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  2. Non-Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Non-Euclidean_geometry

    The simplest of these is called elliptic geometry and it is considered a non-Euclidean geometry due to its lack of parallel lines. [12] By formulating the geometry in terms of a curvature tensor, Riemann allowed non-Euclidean geometry to apply to higher dimensions. Beltrami (1868) was the first to apply Riemann's geometry to spaces of negative ...

  3. MathPath - Wikipedia

    en.wikipedia.org/wiki/MathPath

    MathPath was founded in 2002 by George Rubin Thomas, who had previously founded Mathcamp for high school students and has since founded Epsiloncamp for children age 7–11 (in 2011, originally aged 8–11) and Delta Camp for children 6 and 7 (in 2014 and 2015, now merged with Epsilon Camp). His goal was to inspire and advance the most ...

  4. Foundations of geometry - Wikipedia

    en.wikipedia.org/wiki/Foundations_of_geometry

    In the 1960s a new set of axioms for Euclidean geometry, suitable for American high school geometry courses, was introduced by the School Mathematics Study Group (SMSG), as a part of the New math curricula. This set of axioms follows the Birkhoff model of using the real numbers to gain quick entry into the geometric fundamentals.

  5. Erlangen program - Wikipedia

    en.wikipedia.org/wiki/Erlangen_program

    One example: oriented (i.e., reflections not included) elliptic geometry (i.e., the surface of an n-sphere with opposite points identified) and oriented spherical geometry (the same non-Euclidean geometry, but with opposite points not identified) have isomorphic automorphism group, SO(n+1) for even n. These may appear to be distinct.

  6. Journey into Geometries - Wikipedia

    en.wikipedia.org/wiki/Journey_into_Geometries

    Journey into Geometries is a book on non-Euclidean geometry. It was written by Hungarian-Australian mathematician Márta Svéd and published in 1991 by the Mathematical Association of America in their MAA Spectrum book series.

  7. Category:Non-Euclidean geometry - Wikipedia

    en.wikipedia.org/.../Category:Non-Euclidean_geometry

    Within contemporary geometry there are many kinds of geometry that are quite different from Euclidean geometry, first encountered in the forms of elementary geometry, plane geometry of triangles and circles, and solid geometry. The conventional meaning of Non-Euclidean geometry is the one set in the nineteenth century: the fields of elliptic ...

  8. Lénárt sphere - Wikipedia

    en.wikipedia.org/wiki/Lénárt_sphere

    The Lénárt sphere was invented by István Lénárt in Hungary in the early 1990s and its use is described in his 2003 book comparing planar and spherical geometry. [4] The Lénárt sphere is widely used throughout Europe in university courses on non-Euclidean geometry and geographic information systems (GIS).

  9. Birkhoff's axioms - Wikipedia

    en.wikipedia.org/wiki/Birkhoff's_axioms

    Birkhoff's axiomatic system was utilized in the secondary-school textbook by Birkhoff and Beatley. [2] These axioms were also modified by the School Mathematics Study Group to provide a new standard for teaching high school geometry, known as SMSG axioms. A few other textbooks in the foundations of geometry use variants of Birkhoff's axioms. [3]

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