horocycle


horocycle

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  • Horocycle — A blue horocycle in the Poincaré disk model and some red normals. The normals converge asymptotically to the upper central point. In hyperbolic geometry, a horocycle (Greek: όριο + κύκλος border + circle) is a curve whose normals all converge… …   Wikipedia

  • Hyperbolic geometry — Lines through a given point P and asymptotic to line R. A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparall …   Wikipedia

  • Ergodic theory — is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical …   Wikipedia

  • Ford circle — In mathematics, a Ford circle is a circle with centre at ( p/q , 1/(2 q 2)) and radius 1/(2 q 2), where p/q is an irreducible fraction, i.e. p and q are coprime integers.HistoryFord circles are named after American mathematician Lester R. Ford,… …   Wikipedia

  • List of mathematics articles (H) — NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… …   Wikipedia

  • List of circle topics — This list of circle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or concretely in physical space. It does not include metaphors like inner circle or circular reasoning in… …   Wikipedia

  • Anosov diffeomorphism — In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of expansion and contraction .… …   Wikipedia

  • Hillel Furstenberg — Hillel (Harry) Furstenberg ( he. הלל (הארי) פורסטנברג) is an Israeli mathematician, a member of the Israel Academy of Sciences and Humanities and U.S. National Academy of Sciences and a laureate of the Wolf Prize in Mathematics. He is known for… …   Wikipedia

  • Hypercycle (geometry) — In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line.Given a straight line L and a point P not on L, we can construct a hypercycle by taking… …   Wikipedia

  • Horoball — In mathematics, particularly hyperbolic geometry, a horoball is a specific kind of n dimensional object in hyperbolic n space. Consider the upper half space model of hyperbolic space. Then a horosphere is given by a horizontal plane, and the… …   Wikipedia

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