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There are a number of tilings of various shapes by all the 12 order n=6 polyiamonds, summarized in the following table. Several of these (starred in the table below) are also ...

The hyperbolic cotangent is defined as cothz=(e^z+e^(-z))/(e^z-e^(-z))=(e^(2z)+1)/(e^(2z)-1). (1) The notation cthz is sometimes also used (Gradshteyn and Ryzhik 2000, p. ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

The problem of determining how many nonattacking knights K(n) can be placed on an n×n chessboard. For n=8, the solution is 32 (illustrated above). In general, the solutions ...

There are two distinct entities both known as the Lagrange number. The more common one arises in rational approximation theory (Conway and Guy 1996), while the other refers ...

A second-order ordinary differential equation arising in the study of stellar interiors, also called the polytropic differential equations. It is given by ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

The Maclaurin trisectrix is a curve first studied by Colin Maclaurin in 1742. It was studied to provide a solution to one of the geometric problems of antiquity, in ...

Given a map with genus g>0, Heawood showed in 1890 that the maximum number N_u of colors necessary to color a map (the chromatic number) on an unbounded surface is N_u = ...

A Markov chain is collection of random variables {X_t} (where the index t runs through 0, 1, ...) having the property that, given the present, the future is conditionally ...