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The quadrifolium is the 4-petalled rose curve having n=2. It has polar equation r=asin(2theta) (1) and Cartesian equation (x^2+y^2)^3=4a^2x^2y^2. (2) The area of the ...

A rounded rectangle is the shape obtained by taking the convex hull of four equal circles of radius r and placing their centers at the four corners of a rectangle with side ...

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...

As shown by Schnirelman (1944), a square can be inscribed in any closed convex curve, although it is not known if this holds true for every Jordan curve (Steinhaus 1999, p. ...

Egg-shaped curves constructed using multiple circles which Thom (1967) used to model Megalithic stone rings in Britain.

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

A Gray code is an encoding of numbers so that adjacent numbers have a single digit differing by 1. The term Gray code is often used to refer to a "reflected" code, or more ...

The Wigner 6j-symbols (Messiah 1962, p. 1062), commonly simply called the 6j-symbols, are a generalization of Clebsch-Gordan coefficients and Wigner 3j-symbol that arise in ...

"Conext 21 polyhedron" is the name given here to the solid underlying the soccer ball of the 2020 Tokyo Olympic Games (held in 2021). It is implemented in the Wolfram ...

Let Delta denote an integral convex polytope of dimension n in a lattice M, and let l_Delta(k) denote the number of lattice points in Delta dilated by a factor of the integer ...