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In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

Sangaku problems, often written "san gaku," are geometric problems of the type found on devotional mathematical wooden tablets ("sangaku") which were hung under the roofs of ...

The digits in the number 2187 form the two vampire numbers: 21×87=1827 and 2187=27×81. 2187 is also given by 3^7.

An Alexander matrix is a presentation matrix for the Alexander invariant H_1(X^~) of a knot K. If V is a Seifert matrix for a tame knot K in S^3, then V^(T)-tV and V-tV^(T) ...

The Bolyai expansion of a real number x is a nested root of the form x=a_0-1+RadicalBox[{{a, _, 1}, +, RadicalBox[{{a, _, 2}, +, RadicalBox[{{a, _, 3}, +, ...}, m]}, m]}, m], ...

The Machin-like formula 1/4pi=cot^(-1)(2)+cot^(-1)(3). The other 2-term Machin-like formulas are Hermann's formula, hutton's formula, and Machin's formula.

Let M subset R^3 be a regular surface and u_(p) a unit tangent vector to M, and let Pi(u_(p),N(p)) be the plane determined by u_(p) and the normal to the surface N(p). Then ...

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 ...

A triangle with side lengths a, b, and c and triangle area Delta satisfies a^2+b^2+c^2>=4sqrt(3)Delta. Equality holds iff the triangle is equilateral.

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property ...