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45 relations: American Mathematical Society, Automorphic function, Bring's curve, Cambridge University Press, Carl Ludwig Siegel, Cayley transform, Conformal map, Conjugacy class, Continued fraction, Cornell University, Covering space, Cross-ratio, Erich Hecke, Farey sequence, Free product, Fundamental domain, Group action, Henri Poincaré, Hermann Schwarz, Hyperbolic triangle, Hypergeometric function, Ideal triangle, Jordan curve theorem, Mathematics, Möbius transformation, Modular group, Modular lambda function, Monodromy, Monodromy theorem, Ordinary differential equation, Oxford University Press, Princeton University Press, Projective harmonic conjugate, Regular singular point, Riemann sphere, Riemann surface, Riemannian manifold, Schottky group, Schwarz reflection principle, Schwarz triangle, Schwarz–Christoffel mapping, Schwarzian derivative, Stern–Brocot tree, Tessellation, Upper half-plane.
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Automorphic function
In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient space.
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Bring's curve
In mathematics, Bring's curve (also called Bring's surface) is the curve given by the equations It was named by after Erland Samuel Bring who studied a similar construction in 1786 in a Promotionschrift submitted to the University of Lund.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Carl Ludwig Siegel
Carl Ludwig Siegel (December 31, 1896 – April 4, 1981) was a German mathematician specialising in number theory and celestial mechanics.
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Cayley transform
In mathematics, the Cayley transform, named after Arthur Cayley, is any of a cluster of related things.
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Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
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Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
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Continued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.
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Cornell University
Cornell University is a private and statutory Ivy League research university located in Ithaca, New York.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Cross-ratio
In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line.
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Erich Hecke
Erich Hecke (20 September 1887 – 13 February 1947) was a German mathematician.
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Farey sequence
In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions between 0 and 1 which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size.
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Free product
In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “most general” group having these properties.
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Fundamental domain
Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.
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Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
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Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
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Hermann Schwarz
Karl Hermann Amandus Schwarz (25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis.
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Hyperbolic triangle
In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane.
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Hypergeometric function
In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.
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Ideal triangle
In hyperbolic geometry an ideal triangle is a hyperbolic triangle whose three vertices all are ideal points.
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Jordan curve theorem
In topology, a Jordan curve, sometimes called a plane simple closed curve, is a non-self-intersecting continuous loop in the plane.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Möbius transformation
In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.
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Modular group
In mathematics, the modular group is the projective special linear group PSL(2,Z) of 2 x 2 matrices with integer coefficients and unit determinant.
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Modular lambda function
In mathematics, the elliptic modular lambda function λ(&tau) is a highly symmetric holomorphic function on the complex upper half-plane.
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Monodromy
In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity.
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Monodromy theorem
In complex analysis, the monodromy theorem is an important result about analytic continuation of a complex-analytic function to a larger set.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Oxford University Press
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
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Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
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Projective harmonic conjugate
In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction: The point D does not depend on what point L is taken initially, nor upon what line through C is used to find M and N. This fact follows from Desargues theorem.
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Regular singular point
In mathematics, in the theory of ordinary differential equations in the complex plane \mathbb, the points of \mathbb are classified into ordinary points, at which the equation's coefficients are analytic functions, and singular points, at which some coefficient has a singularity.
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Riemann sphere
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.
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Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
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Riemannian manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
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Schottky group
In mathematics, a Schottky group is a special sort of Kleinian group, first studied by.
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Schwarz reflection principle
In mathematics, applying the Schwarz reflection principle is a way to extend the domain of definition of an analytic function of a complex variable, F, which is defined on the upper half-plane and has well-defined and real number boundary values on the real axis.
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Schwarz triangle
In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere, possibly overlapping, through reflections in its edges.
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Schwarz–Christoffel mapping
In complex analysis, a Schwarz–Christoffel mapping is a conformal transformation of the upper half-plane onto the interior of a simple polygon.
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Schwarzian derivative
In mathematics, the Schwarzian derivative, named after the German mathematician Hermann Schwarz, is a certain operator that is invariant under all linear fractional transformations.
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Stern–Brocot tree
In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree.
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Tessellation
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
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Upper half-plane
In mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part: The term arises from a common visualization of the complex number x + iy as the point (x,y) in the plane endowed with Cartesian coordinates.
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References
[1] https://en.wikipedia.org/wiki/Schwarz_triangle_function
