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The orchard-planting problem (also known as the orchard problem or tree-planting problem) asks that n trees be planted so that there will be r(n,k) straight rows with k trees ...

The variation of a function which exhibits slope changes, also called the saltus of a function. A series may also oscillate, causing it not to converge.

The parabolic cylinder functions are a class of functions sometimes called Weber functions. There are a number of slightly different definitions in use by various authors. ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

A change in a knot projection such that a pair of oppositely oriented strands are passed through another pair of oppositely oriented strands.

A polycube composed of 5 cubes. There are 29 distinct three-dimensional pentacubes (Bouwkamp 1981). Of these, the 12 planar pentacubes (corresponding to solid pentominoes), ...

A short mnemonic for remembering the first seven decimal digits of pi is "How I wish I could calculate pi" (C. Heckman, pers. comm., Feb. 3, 2005). Eight digits are given by ...

The 4-polyhex illustrated above.

A knot obtained from a tangle which can be represented by a finite sequence of integers.

Find the m×n array of single digits which contains the maximum possible number of primes, where allowable primes may lie along any horizontal, vertical, or diagonal line. For ...