex (Honsberger 1995, p. 120) is called the Steiner ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...