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An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only ...

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

In Robert Louis Stevenson's "bottle imp paradox," you are offered the opportunity to buy, for whatever price you wish, a bottle containing a genie who will fulfill your every ...

A function with k continuous derivatives is called a C^k function. In order to specify a C^k function on a domain X, the notation C^k(X) is used. The most common C^k space is ...

A canonical labeling, also called a canonical form, of a graph G is a graph G^' which is isomorphic to G and which represents the whole isomorphism class of G (Piperno 2011). ...

If r is the inradius of a circle inscribed in a right triangle with sides a and b and hypotenuse c, then r=1/2(a+b-c). (1) A Sangaku problem dated 1803 from the Gumma ...

The Cookson Hills series is the series similar to the Flint Hills series, but with numerator sec^2n instead of csc^2n: S_2=sum_(n=1)^infty(sec^2n)/(n^3) (Pickover 2002, p. ...

The Curry triangle, also sometimes called the missing square puzzle, is a dissection fallacy created by American neuropsychiatrist L. Vosburgh Lions as an example of a ...

An implicit method for solving an ordinary differential equation that uses f(x_n,y_n) in y_(n+1). In the case of a heat equation, for example, this means that a linear system ...

A shuffle of a deck of cards obtained by successively exchanging the cards in position 1, 2, ..., n with cards in randomly chosen positions. For 4<=n<=17, the most frequent ...