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The Greek word for 10000.

If J is a simple closed curve in R^2, then the Jordan curve theorem, also called the Jordan-Brouwer theorem (Spanier 1966) states that R^2-J has two components (an "inside" ...

The hexagon obtained from an arbitrary hexagon by connecting the centroids of each consecutive three sides. This hexagon has equal and parallel sides (Wells 1991). A proof of ...

A theorem outlined by Kolmogorov (1954) which was subsequently proved in the 1960s by Arnol'd (1963) and Moser (1962; Tabor 1989, p. 105). It gives conditions under which ...

The self-intersection of a one-sided surface. The word "cross-cap" is sometimes also written without the hyphen as the single word "crosscap." The cross-cap can be thought of ...

In the English language, the probability of encountering the rth most common word is given roughly by P(r)=0.1/r for r up to 1000 or so. The law breaks down for less frequent ...

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

The only Wiedersehen surfaces are the standard round spheres. The conjecture was proven by combining the Berger-Kazdan comparison theorem with A. Weinstein's results for n ...

Relates invariants of a curve defined over the integers. If this inequality were proven true, then Fermat's last theorem would follow for sufficiently large exponents. ...

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...