Relevant bibliographies by topics / Hyperbolic Geometry / Journal articles
To see the other types of publications on this topic, follow the link: Hyperbolic Geometry.

Journal articles on the topic 'Hyperbolic Geometry'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 August 2024

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Hyperbolic Geometry.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Reynolds, William F. "Hyperbolic Geometry on a Hyperboloid." American Mathematical Monthly 100, no. 5 (May 1993): 442. http://dx.doi.org/10.2307/2324297.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Reynolds, William F. "Hyperbolic Geometry on a Hyperboloid." American Mathematical Monthly 100, no. 5 (May 1993): 442–55. http://dx.doi.org/10.1080/00029890.1993.11990430.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Kostin, A. V., and I. Kh Sabitov. "Smarandache Theorem in Hyperbolic Geometry." Zurnal matematiceskoj fiziki, analiza, geometrii 10, no. 2 (June 25, 2014): 221–32. http://dx.doi.org/10.15407/mag10.02.221.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Li, Hongbo. "Hyperbolic geometry with geometric algebra." Chinese Science Bulletin 42, no. 3 (February 1997): 262–63. http://dx.doi.org/10.1007/bf02882454.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Lord, Nick, and B. Iversen. "Hyperbolic Geometry." Mathematical Gazette 79, no. 486 (November 1995): 622. http://dx.doi.org/10.2307/3618121.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Baseilhac, Stephane, and Riccardo Benedetti. "Quantum hyperbolic geometry." Algebraic & Geometric Topology 7, no. 2 (June 20, 2007): 845–917. http://dx.doi.org/10.2140/agt.2007.7.845.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Ungar, Abraham A. "Ptolemy’s Theorem in the Relativistic Model of Analytic Hyperbolic Geometry." Symmetry 15, no. 3 (March 4, 2023): 649. http://dx.doi.org/10.3390/sym15030649.

Full text
Abstract:
Ptolemy’s Theorem in Euclidean geometry, named after the Greek astronomer and mathematician Ptolemy, is well-known. By means of the relativistic model of hyperbolic geometry, we translate Ptolemy’s Theorem from Euclidean geometry into the hyperbolic geometry of Lobachevsky and Bolyai. The relativistic model of hyperbolic geometry is based on the Einstein addition of relativistically admissible velocities and, as such, it coincides with the well-known Beltrami–Klein ball model of hyperbolic geometry. The translation of Ptolemy’s Theorem from Euclidean geometry into hyperbolic geometry is achieved by means of hyperbolic trigonometry, called gyrotrigonometry, to which the relativistic model of analytic hyperbolic geometry gives rise.
APA, Harvard, Vancouver, ISO, and other styles
8

Eppstein, David, and Michael T. Goodrich. "Succinct Greedy Geometric Routing Using Hyperbolic Geometry." IEEE Transactions on Computers 60, no. 11 (November 2011): 1571–80. http://dx.doi.org/10.1109/tc.2010.257.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Eskew, Russell Clark. "Suspending the Principle of Relativity." Applied Physics Research 8, no. 2 (March 29, 2016): 82. http://dx.doi.org/10.5539/apr.v8n2p82.

Full text
Abstract:
A unique hyperbolic geometry paradigm requires suspending the Relativistic principle that absolute velocity is unmeasurable. The idea that of two observers each sees the same constant velocity, therefore there is no absolute velocity, is true only because Relativity uses a particular Lorentz geometry. Our mathematical geometry constructs circle and hyperbola vectors with hyperbolic terms in an original formulation of complex numbers. We use a point on a hyperbola as a frame of reference. A theory of time is given. The physical laws of motion by Galileo, Newton and Einstein are forged using the absolute velocity and the precondition to electromagnetic velocity. The field of real and fictitious force accelerations is established. We utilize Galilean Invariance to measure absolute velocity. An experiment exemplifies the math from the Earth’s frame of reference. But Relativity is based on local Lorentz geometry. We discover a possible dark energy and gravitational accelerations and a geometry of gravitational collapse.
APA, Harvard, Vancouver, ISO, and other styles
10

Lohkamp, Joachim. "Hyperbolic Unfoldings of Minimal Hypersurfaces." Analysis and Geometry in Metric Spaces 6, no. 1 (August 1, 2018): 96–128. http://dx.doi.org/10.1515/agms-2018-0006.

Full text
Abstract:
Abstract We study the intrinsic geometry of area minimizing hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. Namely, for any such hypersurface H we define and construct a so-called S-structure. This new and natural concept reveals some unexpected geometric and analytic properties of H and its singularity set Ʃ. Moreover, it can be used to prove the existence of hyperbolic unfoldings of H\Ʃ. These are canonical conformal deformations of H\Ʃ into complete Gromov hyperbolic spaces of bounded geometry with Gromov boundary homeomorphic to Ʃ. These new concepts and results naturally extend to the larger class of almost minimizers.
APA, Harvard, Vancouver, ISO, and other styles
11

Eskew, Russell Clark. "Altering the Principle of Relativity." Applied Physics Research 10, no. 3 (May 31, 2018): 21. http://dx.doi.org/10.5539/apr.v10n3p23.

Full text
Abstract:
A unique hyperbolic geometry paradigm requires altering the Relativistic principle that absolute velocity is unmeasurable. There is no absolute velocity, but in the case where a constant velocity is made from a half-angle velocity, a variable velocity is the same as (absolute) acceleration. Relativity is based on local Lorentz geometry. Our mathematical geometry constructs circle and hyperbola vectors with hyperbolic terms in an original formulation of complex numbers. We use a point on a hyperbola as a frame of reference. A theory is given that time and our velocity are inversely related. The physical laws of motion by Galileo, Newton and Einstein are forged using the half-angle velocity to electromagnetic velocity. The field of kinetic, potential and gravitational force accelerations is established. An experiment exemplifies the math from the Earth’s frame of reference. We discover a possible dark energy and gravitational accelerations and a geometry of gravitational collapse.
APA, Harvard, Vancouver, ISO, and other styles
12

Zeitler, H. "Packings in hyperbolic geometry." Teaching Mathematics and Computer Science 2, no. 2 (November 9, 2015): 209–29. http://dx.doi.org/10.5485/tmcs.2004.0040.

Full text
APA, Harvard, Vancouver, ISO, and other styles
13

Crilly, Tony, John Stillwell, and Michael Henle. "Sources of Hyperbolic Geometry." Mathematical Gazette 83, no. 497 (July 1999): 357. http://dx.doi.org/10.2307/3619103.

Full text
APA, Harvard, Vancouver, ISO, and other styles
14

Guillopé, Laurent. "Hyperfunctions in hyperbolic geometry." Complex Variables and Elliptic Equations 59, no. 11 (July 10, 2013): 1559–71. http://dx.doi.org/10.1080/17476933.2013.805412.

Full text
APA, Harvard, Vancouver, ISO, and other styles
15

Ratcliffe, John G., Arlan Ramsay, and Robert D. Richtmyer. "Introduction to Hyperbolic Geometry." American Mathematical Monthly 103, no. 2 (February 1996): 185. http://dx.doi.org/10.2307/2975123.

Full text
APA, Harvard, Vancouver, ISO, and other styles
16

Gehring, F. W., and K. Hag. "Hyperbolic geometry and disks." Journal of Computational and Applied Mathematics 105, no. 1-2 (May 1999): 275–84. http://dx.doi.org/10.1016/s0377-0427(99)00016-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
17

Nash, C. "Geometry of hyperbolic monopoles." Journal of Mathematical Physics 27, no. 8 (August 1986): 2160–64. http://dx.doi.org/10.1063/1.526985.

Full text
APA, Harvard, Vancouver, ISO, and other styles
18

Horváth, Ákos G. "Hyperbolic plane geometry revisited." Journal of Geometry 106, no. 2 (November 22, 2014): 341–62. http://dx.doi.org/10.1007/s00022-014-0252-0.

Full text
APA, Harvard, Vancouver, ISO, and other styles
19

Kemper, Matthias, and Joachim Lohkamp. "Potential Theory on Gromov Hyperbolic Spaces." Analysis and Geometry in Metric Spaces 10, no. 1 (January 1, 2022): 394–431. http://dx.doi.org/10.1515/agms-2022-0147.

Full text
Abstract:
Abstract Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Herewe extend Ancona’s potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov hyperbolic metric measure spaces, unifying these settings in a common framework ready for applications to singular spaces such as RCD spaces or minimal hypersurfaces. Results include boundary Harnack inequalities and a complete classification of positive harmonic functions in terms of the Martin boundary which is identified with the geometric Gromov boundary.
APA, Harvard, Vancouver, ISO, and other styles
20

Bao, Hui, and Xingdi Chen. "A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications." Journal of Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/838497.

Full text
Abstract:
We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyperbolic area and length formula of Euclidean disk and a circle represented by its Euclidean center and radius. Replacing interior angles with vertices coordinates, we also obtain a new hyperbolic area formula of a hyperbolic triangle. As its application, we give the hyperbolic area of a Lambert quadrilateral and some geometric characterizations of Lambert quadrilaterals and Saccheri quadrilaterals.
APA, Harvard, Vancouver, ISO, and other styles
21

Knieper, Gerhard, Leonid Polterovich, and Leonid Potyagailo. "Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry." Oberwolfach Reports 9, no. 3 (2012): 2139–203. http://dx.doi.org/10.4171/owr/2012/35.

Full text
APA, Harvard, Vancouver, ISO, and other styles
22

Gallego, Eduardo, and Gil Solanes. "Integral geometry and geometric inequalities in hyperbolic space." Differential Geometry and its Applications 22, no. 3 (May 2005): 315–25. http://dx.doi.org/10.1016/j.difgeo.2005.01.006.

Full text
APA, Harvard, Vancouver, ISO, and other styles
23

Ungar, Abraham A. "The Hyperbolic Ptolemy’s Theorem in the Poincaré Ball Model of Analytic Hyperbolic Geometry." Symmetry 15, no. 8 (July 27, 2023): 1487. http://dx.doi.org/10.3390/sym15081487.

Full text
Abstract:
Ptolemy’s theorem in Euclidean geometry, named after the Greek astronomer and mathematician Claudius Ptolemy, is well known. We translate Ptolemy’s theorem from analytic Euclidean geometry into the Poincaré ball model of analytic hyperbolic geometry, which is based on the Möbius addition and its associated symmetry gyrogroup. The translation of Ptolemy’s theorem from Euclidean geometry into hyperbolic geometry is achieved by means of hyperbolic trigonometry, called gyrotrigonometry, to which the Poincaré ball model gives rise, and by means of the duality of trigonometry and gyrotrigonometry.
APA, Harvard, Vancouver, ISO, and other styles
24

Mochizuki, Shinichi. "Galois Sections in Absolute Anabelian Geometry." Nagoya Mathematical Journal 179 (2005): 17–45. http://dx.doi.org/10.1017/s0027763000025599.

Full text
Abstract:
AbstractWe show that isomorphisms between arithmetic fundamental groups of hyperbolic curves over p-adic local fields preserve the decomposition groups of all closed points (respectively, closed points arising from torsion points of the underlying elliptic curve), whenever the hyperbolic curves in question are isogenous to hyperbolic curves of genus zero defined over a number field (respectively, are once-punctured elliptic curves [which are not necessarily defined over a number field]). We also show that, under certain conditions, such isomorphisms preserve certain canonical “integral structures” at the cusps [i.e., points at infinity] of the hyperbolic curve.
APA, Harvard, Vancouver, ISO, and other styles
25

Ungar, Abraham A. "When Four Cyclic Antipodal Pairs Are Ordered Counterclockwise in Euclidean and Hyperbolic Geometry." Symmetry 16, no. 6 (June 11, 2024): 729. http://dx.doi.org/10.3390/sym16060729.

Full text
Abstract:
A cyclic antipodal pair of a circle is a pair of points that are the intersection of the circle with the diameter of the circle. In this article, a recent proof of Ptolemy’s Theorem—simultaneously in both (i) Euclidean geometry and (ii) the relativistic model of hyperbolic geometry (also known as the Klein model)—motivates the study of four cyclic antipodal pairs of a circle, ordered arbitrarily counterclockwise. The translation of results from Euclidean geometry into hyperbolic geometry is obtained by means of hyperbolic trigonometry, called gyrotrigonometry, to which Einstein addition gives rise. Identities that extend the Pythagorean identity in both Euclidean and hyperbolic geometry are obtained.
APA, Harvard, Vancouver, ISO, and other styles
26

Long, D. D., and A. W. Reid. "Virtually spinning hyperbolic manifolds." Proceedings of the Edinburgh Mathematical Society 63, no. 2 (December 5, 2019): 305–13. http://dx.doi.org/10.1017/s0013091519000324.

Full text
Abstract:
AbstractWe give a new proof of a result of Sullivan [Hyperbolic geometry and homeomorphisms, in Geometric topology (ed. J. C. Cantrell), pp. 543–555 (Academic Press, New York, 1979)] establishing that all finite volume hyperbolic n-manifolds have a finite cover admitting a spin structure. In addition, in all dimensions greater than or equal to 5, we give the first examples of finite-volume hyperbolic n-manifolds that do not admit a spin structure.
APA, Harvard, Vancouver, ISO, and other styles
27

IZUMIYA, SHYUICHI, DONGHE PEI, and TAKASI SANO. "SINGULARITIES OF HYPERBOLIC GAUSS MAPS." Proceedings of the London Mathematical Society 86, no. 2 (March 2003): 485–512. http://dx.doi.org/10.1112/s0024611502013850.

Full text
Abstract:
In this paper we adopt the hyperboloid in Minkowski space as the model of hyperbolic space. We define the hyperbolic Gauss map and the hyperbolic Gauss indicatrix of a hypersurface in hyperbolic space. The hyperbolic Gauss map has been introduced by Ch. Epstein [J. Reine Angew. Math. 372 (1986) 96–135] in the Poincaré ball model, which is very useful for the study of constant mean curvature surfaces. However, it is very hard to perform the calculation because it has an intrinsic form. Here, we give an extrinsic definition and we study the singularities. In the study of the singularities of the hyperbolic Gauss map (indicatrix), we find that the hyperbolic Gauss indicatrix is much easier to calculate. We introduce the notion of hyperbolic Gauss–Kronecker curvature whose zero sets correspond to the singular set of the hyperbolic Gauss map (indicatrix). We also develop a local differential geometry of hypersurfaces concerning their contact with hyperhorospheres.2000 Mathematical Subject Classification: 53A25, 53A05, 58C27.
APA, Harvard, Vancouver, ISO, and other styles
28

Manin, Yu I. "Three-dimensional hyperbolic geometry as ∞-adic Arakelov geometry." Inventiones mathematicae 104, no. 1 (December 1991): 223–43. http://dx.doi.org/10.1007/bf01245074.

Full text
APA, Harvard, Vancouver, ISO, and other styles
29

Guo, Ren. "A Characterization of Hyperbolic Geometry among Hilbert Geometry." Journal of Geometry 89, no. 1-2 (September 22, 2008): 48–52. http://dx.doi.org/10.1007/s00022-008-1989-0.

Full text
APA, Harvard, Vancouver, ISO, and other styles
30

Hongnan Chen. "A Steward inequality in the Hyperbolic Geometry." Journal of Electrical Systems 20, no. 10s (July 10, 2024): 2326–33. http://dx.doi.org/10.52783/jes.5579.

Full text
Abstract:
The main aim of this study is to show that the steward inequality holds for any hyperbolic domain and distinct points , where denote the hyperbolic metric in and be a hyperbolic geodesic triangle with vertices and sides and be a point on .
APA, Harvard, Vancouver, ISO, and other styles
31

Zhou, Yuansheng, and Tatyana O. Sharpee. "Hyperbolic geometry of gene expression." iScience 24, no. 3 (March 2021): 102225. http://dx.doi.org/10.1016/j.isci.2021.102225.

Full text
APA, Harvard, Vancouver, ISO, and other styles
32

Fei, Bao Jun, and Zhi Gang Li. "Relativistic Velocity and Hyperbolic Geometry." Physics Essays 10, no. 2 (June 1997): 248–55. http://dx.doi.org/10.4006/1.3028713.

Full text
APA, Harvard, Vancouver, ISO, and other styles
33

Mejia, Diego, and C. David Minda. "Hyperbolic geometry ink-convex regions." Pacific Journal of Mathematics 141, no. 2 (February 1, 1990): 333–54. http://dx.doi.org/10.2140/pjm.1990.141.333.

Full text
APA, Harvard, Vancouver, ISO, and other styles
34

Shenitzer, Abe. "How Hyperbolic Geometry Became Respectable." American Mathematical Monthly 101, no. 5 (May 1994): 464. http://dx.doi.org/10.2307/2974912.

Full text
APA, Harvard, Vancouver, ISO, and other styles
35

Farup, Ivar. "Hyperbolic geometry for colour metrics." Optics Express 22, no. 10 (May 14, 2014): 12369. http://dx.doi.org/10.1364/oe.22.012369.

Full text
APA, Harvard, Vancouver, ISO, and other styles
36

KIM, INKANG, and JOHN R. PARKER. "Geometry of quaternionic hyperbolic manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 135, no. 2 (September 2003): 291–320. http://dx.doi.org/10.1017/s030500410300687x.

Full text
APA, Harvard, Vancouver, ISO, and other styles
37

Bal, Guillaume. "Ray transforms in hyperbolic geometry." Journal de Mathématiques Pures et Appliquées 84, no. 10 (October 2005): 1362–92. http://dx.doi.org/10.1016/j.matpur.2005.02.001.

Full text
APA, Harvard, Vancouver, ISO, and other styles
38

Marshall, T. H. "Hyperbolic geometry and reflection groups." Bulletin of the Australian Mathematical Society 53, no. 1 (February 1996): 173–74. http://dx.doi.org/10.1017/s0004972700016853.

Full text
APA, Harvard, Vancouver, ISO, and other styles
39

Gramlich, Ralf. "On the hyperbolic symplectic geometry." Journal of Combinatorial Theory, Series A 105, no. 1 (January 2004): 97–110. http://dx.doi.org/10.1016/j.jcta.2003.10.005.

Full text
APA, Harvard, Vancouver, ISO, and other styles
40

Wildberger, N. J. "Universal hyperbolic geometry I: trigonometry." Geometriae Dedicata 163, no. 1 (June 8, 2012): 215–74. http://dx.doi.org/10.1007/s10711-012-9746-9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
41

Ruggiero, Rafael O. "Expansive dynamics and hyperbolic geometry." Boletim da Sociedade Brasileira de Matem�tica 25, no. 2 (September 1994): 139–72. http://dx.doi.org/10.1007/bf01321305.

Full text
APA, Harvard, Vancouver, ISO, and other styles
42

Bielawski, Roger, and Lorenz Schwachhöfer. "Pluricomplex Geometry and Hyperbolic Monopoles." Communications in Mathematical Physics 323, no. 1 (July 14, 2013): 1–34. http://dx.doi.org/10.1007/s00220-013-1761-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
43

Shenitzer, Abe. "How Hyperbolic Geometry Became Respectable." American Mathematical Monthly 101, no. 5 (May 1994): 464–70. http://dx.doi.org/10.1080/00029890.1994.11996976.

Full text
APA, Harvard, Vancouver, ISO, and other styles
44

Corlette, Kevin. "Archimedean Superrigidity and Hyperbolic Geometry." Annals of Mathematics 135, no. 1 (January 1992): 165. http://dx.doi.org/10.2307/2946567.

Full text
APA, Harvard, Vancouver, ISO, and other styles
45

Popescu, Gelu. "Hyperbolic geometry on noncommutative balls." Documenta Mathematica 14 (2009): 595–651. http://dx.doi.org/10.4171/dm/283.

Full text
APA, Harvard, Vancouver, ISO, and other styles
46

Parker, John R., and Ser Peow Tan. "Caroline Series and Hyperbolic Geometry." Notices of the American Mathematical Society 70, no. 03 (March 1, 2023): 1. http://dx.doi.org/10.1090/noti2651.

Full text
APA, Harvard, Vancouver, ISO, and other styles
47

Cesaratto, E., S. Grynberg, R. Hansen, and M. Piacquadio. "Multifractal spectra and hyperbolic geometry." Chaos, Solitons & Fractals 6 (January 1995): 75–82. http://dx.doi.org/10.1016/0960-0779(95)80013-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
48

Knüppel, Frieder. "Transversals in plane hyperbolic geometry." Journal of Geometry 105, no. 1 (October 27, 2013): 13–20. http://dx.doi.org/10.1007/s00022-013-0187-x.

Full text
APA, Harvard, Vancouver, ISO, and other styles
49

Altmann, Kristina, and Ralf Gramlich. "On the hyperbolic unitary geometry." Journal of Algebraic Combinatorics 31, no. 4 (September 1, 2009): 547–83. http://dx.doi.org/10.1007/s10801-009-0200-5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
50

Lindstrom, Scott B., and Paul Vrbik. "Phase Portraits of Hyperbolic Geometry." Mathematical Intelligencer 41, no. 3 (April 16, 2019): 1–9. http://dx.doi.org/10.1007/s00283-019-09882-y.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the bibliographies on the topic 'Hyperbolic Geometry' for other source types:
Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography