Getting this item's online copy...
Find a copy in the library
Getting this item's location and availability...
Find it in libraries globally
|Additional Physical Format:||Print version:|
|Material Type:||Document, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
Arlan Ramsay; Robert D Richtmyer
|Description:||1 online resource (xii, 289 pages).|
|Contents:||1 Axioms for Plane Geometry --
2 Some Neutral Theorems of Plane Geometry --
3 Qualitative Description of the Hyperbolic Plane --
4?3 and Euclidean Approximations in?2 --
5 Differential Geometry of Surfaces --
6 Quantitative Considerations --
7 Consistency and Categoricalness of the Hyperbolic Axioms; The Classical Models --
8 Matrix Representation of the Isometry Group --
9 Differential and Hyperbolic Geometry in More Dimensions --
10 Connections with the Lorentz Group of Special Relativity --
11 Constructions by Straightedge and Compass in the Hyperbolic Plane.
|Responsibility:||by Arlan Ramsay, Robert D. Richtmyer.|
This text for advanced undergraduates emphasizes the logical connections of the subject. The derivations of formulas from the axioms do not make use of models of the hyperbolic plane until the axioms are shown to be categorical; the differential geometry of surfaces is developed far enough to establish its connections to the hyperbolic plane; and the axioms and proofs use the properties of the real number system to avoid the tedium of a completely synthetic approach. The development includes properties of the isometry group of the hyperbolic plane, tilings, and applications to special relativity. Elementary techniques from complex analysis, matrix theory, and group theory are used, and some mathematical sophistication on the part of students is thus required, but a formal course in these topics is not a prerequisite.
Retrieving notes about this item