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A function f(z) is said to be doubly periodic if it has two periods omega_1 and omega_2 whose ratio omega_2/omega_1 is not real. A doubly periodic function that is analytic ...

A doubly stochastic matrix is a matrix A=(a_(ij)) such that a_(ij)>=0 and sum_(i)a_(ij)=sum_(j)a_(ij)=1 is some field for all i and j. In other words, both the matrix itself ...

A hypergeometric identity discovered by Ramanujan around 1910. From Hardy (1999, pp. 13 and 102-103), (1) where a^((n))=a(a+1)...(a+n-1) (2) is the rising factorial (a.k.a. ...

A simple way to describe a knot projection. The advantage of this notation is that it enables a knot diagram to be drawn quickly. For an oriented alternating knot with n ...

The Droz-Farny circles are a pair of circles of equal radius obtained by particular geometric constructions. The following amazing property of a triangle, first given by ...

If two perpendicular lines are drawn through the orthocenter H of any triangle, these lines intercept each side (or its extension) in two points (labeled P_(12), P_(12)^', ...

[scale=.3]/troves/MathOzTeX/graphics/gifs/melencol.jpg Dürer's magic square is a magic square with magic constant 34 used in an engraving entitled Melencolia I by Albrecht ...

The base-12 number system composed of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B. Such a system has been advocated by no less than Herbert Spencer, John Quincy Adams, and ...

A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a smooth action of the reals or the integers on ...

The EKG sequence is the integer sequence having 1 as its first term, 2 as its second, and with each succeeding term being the smallest number not already used that shares a ...