Relevant bibliographies by topics / Hyperbolic Geometry

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Hyperbolic Geometry'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Hyperbolic Geometry"

1

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

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

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

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

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

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

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

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

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

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

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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
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Dissertations / Theses on the topic "Hyperbolic Geometry"

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Markham, Sarah. "Hypercomplex hyperbolic geometry." Thesis, Durham University, 2003. http://etheses.dur.ac.uk/3698/.

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The rank one symmetric spaces of non-compact type are the real, complex, quaternionic and octonionic hyperbolic spaces. Real hyperbolic geometry is widely studied complex hyperbolic geometry less so, whilst quaternionic hyperbolic geometry is still in its infancy. The purpose of this thesis is to investigate the conditions for discrete group action in quaternionic and octonionic hyperbolic 2-spaces and their geometric consequences, in the octonionic case, in terms of lower bounds on the volumes of non-compact manifolds. We will also explore the eigenvalue problem for the 3 x 3 octonionic matri
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Marshall, T. H. (Timothy Hamilton). "Hyperbolic Geometry and Reflection Groups." Thesis, University of Auckland, 1994. http://hdl.handle.net/2292/2140.

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The n-dimensional pseudospheres are the surfaces in Rn+l given by the equations x12+x22+...+xk2-xk+12-...-xn+12=1(1 ≤ k ≤ n+1). The cases k=l, n+1 give, respectively a pair of hyperboloids, and the ordinary n-sphere. In the first chapter we consider the pseudospheres as surfaces h En+1,k, where Em,k=Rk x (iR)m-k, and investigate their geometry in terms of the linear algebra of these spaces. The main objects of investigation are finite sequences of hyperplanes in a pseudosphere. To each such sequence we associate a square symmetric matrix, the Gram matrix, which gives information about angle an
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Murray, Marilee Anne. "Hyperbolic Geometry and Coxeter Groups." Bowling Green State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1343040882.

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Walker, Mairi. "Continued fractions and hyperbolic geometry." Thesis, Open University, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.700134.

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This thesis uses hyperbolic geometry to study various classes of both real and complex continued fractions. This intuitive approach gives insight into the theory of continued fractions that is not so easy to obtain from traditional algebraic methods. Using it, we provide a more extensive study of both Rosen continued fractions and even-integer continued fractions than many previous works, yielding new results, and revisiting classical theorems. We also study two types of complex continued fractions, namely Gaussian integer continued fractions and Bianchi continued fractions. As well as providi
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Thorgeirsson, Sverrir. "Hyperbolic geometry: history, models, and axioms." Thesis, Uppsala universitet, Algebra och geometri, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-227503.

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Gharamti, Moustafa. "Supersymmetry and geometry of hyperbolic monopoles." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10479.

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This thesis studies the geometry of hyperbolic monopoles using supersymmetry in four and six dimensions. On the one hand, we show that starting with a four dimensional supersymmetric Yang-Mills theory provides the necessary information to study the geometry of the complex moduli space of hyperbolic monopoles. On the other hand, we require to start with a six dimensional supersymmetric Yang-Mills theory to study the geometry of the real moduli space of hyperbolic monopoles. In chapter two, we construct an off-shell supersymmetric Yang-Mills-Higgs theory with complex fields on three-dimensional
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Rippy, Scott Randall. "Applications of hyperbolic geometry in physics." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1099.

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Naeve, Trent Phillip. "Conics in the hyperbolic plane." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3075.

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An affine transformation such as T(P)=Q is a locus of an affine conic. Any affine conic can be produced from this incidence construction. The affine type of conic (ellipse, parabola, hyperbola) is determined by the invariants of T, the determinant and trace of its linear part. The purpose of this thesis is to obtain a corresponding classification in the hyperbolic plane of conics defined by this construction.
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Bowen, Lewis Phylip. "Density in hyperbolic spaces." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3077409.

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Saratchandran, Hemanth. "Four dimensional hyperbolic link complements via Kirby calculus." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:ba72ee75-c22f-4800-a38c-76e5cf411ad9.

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The primary aim of this thesis is to construct explicit examples of four dimensional hyperbolic link complements. Using the theory of Kirby diagrams and Kirby calculus we set up a general framework that one can use to attack such a problem. We use this framework to construct explicit examples in a smooth standard S<sup>4</sup> and a smooth standard S<sup>2</sup> x S<sup>2</sup>. We then characterise which homeomorphism types of smooth simply connected closed 4-manifolds can admit a hyperbolic link complement, along the way giving constructions of explicit examples.
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Books on the topic "Hyperbolic Geometry"

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Anderson, James W. Hyperbolic Geometry. Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-3987-4.

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Anderson, James W. Hyperbolic geometry. Springer, 1999.

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Ramsay, Arlan. Introduction to hyperbolic geometry. Springer-Verlag, 1995.

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Benedetti, Riccardo, and Carlo Petronio. Lectures on Hyperbolic Geometry. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-58158-8.

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Ramsay, Arlan, and Robert D. Richtmyer. Introduction to Hyperbolic Geometry. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4757-5585-5.

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Stillwell, John. Sources of hyperbolic geometry. American Mathematical Society, 1996.

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Benedetti, R. Lectures on hyperbolic geometry. Springer-Verlag, 1992.

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Boskoff, Wladimir-Georges. Hyperbolic geometry and barbilian spaces. Hadronic Press, 1996.

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Ratcliffe, John G. Foundations of hyperbolic manifolds. Springer-Verlag, 1994.

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1864-, Schlesinger Ludwig, ed. Libellus post saeculum quam Ioannes Bolyai: De Bolya anno MDCCCII A.D. XVIII kalendas ianuarias Claudiopoli natus est ad celebrandam memoriam eius immortalem. [typis Societatis franklinianae budapestinensis], 1991.

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Book chapters on the topic "Hyperbolic Geometry"

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Millman, Richard S., and George D. Parker. "Hyperbolic Geometry." In Geometry. Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-4436-3_8.

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Trudeau, Richard J. "Hyperbolic Geometry." In The Non-Euclidean Revolution. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-2102-9_6.

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Pressley, Andrew. "Hyperbolic geometry." In Elementary Differential Geometry. Springer London, 2010. http://dx.doi.org/10.1007/978-1-84882-891-9_11.

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Ratcliffe, John G. "Hyperbolic Geometry." In Foundations of Hyperbolic Manifolds. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4757-4013-4_3.

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Richter-Gebert, Jürgen. "Hyperbolic Geometry." In Perspectives on Projective Geometry. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-17286-1_25.

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Li, Hongbo. "Hyperbolic Geometry." In Geometric Algebra with Applications in Science and Engineering. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0159-5_4.

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Hariri, Parisa, Riku Klén, and Matti Vuorinen. "Hyperbolic Geometry." In Springer Monographs in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-32068-3_4.

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Ratcliffe, John G. "Hyperbolic Geometry." In Foundations of Hyperbolic Manifolds. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31597-9_3.

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Beals, Richard, and Roderick S. C. Wong. "Hyperbolic geometry." In Explorations in Complex Functions. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54533-8_3.

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Agricola, Ilka, and Thomas Friedrich. "Hyperbolic geometry." In Elementary Geometry. American Mathematical Society, 2008. http://dx.doi.org/10.1090/stml/043/04.

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Conference papers on the topic "Hyperbolic Geometry"

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Misik, Adam, Driton Salihu, Xin Su, Heike Brock, and Eckehard Steinbach. "HypCAD: Geometry-Enhanced Hyperbolic Contrastive Learning for CAD Model Retrieval." In ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2025. https://doi.org/10.1109/icassp49660.2025.10887722.

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Guan, Yao, Wenzhu Yan, Ting Yuan, and Yanmeng Li. "Advanced Graph-MLPs Distillation based on Global and Local Hyperbolic Geometry Learning." In ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2025. https://doi.org/10.1109/icassp49660.2025.10888559.

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Huang, Chenxingyu, H. Y. Fu, and Qian Li. "Pinning Effect with Geometry-Independent Resonances Controlled by Epsilon-Near-Zero Hyperbolic Metamaterials." In 2024 Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR). IEEE, 2024. http://dx.doi.org/10.1109/cleo-pr60912.2024.10676541.

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Gries, Matthew B., David W. Whitmore, Kevin A. Michols, Matt Miltenberger, and John S. Lawler. "Evaluation and Repair of Natural Draft Cooling Towers." In CORROSION 2018. NACE International, 2018. https://doi.org/10.5006/c2018-11005.

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Abstract Reinforced concrete cooling towers exposed to harsh operating environments can develop severe corrosion of embedded steel reinforcing, concrete delamination and spalling. Condition assessment of cooling towers is challenging due to their size, geometry and operational constraints but careful investigation can provide critical knowledge to effectively characterize structural health, plan maintenance, and prioritize repairs to maximize service life. A case history is presented to illustrate how assessment data was collected, interpreted, and used to develop and implement repair strategi
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Costa, S. I. R., S. A. Santos, and J. E. Strapasson. "Fisher information matrix and hyperbolic geometry." In IEEE Information Theory Workshop, 2005. IEEE, 2005. http://dx.doi.org/10.1109/itw.2005.1531851.

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Sleator, D. D., R. E. Tarjan, and W. P. Thurston. "Rotation distance, triangulations, and hyperbolic geometry." In the eighteenth annual ACM symposium. ACM Press, 1986. http://dx.doi.org/10.1145/12130.12143.

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You, Di, Thanh Tran, and Kyumin Lee. "Multi-Behavior Recommendation with Hyperbolic Geometry." In 2022 IEEE International Conference on Big Data (Big Data). IEEE, 2022. http://dx.doi.org/10.1109/bigdata55660.2022.10020616.

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Zhu, Yudong, Di Zhou, Jinghui Xiao, Xin Jiang, Xiao Chen, and Qun Liu. "HyperText: Endowing FastText with Hyperbolic Geometry." In Findings of the Association for Computational Linguistics: EMNLP 2020. Association for Computational Linguistics, 2020. http://dx.doi.org/10.18653/v1/2020.findings-emnlp.104.

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Saaty, Thomas L. "Reciprocal Comparisons, Inversion, and Hyperbolic Geometry (From Psychology to Geometry)." In The International Symposium on the Analytic Hierarchy Process. Creative Decisions Foundation, 1994. http://dx.doi.org/10.13033/isahp.y1994.040.

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SERIES, CAROLINE. "WHY IS THERE HYPERBOLIC GEOMETRY IN DYNAMICS?" In Proceedings of the Tenth General Meeting. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704276_0010.

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Reports on the topic "Hyperbolic Geometry"

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Ungar, Abraham A. Hyperbolic Geometry. GIQ, 2014. http://dx.doi.org/10.7546/giq-15-2014-259-282.

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Ungar, Abraham A. Hyperbolic Geometry. Jgsp, 2013. http://dx.doi.org/10.7546/jgsp-32-2013-61-86.

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Brezov, Danail S., Clementina D. Mladenova, and Ivaïlo M. Mladenov. Vector Parameters in Classical Hyperbolic Geometry. GIQ, 2014. http://dx.doi.org/10.7546/giq-15-2014-79-105.

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Brezov, Danail, Clementina Mladenova, and Ivaïlo Mladenov. Vector Parameters in Classical Hyperbolic Geometry. Journal of Geometry and Symmetry in Physics, 2013. http://dx.doi.org/10.7546/jgsp-30-2013-19-.

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Brezov, Danail, Clementina Mladenova, and Ivaïlo Mladenov. Vector Parameters in Classical Hyperbolic Geometry. Journal of Geometry and Symmetry in Physics, 2013. http://dx.doi.org/10.7546/jgsp-30-2013-19-48.

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Hasslacher, B., and R. Mainieri. Geometry in the large and hyperbolic chaos. Office of Scientific and Technical Information (OSTI), 1998. http://dx.doi.org/10.2172/674860.

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Holzapfel, Rolf-Peter. Enumerative Geometry on Quasi-Hyperbolic 4-Spaces with Cusps. GIQ, 2012. http://dx.doi.org/10.7546/giq-4-2003-42-87.

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