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The Hadwiger-Nelson problem asks for the chromatic number of the plane, i.e., the minimum number of colors needed to color the plane if no two points at unit distance one ...

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...

Bouwer graphs, a term coined here for the first time, are a family of regular graphs which includes members that are symmetric but not arc-transitive. Such graphs are termed ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

The number of digits D in an integer n is the number of numbers in some base (usually 10) required to represent it. The numbers 1 to 9 are therefore single digits, while the ...

There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

A repunit prime is a repunit (i.e., a number consisting of copies of the single digit 1) that is also a prime number. The base-10 repunit (possibly probable) primes ...

The hundred-dollar, hundred-digits challenge problems are a set of ten problems in numerical analysis published in the January/February 2002 issue of SIAM News ...

The curlicue fractal is a figure obtained by the following procedure. Let s be an irrational number. Begin with a line segment of unit length, which makes an angle phi_0=0 to ...

A very useful active feedback method for controlling things like temperature control systems, servo motors, and flow control valves.