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The Möbius strip, also called the twisted cylinder (Henle 1994, p. 110), is a one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving ...

Pascal's triangle is a number triangle with numbers arranged in staggered rows such that a_(nr)=(n!)/(r!(n-r)!)=(n; r), (1) where (n; r) is a binomial coefficient. The ...

The simple continued fraction for pi is given by [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, ...] (OEIS A001203). A plot of the first 256 terms of the ...

A ring in the mathematical sense is a set S together with two binary operators + and * (commonly interpreted as addition and multiplication, respectively) satisfying the ...

A run is a sequence of more than one consecutive identical outcomes, also known as a clump. Let R_p(r,n) be the probability that a run of r or more consecutive heads appears ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler, states "at least it seems that every number ...