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- The specific set of points in the unit disc, and hence, its visual appearance, depends on the metric being used. With the standard metric, unit discs look like circles of radius one, but changing the metric changes also the corresponding set of points and therefore the shape of the discs.Canonical name: UnitDiscDate of creation: 2013-03-22 15:47:01Last modified on: 2013-03-22 15:47:01Title: unit discplanetmath.org/unitdisc
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See all on WikipediaUnit disk - Wikipedia
Without further specifications, the term unit disk is used for the open unit disk about the origin, (), with respect to the standard Euclidean metric. It is the interior of a circle of radius 1, centered at the origin. See more
In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1:
See moreOne also considers unit disks with respect to other metrics. For instance, with the taxicab metric and the Chebyshev metric disks look like … See more
• Weisstein, Eric W. "Unit disk". MathWorld.
• On the Perimeter and Area of the Unit Disc, by J.C. Álvarez Pavia and A.C. Thompson See more
The open unit disk forms the set of points for the Poincaré disk model of the hyperbolic plane. Circular arcs perpendicular to the … See more
Wikipedia text under CC-BY-SA license Poincaré metric - Wikipedia
WEBIn mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two-dimensional surface of constant negative curvature. It is the natural …
Poincaré disk model - Wikipedia
WEBIn geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and …
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Natural metric on unit disk - Mathematics Stack Exchange
WEBIt seems that the only natural metric on the unit disk is the hyperbolic one. I think the answer is negative because the metric is induced by the Riemann surface structure and …
unit disc - PlanetMath.org
WEBWith the standard metric, unit discs look like circles of radius one, but changing the metric changes also the corresponding set of points and therefore the shape of the discs. For …
Poincaré Hyperbolic Disk -- from Wolfram MathWorld
WEBThe Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ds^2=(dx^2+dy^2)/((1-x^2 …
WEBthe Mobius group and Bergman metric on the unit disk, and¨ discusses the theory of atomic decomposition and some ap-plications. We refer the reader to the references …
WEBThe hyperbolic plane is the unit disk D with the hyperbolic metric λD(z)|dz| = 2|dz| 1−|z|2. This metric induces a hyperbolic distance dD(z,w) between two points z and w in D in …
WEBIn order to give a model for H 2, we need to decide on a set of points, then determine what lines are and how to measure distance. For Poincar ́e’s Disk Model we take the set of …
Triangular ratio metric in the unit disk - Taylor & Francis Online
WEBThe triangular ratio metric is studied in a domain G ⊊ R n, n ≥ 2. Several sharp bounds are proven for this metric, especially in the case where the domain is the unit disk of the …
WEBIn this paper, we will provide an introduction to the constructs of hyperbolic geometry using two of these models. The rst part will be a development of hyperbolic geometry in the …
WEBIn this paper, we show that for the metric induced by the unit-disk graph on n points and for any constant c ̧ 1, there does exist a c-well-separated pair decomposition with O(n …
2 - Hyperbolic metric in the unit disk - Cambridge University Press ...
WEBHyperbolic metric in the unit disk Linda Keen , City University of New York , Nikola Lakic , City University of New York Book: Hyperbolic Geometry from a Local Viewpoint
Curvature of complete conformal metrics on the open unit disk
WEBLet $D$ be the unit disk in the complex plane, and assume that $g$ is a Riemannian metric on $D$ which is complete and conformal to the standard Euclidean metric. Can …
Local moduli space of flat metrics of a punctured disk.
WEBLet us consider a 2-dimensional unit disk $U_0$ with a puncture at $0$ and some Riemannian metric $g$ on it, which is $\textbf{flat}$ near the puncture. ( Remark: $g$ …
WEBThe pseudohyperbolic metric in the unit disk D is defined by the formula ρ(z,w)=|ϕ w(z)|,ϕ w(z)= w−z 1−wz, where z,w∈ D. It is a true metric; in fact, the triangle inequality …
complex analysis - Möbius Transforms that preserve the unit disk ...
WEBProve that every automorphism of the unit disc can be written in the following form: A(z) =eiθ z+a 1+a¯z, where θ is a real number and a is a point in the unit disk which is …
List of metric units - Wikipedia
WEBThe first group of metric units are those that are at present defined as units within the International System of Units (SI). In its most restrictive interpretation, this is what may …
Isometry from unit disc onto itself with the hyperbolic metric
WEBThe hyperbolic metric is defined in the book by $$g(v, w) = \frac{4 v \bullet w}{(1 - ||p||^{2})^{2}},$$ where $p$ is a point in the unit disc $U = \{ (x_{1}, x_{2}) \in …
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