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Daina Taimiņa
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mathematics at Cornell University, known for developing a way of modeling hyperbolic geometry with crocheted objects. Taimiņa received all of her formal educationList of lemmas (524 words) [view diff] no match in snippet view article find links to article

This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also listBoundedly generated group (1,781 words) [view diff] no match in snippet view article find links to article

In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generationList of topologies (2,023 words) [view diff] no match in snippet view article find links to article

The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. ThisMichael Kapovich (872 words) [view diff] exact match in snippet view article find links to article

deals with low-dimensional geometry and topology, Kleinian groups, hyperbolic geometry, geometric group theory, geometric representation theory in Lie groupsAlternated hexagonal tiling honeycomb (473 words) [view diff] exact match in snippet view article find links to article

In three-dimensional hyperbolic geometry, the alternated hexagonal tiling honeycomb, h{6,3,3}, or , is a semiregular tessellation with tetrahedron andHexagonal tiling honeycomb (843 words) [view diff] exact match in snippet view article find links to article

In the field of hyperbolic geometry, the hexagonal tiling honeycomb is one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. ItJohn Hazzidakis (987 words) [view diff] exact match in snippet view article find links to article

in proving Hilbert's theorem on negative curvature, stating that hyperbolic geometry does not have a model in 3-dimensional Euclidean space. He was bornVladimir Shukhov (2,067 words) [view diff] exact match in snippet view article find links to article

doubly curved structural forms. These forms, based on non-Euclidean hyperbolic geometry, are known today as hyperboloids of revolution. Shukhov developedMatti Vuorinen (350 words) [view diff] exact match in snippet view article find links to article

quasiconformal mappings, computational potential theory, and generalized hyperbolic geometry. He has worked as a professor of mathematics at the University ofOrder-6 hexagonal tiling honeycomb (961 words) [view diff] exact match in snippet view article find links to article

In the field of hyperbolic geometry, the order-6 hexagonal tiling honeycomb is one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic spaceOrder-5 hexagonal tiling honeycomb (832 words) [view diff] exact match in snippet view article find links to article

In the field of hyperbolic geometry, the order-5 hexagonal tiling honeycomb arises as one of 11 regular paracompact honeycombs in 3-dimensional hyperbolicCircular triangle (715 words) [view diff] exact match in snippet view article find links to article

triangle that has straight sides in hyperbolic geometry, but is drawn as circular in some models of hyperbolic geometry Lune and Lens, two-sided figuresIdentity function (616 words) [view diff] case mismatch in snippet view article find links to article

Mathematical Assn of Amer. ISBN 978-0883857519. James W. Anderson, Hyperbolic Geometry, Springer 2005, ISBN 1-85233-934-9 Conover, Robert A. (2014-05-21)Laguerre transformations (3,424 words) [view diff] no match in snippet view article find links to article

The Laguerre transformations or axial homographies are an analogue of Möbius transformations over the dual numbers. When studying these transformationsYair Minsky (398 words) [view diff] case mismatch in snippet view article find links to article

supervision of William Paul Thurston, with the thesis Harmonic Maps and Hyperbolic Geometry. His Ph.D. students include Jason Behrstock, Erica Klarreich, HosseinOrder-4 hexagonal tiling honeycomb (976 words) [view diff] exact match in snippet view article find links to article

In the field of hyperbolic geometry, the order-4 hexagonal tiling honeycomb arises as one of 11 regular paracompact honeycombs in 3-dimensional hyperbolicFrancis Bonahon (625 words) [view diff] exact match in snippet view article find links to article

three-dimensional topology, knot theory, surface diffeomorphisms, hyperbolic geometry, and Kleinian groups. He received in 1985 a bronze medal from CNRSList of misnamed theorems (1,976 words) [view diff] exact match in snippet view article find links to article

Dirichlet's lecture notes were not published until 1904. Models of hyperbolic geometry. "By one of the injustices of nomenclature that are so common inHomersham Cox (mathematician) (1,348 words) [view diff] exact match in snippet view article

parts in 1881 and 1882) he described homogeneous coordinates for hyperbolic geometry, now called Weierstrass coordinates of the hyperboloid model introducedVirtually fibered conjecture (663 words) [view diff] exact match in snippet view article find links to article

William P. (1982). "Three dimensional manifolds, Kleinian groups and hyperbolic geometry". Bulletin of the American Mathematical Society. 6 (3): 357–382.Paul Jean Joseph Barbarin (839 words) [view diff] exact match in snippet view article find links to article

non euclidienne ... This is an excellent introductory textbook on hyperbolic geometry, although it presents some of the results without complete proofsArithmetic group (3,301 words) [view diff] exact match in snippet view article find links to article

William (1982). "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry". Bull. Amer. Math. Soc. (N.S.). 6 (3): 357–381. doi:10Mass in special relativity (6,288 words) [view diff] exact match in snippet view article find links to article

space, the velocity-space is bounded by c and has the geometry of hyperbolic geometry where relativistic mass plays an analogous role to that of NewtonianVelocity-addition formula (11,057 words) [view diff] no match in snippet view article find links to article

In relativistic physics, a velocity-addition formula is an equation that specifies how to combine the velocities of objects in a way that is consistentNevanlinna theory (2,603 words) [view diff] exact match in snippet view article find links to article

functional equations holomorphic dynamics, minimal surfaces, and complex hyperbolic geometry, which deals with generalizations of Picard's theorem to higher dimensionsScale-free network (6,723 words) [view diff] exact match in snippet view article find links to article

x_{i}x_{j}}{1+\delta x_{i}x_{j}}}.} Assuming that a network has an underlying hyperbolic geometry, one can use the framework of spatial networks to generate scale-freeHyperboloid structure (1,570 words) [view diff] exact match in snippet view article find links to article

as well as the full set of supporting calculations analyzing the hyperbolic geometry and sizing the network of members, was completed by February 1919Form constant (1,048 words) [view diff] exact match in snippet view article find links to article

vision Uniform tilings in hyperbolic plane – Symmetric subdivision in hyperbolic geometry Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, PeterFive-dimensional space (1,598 words) [view diff] case mismatch in snippet view article find links to article

Relativity: The 5th dimension (abridged). p. 442. Steven Booth. "Hyperbolic Geometry" (PDF). "The Lattice A5". www.math.rwth-aachen.de. Sphere packingsOhsawa–Takegoshi L2 extension theorem (459 words) [view diff] exact match in snippet view article find links to article

S2CID 242194764. Siu, Yum-Tong (2011). "Section extension from hyperbolic geometry of punctured disk and holomorphic family of flat bundles". ScienceInversion transformation (910 words) [view diff] case mismatch in snippet view article find links to article

reflections Spacetime symmetries CPT symmetry Field (physics) superstrings "Chapter 5 Inversion" (PDF). "THE POINCARE DISK MODEL OF HYPERBOLIC GEOMETRY" (PDF).Kaleidoscope (2,472 words) [view diff] exact match in snippet view article find links to article

Teleidoscope Uniform tilings in hyperbolic plane – Symmetric subdivision in hyperbolic geometry Brewster, David (1858). The Kaleidoscope: Its History, Theory, andAnne Bennett Prize (796 words) [view diff] exact match in snippet view article find links to article

Caroline Series, in recognition of her leading contributions to hyperbolic geometry and symbolic dynamics, and of the major impact of her numerous initiativesTree rotation (1,443 words) [view diff] exact match in snippet view article find links to article

Thurston, William P. (1988), "Rotation distance, triangulations, and hyperbolic geometry", Journal of the American Mathematical Society, 1 (3): 647–681, doi:10Alexandrov's uniqueness theorem (1,730 words) [view diff] exact match in snippet view article find links to article

Euclidean convex polyhedra: every two-dimensional manifold with uniform hyperbolic geometry and finite area, combinatorially equivalent to a finitely-puncturedIgor Rivin (821 words) [view diff] case mismatch in snippet view article find links to article

Neumann, Walter David; Stoltzfus, Neal W. (eds.). Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory. Vol. 541. Providence (R.I.):Heavy-light decomposition (994 words) [view diff] exact match in snippet view article find links to article

Goodrich, Michael T. (2011), "Succinct greedy geometric routing using hyperbolic geometry", IEEE Transactions on Computers, 60 (11): 1571–1580, doi:10.1109/TCVirtually Haken conjecture (627 words) [view diff] case mismatch in snippet view article find links to article

ISBN 9780821867891, MR 0520548. Klarreich, Erica (2012-10-02). "Getting Into Shapes: From Hyperbolic Geometry to Cube Complexes and Back". Quanta Magazine. v t eAlan Reid (mathematician) (403 words) [view diff] exact match in snippet view article

Reid, A. W.; Spitler, R. (2020). "Absolute profinite rigidity and hyperbolic geometry". Annals of Mathematics. 192 (3). arXiv:1811.04394. doi:10.4007/annalsAssociahedron (1,455 words) [view diff] exact match in snippet view article find links to article

Thurston, William (1988), "Rotation distance, triangulations, and hyperbolic geometry", Journal of the American Mathematical Society, 1 (3): 647–681, doi:10Euclidean distance (3,187 words) [view diff] exact match in snippet view article find links to article

Psychophysics, 7 (2): 103–107, doi:10.3758/bf03210143 Milnor, John (1982), "Hyperbolic geometry: the first 150 years" (PDF), Bulletin of the American MathematicalNoether Lecture (438 words) [view diff] case mismatch in snippet view article find links to article

Networks of Them: Which Differences Make a Difference 1993 Linda Keen Hyperbolic Geometry and Spaces of Riemann Surfaces 1994 Lesley Sibner Analysis in GaugeG. Peter Scott (664 words) [view diff] exact match in snippet view article find links to article

the geometric topology of 3-dimensional manifolds, 3-dimensional hyperbolic geometry, minimal surface theory, hyperbolic groups, and Kleinian groups withList of NYU Courant Institute people (961 words) [view diff] exact match in snippet view article find links to article

2011), professor at Columbia University Charles Epstein (PhD 1983), hyperbolic geometry Corwin Hansch (PhD 1944), statistics Joseph B. Keller, 1988 NationalEugenio Beltrami (1,092 words) [view diff] exact match in snippet view article find links to article

1090/s0002-9904-1909-01882-8. Stillwell, John (1996). Sources of hyperbolic geometry. History of Mathematics. Vol. 10. Providence, R.I.: American MathematicalCharles Epstein (mathematician) (751 words) [view diff] exact match in snippet view article

and medical imaging, and numerical analysis; he has also worked in hyperbolic geometry, univalent function theory, several complex variables, microlocalHyperbolic angle (2,439 words) [view diff] case mismatch in snippet view article find links to article

Mathematical Monographs volume 170, American Mathematical Society Hyperbolic Geometry pp 5–6, Fig 15.1 Weisstein, Eric W. "Minkowski Metric". mathworldNP-intermediate (1,534 words) [view diff] exact match in snippet view article find links to article

Thurston, William P. (1988). "Rotation distance, triangulations, and hyperbolic geometry". Journal of the American Mathematical Society. 1 (3): 647–681. doi:10Frame of reference (3,440 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-0-8218-3900-3. Arlan Ramsay; Robert D. Richtmyer (1995). Introduction to Hyperbolic Geometry. Springer. p. 11. ISBN 0-387-94339-0. geometry axiom coordinate systemLatent space (1,180 words) [view diff] exact match in snippet view article find links to article

Marián; Allard, Antoine; Serrano, M. Ángeles (2016-09-16). "The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013". ScientificJohn Morgan (mathematician) (1,518 words) [view diff] exact match in snippet view article

112, Academic Press, Orlando, FL, 1984. John W. Morgan. Trees and hyperbolic geometry. Proceedings of the International Congress of Mathematicians, VolKleinian group (2,282 words) [view diff] exact match in snippet view article find links to article

William P. (1982), "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry", Bulletin of the American Mathematical Society, New Series, 6 (3):Yuri Manin (1,548 words) [view diff] exact match in snippet view article find links to article

S2CID 25731842. Manin, Yu. I. (December 1991). "Three-dimensional hyperbolic geometry as ∞-adic Arakelov geometry". Inventiones Mathematicae. 104 (1):Florin Diacu (1,143 words) [view diff] exact match in snippet view article find links to article

proposed by János Bolyai and Nikolai Lobachevsky, the founders of hyperbolic geometry. But though many papers were written on this subject, the equationsFlip graph (1,723 words) [view diff] exact match in snippet view article find links to article

Thurston, William P. (1988). "Rotation distance, triangulations, and hyperbolic geometry". Journal of the American Mathematical Society. 1 (3): 647–681. doi:10SABR volatility model (2,432 words) [view diff] exact match in snippet view article find links to article

(2005-02-15). "Unifying the BGM and SABR models: a short ride in hyperbolic geometry". arXiv:physics/0602102. Jordan, Richard; Tier, Charles (2011-05-17)Riemann sphere (3,325 words) [view diff] case mismatch in snippet view article find links to article

Retrieved December 12, 2021. William Mark Goldman (1999) Complex Hyperbolic Geometry, page 1, Clarendon Press ISBN 0-19-853793-X R. Penrose (2007). TheGreedy embedding (1,445 words) [view diff] exact match in snippet view article find links to article

Goodrich, M. T. (2011), "Succinct greedy geometric routing using hyperbolic geometry", IEEE Transactions on Computers, 60 (11): 1571–1580, doi:10.1109/TCHyperboloid (2,624 words) [view diff] exact match in snippet view article find links to article

with another suitably chosen metric can also be used as a model for hyperbolic geometry. Imaginary hyperboloids are frequently found in mathematics of higherWilliam Goldman (mathematician) (868 words) [view diff] exact match in snippet view article

American Mathematical Society. Goldman, William M. (1999). Complex hyperbolic geometry. Oxford Mathematical Monographs. Oxford Science Publications. NewCeva's theorem (1,923 words) [view diff] exact match in snippet view article find links to article

The theorem also has a well-known generalization to spherical and hyperbolic geometry, replacing the lengths in the ratios with their sines and hyperbolicSimple Lie group (2,262 words) [view diff] exact match in snippet view article find links to article

a generalization of the well known duality between spherical and hyperbolic geometry. A symmetric space with a compatible complex structure is calledSamuel James Patterson (1,503 words) [view diff] exact match in snippet view article find links to article

algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry. A portion of the collected contributions have been developed fromOrder-6 cubic honeycomb (908 words) [view diff] exact match in snippet view article find links to article

omnitruncated order-4 hexagonal tiling honeycomb. In three-dimensional hyperbolic geometry, the alternated order-6 hexagonal tiling honeycomb is a uniform compactCourant Institute of Mathematical Sciences (4,448 words) [view diff] exact match in snippet view article find links to article

2011), professor at Columbia University Charles Epstein (PhD 1983), hyperbolic geometry Kenneth M. Golden (PhD 1984), applied mathematics of sea ice, FellowSchwarz triangle (10,928 words) [view diff] exact match in snippet view article find links to article

University Press. ISBN 0-521-37510-X. MR 1066460. Iversen, Birger (1992), Hyperbolic geometry, London Mathematical Society Student Texts, vol. 25, Cambridge UniversityFundamental polygon (5,995 words) [view diff] exact match in snippet view article find links to article

Bourdon, Marc; Pajot, Hervé (2002), "Quasiconformal geometry and hyperbolic geometry", in Marc Burger; Alessandra Iozzi (eds.), Rigidity in dynamics andCoxeter–Dynkin diagram (3,213 words) [view diff] case mismatch in snippet view article find links to article

Type Finite Affine Hyperbolic Geometry ... Coxeter diagram Bracket notation [ ] [2] [3] [4] [p] [∞] [∞] [iπ/λ] Order 2 4 6 8 2p ∞ Mirror lines are coloredTriangle inequality (5,176 words) [view diff] exact match in snippet view article find links to article

ISBN 978-0-262-51309-8. Arlan Ramsay; Robert D. Richtmyer (1995). Introduction to hyperbolic geometry. Springer. p. 17. ISBN 0-387-94339-0. Harold R. Jacobs (2003). Geometry:List of University of Warwick people (2,747 words) [view diff] exact match in snippet view article find links to article

professor David Epstein FRS – mathematician known for his work in hyperbolic geometry; co-founder of the University of Warwick mathematics department MartinGrigori Perelman (6,347 words) [view diff] exact match in snippet view article find links to article

Thurston, William P. Three-dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357–381. John MorganMikhael Gromov (mathematician) (3,749 words) [view diff] exact match in snippet view article

(1980), no. 1, 73–111. Kevin Corlette. Archimedean superrigidity and hyperbolic geometry. Ann. of Math. (2) 135 (1992), no. 1, 165–182. Korevaar, NicholasList of Jewish mathematicians (15,770 words) [view diff] exact match in snippet view article find links to article

(1920–2005), mathematician and physicist David Epstein (born 1937), hyperbolic geometry, 3-manifolds, and group theory Paul Epstein (1871–1939), number theoryAtiyah–Singer index theorem (7,529 words) [view diff] exact match in snippet view article find links to article

Studies in Mathematics, vol. 70, pp. 171–185 Sullivan, D. (1979), "Hyperbolic geometry and homeomorphisms", J.C. Candrell, "Geometric Topology", Proc. GeorgiaArc diagram (2,372 words) [view diff] exact match in snippet view article find links to article

sequences and intersection numbers" (PDF), Complex manifolds and hyperbolic geometry (Guanajuato, 2001), Contemporary Mathematics, vol. 311, ProvidenceInteractive visual analysis (1,843 words) [view diff] exact match in snippet view article find links to article

Ramana Rao, and Peter Pirolli. "A focus+ context technique based on hyperbolic geometry for visualizing large hierarchies." Proceedings of the SIGCHI conferenceList of University of the Witwatersrand people (3,698 words) [view diff] exact match in snippet view article find links to article

Witwatersrand David B. A. Epstein, is a mathematician known for his work in hyperbolic geometry, 3-manifolds, and group theory, amongst other fields Garth SalonerWigner rotation (6,192 words) [view diff] exact match in snippet view article find links to article

of admissible velocities in the literature. It is endowed with a hyperbolic geometry described in the linked article. The generators of boosts, K1, K2Basel problem (7,373 words) [view diff] no match in snippet view article find links to article

to the Basel problem. This approach shows the connection between (hyperbolic) geometry and arithmetic, and can be inverted to give a proof of the Weil conjectureBarycentric coordinate system (8,186 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-0-471-50458-0. Zbl 0181.48101. Barycentric Calculus In Euclidean And Hyperbolic Geometry: A Comparative Introduction, Abraham Ungar, World Scientific, 2010Flip distance (1,422 words) [view diff] exact match in snippet view article find links to article

Thurston, William P. (1988). "Rotation distance, triangulations, and hyperbolic geometry". Journal of the American Mathematical Society. 1 (3). American MathematicalList of Italian inventions and discoveries (25,900 words) [view diff] exact match in snippet view article find links to article

the fundamental concept of angle of parallelism. Later, fathers of hyperbolic geometry were Gauss, Janos Bolyai, and Lobachevsky. Scientific method (consistingMapping class group of a surface (4,595 words) [view diff] case mismatch in snippet view article find links to article

decompositions and the Weil–Petersson metric". Complex Manifolds and Hyperbolic Geometry. American Mathematical Society. MR 1940162. Dehn, Max (1938). "DieList of Guggenheim Fellowships awarded in 2007 (3,693 words) [view diff] exact match in snippet view article find links to article

Mathematics, Brown University: Models, bounds, and effective rigidity in hyperbolic geometry. Kevin Brockmeier, Writer, Little Rock, Arkansas: Fiction. ElizabethHarmonic map (5,239 words) [view diff] exact match in snippet view article find links to article

Zbl 0652.58024. Corlette, Kevin (1992). "Archimedean superrigidity and hyperbolic geometry". Annals of Mathematics. Second Series. 135 (1): 165–182. doi:10List of examples of Stigler's law (5,014 words) [view diff] exact match in snippet view article find links to article

1983. The Poincaré disk model and the Poincaré half-plane model of hyperbolic geometry are named after Henri Poincaré who studied them in 1882. HoweverGeometric algebra (13,928 words) [view diff] exact match in snippet view article find links to article

geometric algebra for discussion of homogeneous models of elliptic and hyperbolic geometry compared with the euclidean geometry derived from PGA. Working withinList of Stuyvesant High School people (6,798 words) [view diff] exact match in snippet view article find links to article

Peter Shalen (1962) – low-dimensional topology, Kleinian groups, hyperbolic geometry (University of Illinois at Chicago) Robert Zimmer (1964) – ergodicList of women in mathematics (22,629 words) [view diff] exact match in snippet view article find links to article

geometric topologist Ruth Kellerhals (born 1957), Swiss expert on hyperbolic geometry, geometric group theory and polylogarithm identities Christine KelleyZonal spherical function (6,693 words) [view diff] exact match in snippet view article find links to article

functions for SL(2,R) originated in the work of Mehler in 1881 on hyperbolic geometry. He discovered the analogue of the Plancherel theorem, which wasCoxeter notation (6,423 words) [view diff] case mismatch in snippet view article find links to article

Example rank 2 finite and hyperbolic symmetries Type Finite Affine Hyperbolic Geometry ... Coxeter [ ] = [2]=[ ]×[ ] [3] [4] [p] [∞] [∞] [iπ/λ] Order 2Plane-based geometric algebra (4,198 words) [view diff] exact match in snippet view article find links to article

But we instead choose to have a basis element squaring to 1 or −1 instead of 0, euclidean geometry can be changed to spherical or hyperbolic geometry.Beltrami equation (10,901 words) [view diff] exact match in snippet view article find links to article

or Perish, ISBN 0-914098-70-5 Stillwell, John (1996), Sources of hyperbolic geometry, History of Mathematics, vol. 10, Providence, R.I.: American MathematicalVirasoro conformal block (6,405 words) [view diff] exact match in snippet view article find links to article

Vartanov, G. S. (2012). "6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories". arXiv:1202.4698 [hep-th]. Roussillon