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Study of its Development. 1912. Dover reprint 1955. Also in: Seth Braver Lobachevski illuminated, MAA 2011. Pangeometry. Excerpts translated by Henry P. Manning:...

In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

Łobaczewska) is a Polish-language surname. Its Russian-language version is Lobachevski. Andrzej Łobaczewski, Polish psychiatrist Grażyna Łobaszewska [pl], Polish...

collected works of Hermann Grassmann. Engel translated the works of Nikolai Lobachevski from Russian into German, thus making these works more accessible. With...

E. B. (1984), "Absence of crystallographic groups of reflections in Lobachevski spaces of large dimension", Trudy Moskov. Mat. Obshch., 47 Yokonuma,...

geometry where Euclid's parallel axiom is denied. Gauss, Bolyai and Lobachevski independently constructed hyperbolic geometry, where parallel lines have...

Ernest B. (1984). "Absence of crystallographic groups of reflections in Lobachevski spaces of large dimension". Trudy Moskov. Mat. Obshch. 47. "Coxeter group"...

into the United States through his translations of works by Bolyai, Lobachevski, Saccheri, and Poincaré. He wrote an elementary geometry text, Rational...

hyperbolic, so that "instead of a Euclidean triangle of velocities, we get a Lobachevski triangle of rapidities". However, contrary to the scientific mainstream...

Projective geometry was instrumental in the validation of speculations of Lobachevski and Bolyai concerning hyperbolic geometry by providing models for the...

Chebotaryov, Aleksandr Butlerov, Naum Meiman, Kimal Akishev, Nikolay Lobachevski, Ivan Simonov, Vladimir Markovnikov, Konstantin Mereschkowski, Nikolay...

drei-dimensionalen Lobatschefskijschen Raume (Relativity in Three-Dimensional Lobachevski Space), now available in English. In the period 1909 to 1913 Varićak...

ISBN 0-387-96458-4. Faber 1983, pg. 145 Coxeter 1998, pg. 11 Braver, Seth (2011). Lobachevski Illuminated. American Mathematical Society. p. 58. ISBN 9781470456405...

Square tiling Triangular tiling Hexagonal tiling Apeirogon Dihedron Lobachevski plane Hyperbolic tiling Order-7 heptagrammic tiling Heptagrammic-order...

split-complex number for a line in the Lobachevski plane. Since there are lines ultraparallel to the reference line in the Lobachevski plane, they need coordinates...

French translations of two key publications of non-Euclidean geometry: Lobachevski's Geometrical Studies on the Theory of Parallels and Bolyai's Science...

Euclidean geometry. 1870 – Felix Klein constructs an analytic geometry for Lobachevski's geometry, thereby establishing its self-consistency and the logical...

Mathematics Archive, University of St Andrews Braver, Seth (31 December 2011). Lobachevski Illuminated. American Mathematical Society. pp. 58–59. ISBN 9781470456405...

describe line geometry in the Euclidean plane and P1(M) to describe it for Lobachevski's plane. Yaglom's text A Simple Non-Euclidean Geometry appeared in English...

Möbius strip, 1870 – Felix Klein constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence...

that the Lorentz transformation takes Galilean form when written in Lobachevski coordinates. Walter, Scott A. (1999a), "Minkowski, mathematicians, and...

flat plane, or on a sphere with a constant positive curvature, or on a Lobachevski plane with constant negative curvature. If they are not living on the...

For Christopher, this truly nutty film 'is to other film noirs what Lobachevski's geometry—in which parallel lines eventually intersect—is to Euclid's...

computer. 482 Addison, Thomas 483 Struve, Friedrich Georg Wilhelm Von 484 Lobachevski, Nikolai Ivanovich 485 Mitscherlich, Eilhardt 486 Babinet, Jacques 487...

Back: The Calculus as Algebra and Selected Writings 2015: Seth Braver, Lobachevski Illuminated 2017: Tim Chartier, When Life is Linear: From Computer Graphics...

and exploited. Topics include line coordinates in the Euclidean and Lobachevski planes, and inversive geometry. The first three books were originally...

Sciences in Brussels (2003), Honorary Member of London Math Society (1987), Lobachevski International Prize of the Soviet Academy of Sciences (1981), Bogoliubov...

theorem "For every given angle a there is a line p such that Π(p) = a" Lobachevski, Nicholas (1914). Geometrical Researches on The Theory of Parallels (PDF)...