Poincaré disc model - Factbites

Poincaré disc model - Factbites
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Topic: Poincaré disc model

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	John R. Parker's Home Page
		Our department logo at the top right hand corner of this page depicts the Poincaré disc model of the hyperbolic plane together with the fundamental domain for an ideal triangle group and several of its images.
		Representations of free Fuchsian groups in complex hyperbolic space,
		Combinatorics of simple closed curves on the twice punctured torus
	www.maths.dur.ac.uk /~dma0jrp

	Amazon.com: Hyperbolic Geometry (Springer Undergraduate Mathematics Series): Books: James W Anderson
		Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.
		Provides a self-contained introduction to the subject of hyperbolic geometry, taking the approach that the subject consists of the study of those quantities invariant under the action of a natural group of transformations.
		The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries.
	www.amazon.com /exec/obidos/tg/detail/-/1852331569?v=glance (727 words)

	Amazon.com: Books: Hyperbolic Geometry (Springer Undergraduate Mathematics Series)
		Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincar&; disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.
		The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries.
		Provides a self-contained introduction to the subject of hyperbolic geometry, taking the approach that the subject consists of the study of those quantities invariant under the action of a natural group of transformations.
	www.amazon.com /exec/obidos/tg/detail/-/1852331569?v=glance (609 words)

	Hyperbolic Geometry (Springer Undergraduate Mathematics Series) - Virtual Mall .org
		Topics covered include the upper half-space model of the hyperbolic plane, Mbius transformations, the general Mbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincar disc model, convex subsets of the hyperbolic plane, the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.
		The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics.
		This book provides a self-contained introduction to the subject, taking the approach that hyperbolic geometry consists of the study of those quantities invariant under the action of a natural group of transformations.
	www.virtual-mall.org /Product/Book/48048.html (609 words)

	Amazon.fr : Livres en anglais: Hyperbolic Geometry
		Topics covered include the upper half-space model of the hyperbolic plane, Mbius transformations, the general Mbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincar disc model, convex subsets of the hyperbolic plane, the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.
		The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics.
		This book provides a self-contained introduction to the subject, taking the approach that hyperbolic geometry consists of the study of those quantities invariant under the action of a natural group of transformations.
	www.amazon.fr /exec/obidos/ASIN/1852331569/ww2afvportal-21 (609 words)

	ISTE September (No. 1)
		The first two explorations highlight the difference between hyperbolic and Euclidean geometry, and the last two use the Poincaré disc as a model of absolute geometry.
		If the two points do not lie on a diameter, the task of drawing the orthogonal circle is sufficiently difficult to prevent this model from being a useful pencil-and-paper exploration activity.
		Discovering where the standard Euclidean geometry proof breaks down, that the angle sum of triangle ABC is not 180° in hyperbolic geometry, can be an interesting group project.
	www.iste.org /inhouse/publications/ll/28/1/32c/index.cfm?Section=LL_28_1 (609 words)

	Hyperbolic Geometry
		It was with this in mind that I started to construct a series of Cabri macros and an ever growing menu for constructions for hyperbolic (or non-Euclidean) geometry in the Poincaré disc model.
		The diagram was built up from an initial triangle with a vertex at the centre, by reflection (inversion in a disc line) about one of its sides.
		The menu commands can be used to draw figures that illustrate some of the fascinating results and figures to be found in the hyperbolic plane.
	mcs.open.ac.uk /tcl2/nonE/nonE.html (609 words)

	The Poincaré Disk and the Upper Half Plane
		Another involves stereographically mapping the Poincaré disc directly onto half of a unit sphere, turning the sphere on its side, and then stereographically projecting onto the plane z=0.
		The result is the Upper Half Plane model of hyperbolic 2-space.
		This is another model of hyperbolic space, though not a standard one, and thus we do not cover it in detail.
	www.geom.uiuc.edu /~crobles/hyperbolic/hypr/ibm/puhp (332 words)

	Klein-Beltrami and Upper Half Plane
		We go from the Klein disc to the hemisphere (as in the Klein/Poincaré movie, and from there proceed to the Upper Half Plane, as in the Poincaré/UHP mpeg.
		The Klein-Beltrami Model and the Upper Half Plane
		And now stretch the hemisphere to cover the half plane, using a stereographic projection through the point (0,0,2) at the top of the hemisphere onto the plane z=0, on which the (completed) sphere sits.
	www.geom.uiuc.edu /~crobles/hyperbolic/hypr/ibm/kbuhp (332 words)

	Hyperbolic Geometry
		It was with this in mind that I started to construct a series of Cabri macros and an ever growing menu for constructions for hyperbolic (or non-Euclidean) geometry in the Poincaré disc model.
		The menu commands can be used to draw figures that illustrate some of the fascinating results and figures to be found in the hyperbolic plane.
		Parts of the tessellation are shown in varying degrees of layers in each of the quarters.
	mcs.open.ac.uk /tcl2/nonE/nonE.html (353 words)

	Hyperbolic Geometry
		It was with this in mind that I started to construct a series of Cabri macros and an ever growing menu for constructions for hyperbolic (or non-Euclidean) geometry in the Poincaré disc model.
		The menu commands can be used to draw figures that illustrate some of the fascinating results and figures to be found in the hyperbolic plane.
		Parts of the tessellation are shown in varying degrees of layers in each of the quarters.
	mcs.open.ac.uk /tcl2/nonE/nonE.html (353 words)

	Hyperbolic Geometry
		It was with this in mind that I started to construct a series of Cabri macros and an ever growing menu for constructions for hyperbolic (or non-Euclidean) geometry in the Poincaré disc model.
		The menu commands can be used to draw figures that illustrate some of the fascinating results and figures to be found in the hyperbolic plane.
		A result of both Euclidean and Hyperbolic geometry.
	mcs.open.ac.uk /tcl2/nonE/nonE.html (353 words)

	Hyperbolic Geometry
		It was with this in mind that I started to construct a series of Cabri macros and an ever growing menu for constructions for hyperbolic (or non-Euclidean) geometry in the Poincaré disc model.
		Parts of the tessellation are shown in varying degrees of layers in each of the quarters.
		The menu commands can be used to draw figures that illustrate some of the fascinating results and figures to be found in the hyperbolic plane.
	mcs.open.ac.uk /tcl2/nonE/nonE.html (353 words)

	Hyperbolic Geometry
		It was with this in mind that I started to construct a series of Cabri macros and an ever growing menu for constructions for hyperbolic (or non-Euclidean) geometry in the Poincaré disc model.
		The menu commands can be used to draw figures that illustrate some of the fascinating results and figures to be found in the hyperbolic plane.
		A result of both Euclidean and Hyperbolic geometry.
	mcs.open.ac.uk /tcl2/nonE/nonE.html (353 words)

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