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1000=10^3. The word "thousand" appears in common expressions in a number of languages, for example, "a thousand pardons" in English and "tusen takk" ("a thousand thanks") in ...

The larger an arc is, the smaller its radius appears. For example, the three arcs illustrated above belong circles of the same radius.

The three-chord lemma states that in the figure above, l_1+l_2=2lcostheta.

A logical structure which does not assume the law of the excluded middle. Three truth values are possible: true, false, or undecided. There are 3072 such logics.

The sequence of binary digits of the Thue constant, 0.110110111110110111110110110..._2 (OEIS A014578). A recurrence plot of the limiting value of this sequence is illustrated ...

If n>1, (a,n)=1 (i.e., a and n are relatively prime), and m is the least integer >sqrt(n), then there exist an x and y such that ay=+/-x (mod n) where 0<x<m and 0<y<m (Nagell ...

Maximize the amount of floor space which can be covered with a fixed tile (Hoffman 1998, p. 173).

Due to Lebesgue and Brouwer. If an n-dimensional figure is covered in any way by sufficiently small subregions, then there will exist points which belong to at least n+1 of ...

The operation of multiplication, i.e., a times b. Various notations are a×b, a·b, a*b, ab, and (a)(b). The "multiplication sign" × is based on Saint Andrew's cross (Bergamini ...

A strategy for the iterated prisoner's dilemma in which a prisoner cooperates on the first move, and thereafter copies the previous move of the other prisoner. Any better ...