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A cork plug is a three-dimensional solid that can stopper a square, triangular, or circular hole. There is an infinite family of such shapes. The shape with smallest volume ...

A spiral that gives the solution to the central orbit problem under a radial force law r^..=-mu|r|^(-3)r^^, (1) where mu is a positive constant. There are three solution ...

A family gamma of nonempty subsets of X whose union contains the given set X (and which contains no duplicated subsets) is called a cover (or covering) of X. For example, ...

The Császár polyhedron is a polyhedron that is topologically equivalent to a torus which was discovered in the late 1940s by Ákos Császár (Gardner 1975). It has 7 polyhedron ...

Given the above figure (without looking at the figure below!), determine how to disengage the two slotted cube halves without cutting, breaking, or distorting. One possible ...

An equation of the form y=ax^3+bx^2+cx+d, (1) where the three roots of the equation coincide (and are therefore real), i.e., y=a(x-r)^3=a(x^3-3rx^2-3r^2x-r^3). (2) Loomis ...

The cubitruncated cuboctahedron (called the cubotruncated cuboctahedron by Wenninger 1971, p. 121) is the uniform polyhedron with Maeder index 16 (Maeder 1997), Wenninger ...

The cubohemioctahedron is the uniform polyhedron with Maeder index 15 (Maeder 1997), Wenninger index 78 (Wenninger 1989), Coxeter index 51 (Coxeter et al. 1954), and Har'El ...

An n-gonal cupola Q_n is a polyhedron having n obliquely oriented triangular and n rectangular faces separating an {n} and a {2n} regular polygon, each oriented horizontally. ...

A curve whose centrode revolves about a fixed axis with constant angle and speed when the curve is traversed with unit speed. The tangent indicatrix of a curve of constant ...