zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The hyperbolic triangle defect. (English) Zbl 1062.51013
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 5--12, 2003. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-8-7/pbk). 225-236 (2004).
The author introduces hyperbolic trigonometry by means of gyrovector spaces (for a comprehensive introduction into the theory of gyrogroups and gyrovector spaces see the author’s book [Beyond the Einstein addition law and its gyroscopic Thomas precession. The theory of gyrogroups and gyrovector spaces. Dordrecht: Kluwer (2001; Zbl 0972.83002)]). A special kind of gyrovector spaces is used to describe the Poincaré ball model of hyperbolic geometry [the author, Comput. Math. Appl. 41, No. 1--2, 135--147 (2001; Zbl 0988.51017)]. Within this setting the author derives formulae for the hyperbolic law of sines and cosines, the Pythagorean Theorem, and the angular defect of a hyperbolic triangle. For the entire collection see [Zbl 1048.53002].

51M09Elementary problems in hyperbolic and elliptic geometries
Full Text: Link