Euclidean geometry (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Euclidean geometry" in English language version.

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ams.org

Stillwell 2001, p. 18–21; In four-dimensional Euclidean geometry, a quaternion is simply a (w, x, y, z) Cartesian coordinate. Hamilton did not see them as such when he discovered the quaternions. Schläfli would be the first to consider four-dimensional Euclidean space, publishing his discovery of the regular polyschemes in 1852, but Hamilton would never be influenced by that work, which remained obscure into the 20th century. Hamilton found the quaternions when he realized that a fourth dimension, in some sense, would be necessary in order to model rotations in three-dimensional space. Although he described a quaternion as an ordered four-element multiple of real numbers, the quaternions were for him an extension of the complex numbers, not a Euclidean space of four dimensions. Stillwell, John (January 2001). "The Story of the 120-Cell" (PDF). Notices of the AMS. 48 (1): 17–25.

books.google.com

The assumptions of Euclid are discussed from a modern perspective in Harold E. Wolfe (2007). Introduction to Non-Euclidean Geometry. Mill Press. p. 9. ISBN 978-1-4067-1852-2.
Heath, p. 135. Extract of page 135.
Richard J. Trudeau (2008). "Euclid's axioms". The Non-Euclidean Revolution. Birkhäuser. pp. 39 ff. ISBN 978-0-8176-4782-7.
See, for example: Luciano da Fontoura Costa; Roberto Marcondes Cesar (2001). Shape analysis and classification: theory and practice. CRC Press. p. 314. ISBN 0-8493-3493-4. and Helmut Pottmann; Johannes Wallner (2010). Computational Line Geometry. Springer. p. 60. ISBN 978-3-642-04017-7. The group of motions underlie the metric notions of geometry. See Felix Klein (2004). Elementary Mathematics from an Advanced Standpoint: Geometry (Reprint of 1939 Macmillan Company ed.). Courier Dover. p. 167. ISBN 0-486-43481-8.
Roger Penrose (2007). The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage Books. p. 29. ISBN 978-0-679-77631-4.
A detailed discussion can be found in James T. Smith (2000). "Chapter 2: Foundations". Methods of geometry. Wiley. pp. 19 ff. ISBN 0-471-25183-6.
Société française de philosophie (1900). Revue de métaphysique et de morale, Volume 8. Hachette. p. 592.
Bertrand Russell (2000). "Mathematics and the metaphysicians". In James Roy Newman (ed.). The world of mathematics. Vol. 3 (Reprint of Simon and Schuster 1956 ed.). Courier Dover Publications. p. 1577. ISBN 0-486-41151-6.
Bertrand Russell (1897). "Introduction". An essay on the foundations of geometry. Cambridge University Press.
George David Birkhoff; Ralph Beatley (1999). "Chapter 2: The five fundamental principles". Basic Geometry (3rd ed.). AMS Bookstore. pp. 38 ff. ISBN 0-8218-2101-6.
James T. Smith (10 January 2000). "Chapter 3: Elementary Euclidean Geometry". Cited work. John Wiley & Sons. pp. 84 ff. ISBN 9780471251835.
Edwin E. Moise (1990). Elementary geometry from an advanced standpoint (3rd ed.). Addison–Wesley. ISBN 0-201-50867-2.
John R. Silvester (2001). "§1.4 Hilbert and Birkhoff". Geometry: ancient and modern. Oxford University Press. ISBN 0-19-850825-5.
Alfred Tarski (2007). "What is elementary geometry". In Leon Henkin; Patrick Suppes; Alfred Tarski (eds.). Studies in Logic and the Foundations of Mathematics – The Axiomatic Method with Special Reference to Geometry and Physics (Proceedings of International Symposium at Berkeley 1957–8; Reprint ed.). Brouwer Press. p. 16. ISBN 978-1-4067-5355-4. We regard as elementary that part of Euclidean geometry which can be formulated and established without the help of any set-theoretical devices
Keith Simmons (2009). "Tarski's logic". In Dov M. Gabbay; John Woods (eds.). Logic from Russell to Church. Elsevier. p. 574. ISBN 978-0-444-51620-6.

doi.org

Florence P. Lewis (Jan 1920), "History of the Parallel Postulate", The American Mathematical Monthly, 27 (1), The American Mathematical Monthly, Vol. 27, No. 1: 16–23, doi:10.2307/2973238, JSTOR 2973238.
Perez-Gracia & Thomas 2017; "It is actually Cayley whom we must thank for the correct development of quaternions as a representation of rotations." Perez-Gracia, Alba; Thomas, Federico (2017). "On Cayley's Factorization of 4D Rotations and Applications" (PDF). Adv. Appl. Clifford Algebras. 27: 523–538. doi:10.1007/s00006-016-0683-9. hdl:2117/113067. S2CID 12350382.

handle.net

hdl.handle.net

Perez-Gracia & Thomas 2017; "It is actually Cayley whom we must thank for the correct development of quaternions as a representation of rotations." Perez-Gracia, Alba; Thomas, Federico (2017). "On Cayley's Factorization of 4D Rotations and Applications" (PDF). Adv. Appl. Clifford Algebras. 27: 523–538. doi:10.1007/s00006-016-0683-9. hdl:2117/113067. S2CID 12350382.

jstor.org

Florence P. Lewis (Jan 1920), "History of the Parallel Postulate", The American Mathematical Monthly, 27 (1), The American Mathematical Monthly, Vol. 27, No. 1: 16–23, doi:10.2307/2973238, JSTOR 2973238.

semanticscholar.org

api.semanticscholar.org

Perez-Gracia & Thomas 2017; "It is actually Cayley whom we must thank for the correct development of quaternions as a representation of rotations." Perez-Gracia, Alba; Thomas, Federico (2017). "On Cayley's Factorization of 4D Rotations and Applications" (PDF). Adv. Appl. Clifford Algebras. 27: 523–538. doi:10.1007/s00006-016-0683-9. hdl:2117/113067. S2CID 12350382.

unsw.edu.au

gmat.unsw.edu.au

Rizos, Chris. University of New South Wales. GPS Satellite Signals Archived 2010-06-12 at the Wayback Machine. 1999.

upc.edu

upcommons.upc.edu

Perez-Gracia & Thomas 2017; "It is actually Cayley whom we must thank for the correct development of quaternions as a representation of rotations." Perez-Gracia, Alba; Thomas, Federico (2017). "On Cayley's Factorization of 4D Rotations and Applications" (PDF). Adv. Appl. Clifford Algebras. 27: 523–538. doi:10.1007/s00006-016-0683-9. hdl:2117/113067. S2CID 12350382.

web.archive.org

Tom Hull. "Origami and Geometric Constructions". Archived from the original on 2019-06-18. Retrieved 2013-12-29.
Rizos, Chris. University of New South Wales. GPS Satellite Signals Archived 2010-06-12 at the Wayback Machine. 1999.

wne.edu

mars.wne.edu

Tom Hull. "Origami and Geometric Constructions". Archived from the original on 2019-06-18. Retrieved 2013-12-29.