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In each of the ten cases with zero or unit mass, the finite part of the scalar 3-loop tetrahedral vacuum Feynman diagram reduces to four-letter "words" that represent ...

The trigonometric formulas for pi/5 can be derived using the multiple-angle formula sin(5theta)=5sintheta-20sin^3theta+16sin^5theta. (1) Letting theta=pi/5 and x=sintheta ...

Bertrand's postulate, also called the Bertrand-Chebyshev theorem or Chebyshev's theorem, states that if n>3, there is always at least one prime p between n and 2n-2. ...

A Gray code is an encoding of numbers so that adjacent numbers have a single digit differing by 1. The term Gray code is often used to refer to a "reflected" code, or more ...

Any two rectilinear figures with equal area can be dissected into a finite number of pieces to form each other. This is the Wallace-Bolyai-Gerwien theorem. For minimal ...

A primitive root of a prime p is an integer g such that g (mod p) has multiplicative order p-1 (Ribenboim 1996, p. 22). More generally, if GCD(g,n)=1 (g and n are relatively ...

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is ...

Start with an integer n, known as the digitaddition generator. Add the sum of the digitaddition generator's digits to obtain the digitaddition n^'. A number can have more ...

Define a carefree couple as a pair of positive integers (a,b) such that a and b are relatively prime (i.e., GCD(a,b)=1) and a is squarefree. Similarly, define a strongly ...

A two-player game, also called crosscram, in which player H has horizontal dominoes and player V has vertical dominoes. The two players alternately place a domino on a board ...