In mathematics, a doubly periodic function is a function f defined at all points x in a plane and having two "periods", which are linearly independent vectors u and v such that Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... Two intersecting planes in R3 In mathematics, a plane is a fundamental two-dimensional object. ... In linear algebra, a family of vectors is linearly independent if none of them can be written as a linear combination of finitely many other vectors in the collection. ...

See elliptic function for an account of doubly periodic functions that are meromorphic on the complex plane, and fundamental pair of periods for an account of the lattices involved. Also see Jacobi's elliptic functions and Weierstrass's elliptic functions. In complex analysis, an elliptic function is, roughly speaking, a function defined on the complex plane which is periodic in two directions. ... In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function. ... In mathematics, the complex plane is a way of visualising the space of the complex numbers. ... In mathematics, a fundamental pair of periods is an ordered pair of complex numbers that define a lattice in the complex plane. ... See lattice for other meanings of this term, both within and without mathematics. ... In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that have historical importance with also many features that show up important structure, and have direct relevance to some applications (e. ... In mathematics, Weierstrasss elliptic functions are a standard type of elliptic functions (the other is the Jacobis elliptic functions). ...