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 6 added 2 characters in body edited Dec 3 '16 at 19:12 Jo Wehler 16.2k22 gold badges1818 silver badges6464 bronze badges Euclidean geometry is a mathematical theory, not a scientific theory. It starts from definitions and axioms and makes deductions from the axioms. It is not necessary to go out, to draw lines and angles and to measure real geometric figures. On the other hand, Euclid like everybody until the 19th century thought that Euclidean geometry also describes our world. Prompted by the question whether the parallel postulate can be deduced from the other axioms, mathematicians in the 19th century (Gauss, Bolyai, Lobachevski) detected non-Euclidean geometries. This shows that the parallel postulate is independent from the other axioms. The proof goes by showing that models exists which satisfy all axioms but not the parallel postulate. Hence the question came up whether Euclidean geometry is the only geometry to be used in natural science. As we know today thanks to the General Theory of Relativity, near biglarge mass distribution spacetime is curved and not Euclidean. Here Euclidean geometry does not apply. A nice example is gravitation lensing, see https://en.wikipedia.org/wiki/Gravitational_lens#/media/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG Euclidean geometry is a mathematical theory, not a scientific theory. It starts from definitions and axioms and makes deductions from the axioms. It is not necessary to go out, to draw lines and angles and to measure real geometric figures. On the other hand, Euclid like everybody until the 19th century thought that Euclidean geometry also describes our world. Prompted by the question whether the parallel postulate can be deduced from the other axioms, mathematicians in the 19th century (Gauss, Bolyai, Lobachevski) detected non-Euclidean geometries. This shows that the parallel postulate is independent from the other axioms. The proof goes by showing that models exists which satisfy all axioms but not the parallel postulate. Hence the question came up whether Euclidean geometry is the only geometry to be used in natural science. As we know today thanks to the General Theory of Relativity, near big mass distribution spacetime is curved and not Euclidean. Here Euclidean geometry does not apply. A nice example is gravitation lensing, see https://en.wikipedia.org/wiki/Gravitational_lens#/media/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG Euclidean geometry is a mathematical theory, not a scientific theory. It starts from definitions and axioms and makes deductions from the axioms. It is not necessary to go out, to draw lines and angles and to measure real geometric figures. On the other hand, Euclid like everybody until the 19th century thought that Euclidean geometry also describes our world. Prompted by the question whether the parallel postulate can be deduced from the other axioms, mathematicians in the 19th century (Gauss, Bolyai, Lobachevski) detected non-Euclidean geometries. This shows that the parallel postulate is independent from the other axioms. The proof goes by showing that models exists which satisfy all axioms but not the parallel postulate. Hence the question came up whether Euclidean geometry is the only geometry to be used in natural science. As we know today thanks to the General Theory of Relativity, near large mass distribution spacetime is curved and not Euclidean. Here Euclidean geometry does not apply. A nice example is gravitation lensing, see https://en.wikipedia.org/wiki/Gravitational_lens#/media/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG 5 edited body edited Apr 6 '16 at 14:40 Jo Wehler 16.2k22 gold badges1818 silver badges6464 bronze badges Euclidean geometry is a mathematical theory, not a scientific theory. It starts from definitions and axioms and makes deductions from the axioms. It is not necessary to go out, to draw lines and angles and to measure real geometric figures. On the other hand, Euclid like everybody until the 19th century thought that Euclidean geometry also describes our world. Prompted by the question whether the parallel postulate can be deduced from the other axioms, mathematicians in the 19th century (Gauss, Bolyai, Lobachevski) detected non-Euclidean geometries. This shows that the parallel postulate is independent from the other axioms. The proof goes by showing that models exists which satisfy all axioms but not the parallel postulate. Hence the question came up whether Euclidean geoemtrygeometry is the only geometry to be used in natural science. As we know today thanks to the General Theory of Relativity, near big mass distribution spacetime is curved and not Euclidean. Here Euclidean geometry does not apply. A nice example is gravitation lensing, see https://en.wikipedia.org/wiki/Gravitational_lens#/media/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG Euclidean geometry is a mathematical theory, not a scientific theory. It starts from definitions and axioms and makes deductions from the axioms. It is not necessary to go out, to draw lines and angles and to measure real geometric figures. On the other hand, Euclid like everybody until the 19th century thought that Euclidean geometry also describes our world. Prompted by the question whether the parallel postulate can be deduced from the other axioms, mathematicians in the 19th century (Gauss, Bolyai, Lobachevski) detected non-Euclidean geometries. This shows that the parallel postulate is independent from the other axioms. The proof goes by showing that models exists which satisfy all axioms but not the parallel postulate. Hence the question came up whether Euclidean geoemtry is the only geometry to be used in natural science. As we know today thanks to the General Theory of Relativity, near big mass distribution spacetime is curved and not Euclidean. Here Euclidean geometry does not apply. A nice example is gravitation lensing, see https://en.wikipedia.org/wiki/Gravitational_lens#/media/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG Euclidean geometry is a mathematical theory, not a scientific theory. It starts from definitions and axioms and makes deductions from the axioms. It is not necessary to go out, to draw lines and angles and to measure real geometric figures. On the other hand, Euclid like everybody until the 19th century thought that Euclidean geometry also describes our world. Prompted by the question whether the parallel postulate can be deduced from the other axioms, mathematicians in the 19th century (Gauss, Bolyai, Lobachevski) detected non-Euclidean geometries. This shows that the parallel postulate is independent from the other axioms. The proof goes by showing that models exists which satisfy all axioms but not the parallel postulate. Hence the question came up whether Euclidean geometry is the only geometry to be used in natural science. As we know today thanks to the General Theory of Relativity, near big mass distribution spacetime is curved and not Euclidean. Here Euclidean geometry does not apply. A nice example is gravitation lensing, see https://en.wikipedia.org/wiki/Gravitational_lens#/media/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG 4 edited body edited Nov 28 '15 at 11:36 Jo Wehler 16.2k22 gold badges1818 silver badges6464 bronze badges Euclidean geometry is a mathematical theory, not a scientific theory. It starts from definitions and axioms and makes deductions from the axioms. It is not necessary to go out, to draw lines and angles and to measure real geometric figures. On the other hand, Euclid like everybody until the 19th century thought that Euclidean geometry also describes our world. Prompted by the question whether the parallel postulate can be deduced from the other axioms, mathematicians in the 19th century (Gauss, Bolyai, Lobachevski) detected non-Euclidean geometries. This shows that the parallel postulate is independent from the other axioms. The proof goes by showing that models exists which satisfy all axioms but not the parallel postulate. Hence the question came up whether Euclidean geoemtry is the only geometry to be used in natural science. As we know today thanks to the General Theory of Relativity, near big mass distribution spacetime is curved and not Euclidean. Here Euclidean goemetrygeometry does not apply. A nice example is gravitation lensing, see https://en.wikipedia.org/wiki/Gravitational_lens#/media/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG Euclidean geometry is a mathematical theory, not a scientific theory. It starts from definitions and axioms and makes deductions from the axioms. It is not necessary to go out, to draw lines and angles and to measure real geometric figures. On the other hand, Euclid like everybody until the 19th century thought that Euclidean geometry also describes our world. Prompted by the question whether the parallel postulate can be deduced from the other axioms, mathematicians in the 19th century (Gauss, Bolyai, Lobachevski) detected non-Euclidean geometries. This shows that the parallel postulate is independent from the other axioms. The proof goes by showing that models exists which satisfy all axioms but not the parallel postulate. Hence the question came up whether Euclidean geoemtry is the only geometry to be used in natural science. As we know today thanks to the General Theory of Relativity, near big mass distribution spacetime is curved and not Euclidean. Here Euclidean goemetry does not apply. A nice example is gravitation lensing, see https://en.wikipedia.org/wiki/Gravitational_lens#/media/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG Euclidean geometry is a mathematical theory, not a scientific theory. It starts from definitions and axioms and makes deductions from the axioms. It is not necessary to go out, to draw lines and angles and to measure real geometric figures. On the other hand, Euclid like everybody until the 19th century thought that Euclidean geometry also describes our world. Prompted by the question whether the parallel postulate can be deduced from the other axioms, mathematicians in the 19th century (Gauss, Bolyai, Lobachevski) detected non-Euclidean geometries. This shows that the parallel postulate is independent from the other axioms. The proof goes by showing that models exists which satisfy all axioms but not the parallel postulate. Hence the question came up whether Euclidean geoemtry is the only geometry to be used in natural science. As we know today thanks to the General Theory of Relativity, near big mass distribution spacetime is curved and not Euclidean. Here Euclidean geometry does not apply. A nice example is gravitation lensing, see https://en.wikipedia.org/wiki/Gravitational_lens#/media/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG 3 deleted 1 character in body edited Nov 28 '15 at 10:47 Jo Wehler 16.2k22 gold badges1818 silver badges6464 bronze badges 2 edited body edited Nov 28 '15 at 8:38 Jo Wehler 16.2k22 gold badges1818 silver badges6464 bronze badges 1 answered Nov 28 '15 at 6:57 Jo Wehler 16.2k22 gold badges1818 silver badges6464 bronze badges