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Externally erect a square on the side BC. Now join the new vertices S_(AB) and S_AC of this square with the vertex A, marking the points of intersection Q_(A,BC) and ...

Square triangle picking is the selection of triples of points (corresponding to endpoints of a triangle) randomly placed inside a square. n random triangles can be picked in ...

Intuitively, a model of d-dimensional percolation theory is said to be a Bernoulli model if the open/closed status of an area is completely random. In particular, it makes ...

An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformations (such as rotation, reflection, inversion, or more ...

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...

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 ...

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 ...