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There are a few plane curves known as "bean curves." The bean curve identified by Cundy and Rowllet (1989, p. 72) is the quartic curve given by the implicit equation ...

The curve formed by the intersection of a cylinder and a sphere is known as Viviani's curve. The problem of finding the lateral surface area of a cylinder of radius r ...

Find a closed plane curve of a given perimeter which encloses the greatest area. The solution is a circle. If the class of curves to be considered is limited to smooth ...

By analogy with the squircle, a term first apparently used by Fernández Guasti et al. (2005), the term "rectellipse" (used here for the first time) is a natural ...

Define the minimal bounding rectangle as the smallest rectangle containing a given lattice polygon. If the perimeter of the lattice polygon is equal to that of its minimal ...

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

Given a general quadrilateral with sides of lengths a, b, c, and d, the area is given by K = 1/4sqrt(4p^2q^2-(b^2+d^2-a^2-c^2)^2) (1) = (2) (Coolidge 1939; Ivanov 1960; Beyer ...

Given triangle DeltaA_1A_2A_3, let the point of intersection of A_2Omega and A_3Omega^' be B_1, where Omega and Omega^' are the Brocard points, and similarly define B_2 and ...

A projection which maps a sphere (or spheroid) onto a plane. Map projections are generally classified into groups according to common properties (cylindrical vs. conical, ...