Square pyramid (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Square pyramid" in English language version.

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21books.google.com

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1harvard.edu

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Johnson (1966). Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603.
Simonson (2011), p. 123; Berman (1971), see table IV, line 21. Simonson, Shai (2011). Rediscovering Mathematics: You Do the Math. Mathematical Association of America. ISBN 978-0-88385-912-4. Berman, Martin (1971). "Regular-faced convex polyhedra". Journal of the Franklin Institute. 291 (5): 329–352. doi:10.1016/0016-0032(71)90071-8. MR 0290245.
Hartshorne (2000), p. 464; Johnson (1966). Hartshorne, Robin (2000). Geometry: Euclid and Beyond. Undergraduate Texts in Mathematics. Springer-Verlag. ISBN 9780387986500. Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603.

archive.org

Cromwell (1997), pp. 20–22. Cromwell, Peter R. (1997). Polyhedra. Cambridge University Press. ISBN 978-0-521-55432-9.
Herz-Fischler (2000) surveys many alternative theories for this pyramid's shape. See Chapter 11, "Kepler triangle theory", pp. 80–91, for material specific to the Kepler triangle, and p. 166 for the conclusion that the Kepler triangle theory can be eliminated by the principle that "A theory must correspond to a level of mathematics consistent with what was known to the ancient Egyptians." See note 3, p. 229, for the history of Kepler's work with this triangle. See Rossi (2004), pp. 67–68, quoting that "there is no direct evidence in any ancient Egyptian written mathematical source of any arithmetic calculation or geometrical construction which could be classified as the Golden Section ... convergence to $\varphi$ , and $\varphi$ itself as a number, do not fit with the extant Middle Kingdom mathematical sources"; see also extensive discussion of multiple alternative theories for the shape of the pyramid and other Egyptian architecture, pp. 7–56. See also Rossi & Tout (2002) and Markowsky (1992). Herz-Fischler, Roger (2000). The Shape of the Great Pyramid. Wilfrid Laurier University Press. ISBN 0-88920-324-5. Rossi, Corinna (2004). Architecture and Mathematics in Ancient Egypt. Cambridge University Press. pp. 67–68. Rossi, Corinna; Tout, Christopher A. (2002). "Were the Fibonacci series and the Golden Section known in ancient Egypt?". Historia Mathematica. 29 (2): 101–113. doi:10.1006/hmat.2001.2334. hdl:11311/997099. Markowsky, George (1992). "Misconceptions about the Golden Ratio" (PDF). The College Mathematics Journal. 23 (1). Mathematical Association of America: 2–19. doi:10.2307/2686193. JSTOR 2686193. Retrieved 29 June 2012.

books.google.com

Clissold (2020), p. 180. Clissold, Caroline (2020). Maths 5–11: A Guide for Teachers. Taylor & Francis. ISBN 978-0-429-26907-3.
O'Keeffe & Hyde (2020), p. 141; Smith (2000), p. 98. O'Keeffe, Michael; Hyde, Bruce G. (2020). Crystal Structures: Patterns and Symmetry. Dover Publications. ISBN 978-0-486-83654-6. Smith, James T. (2000). Methods of Geometry. John Wiley & Sons. ISBN 0-471-25183-6.
Freitag (2014), p. 598. Freitag, Mark A. (2014). Mathematics for Elementary School Teachers: A Process Approach. Brooks/Cole. ISBN 978-0-618-61008-2.
Larcombe (1929), p. 177; Perry & Perry (1981), pp. 145–146. Larcombe, H. J. (1929). Cambridge Intermediate Mathematics: Geometry Part II. Cambridge University Press. Perry, O. W.; Perry, J. (1981). Mathematics. Springer. doi:10.1007/978-1-349-05230-1. ISBN 978-1-349-05230-1.
Larcombe (1929), p. 177. Larcombe, H. J. (1929). Cambridge Intermediate Mathematics: Geometry Part II. Cambridge University Press.
Freitag (2014), p. 798. Freitag, Mark A. (2014). Mathematics for Elementary School Teachers: A Process Approach. Brooks/Cole. ISBN 978-0-618-61008-2.
Alexander & Koeberlin (2014), p. 403.
Larcombe (1929), p. 178. Larcombe, H. J. (1929). Cambridge Intermediate Mathematics: Geometry Part II. Cambridge University Press.
Eves (1997), p. 2. Eves, Howard (1997). Foundations and Fundamental Concepts of Mathematics (3rd ed.). Dover Publications. ISBN 978-0-486-69609-6.
Hocevar (1903), p. 44. Hocevar, Franx (1903). Solid Geometry. A. & C. Black.
Uehara (2020), p. 62. Uehara, Ryuhei (2020). Introduction to Computational Origami: The World of New Computational Geometry. Springer. doi:10.1007/978-981-15-4470-5. ISBN 978-981-15-4470-5. S2CID 220150682.
Simonson (2011), p. 123; Berman (1971), see table IV, line 21. Simonson, Shai (2011). Rediscovering Mathematics: You Do the Math. Mathematical Association of America. ISBN 978-0-88385-912-4. Berman, Martin (1971). "Regular-faced convex polyhedra". Journal of the Franklin Institute. 291 (5): 329–352. doi:10.1016/0016-0032(71)90071-8. MR 0290245.
Pisanski & Servatius (2013), p. 21. Pisanski, Tomaž; Servatius, Brigitte (2013). Configuration from a Graphical Viewpoint. Springer. doi:10.1007/978-0-8176-8364-1. ISBN 978-0-8176-8363-4.
Wohlleben (2019), p. 485–486. Wohlleben, Eva (2019). "Duality in Non-Polyhedral Bodies Part I: Polyliner". In Cocchiarella, Luigi (ed.). ICGG 2018 – Proceedings of the 18th International Conference on Geometry and Graphics: 40th Anniversary – Milan, Italy, August 3–7, 2018. International Conference on Geometry and Graphics. Springer. doi:10.1007/978-3-319-95588-9. ISBN 978-3-319-95588-9.
Hartshorne (2000), p. 464; Johnson (1966). Hartshorne, Robin (2000). Geometry: Euclid and Beyond. Undergraduate Texts in Mathematics. Springer-Verlag. ISBN 9780387986500. Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603.
Kinsey, Moore & Prassidis (2011), p. 371. Kinsey, L. Christine; Moore, Teresa E.; Prassidis, Efstratios (2011). Geometry and Symmetry. John Wiley & Sons. ISBN 978-0-470-49949-8.
Feder (2010), p. 34; Takacs & Cline (2015), p. 16. Feder, Kenneth L. (2010). Encyclopedia of Dubious Archaeology: From Atlantis to the Walam Olum: From Atlantis to the Walam Olum. ABC-CLIO. ISBN 978-0-313-37919-2. Takacs, Sarolta Anna; Cline, Eric H. (2015). The Ancient World. Routledge. p. 16. ISBN 978-1-317-45839-5.
Jarvis & Naested (2012), p. 172; Simonson (2011), p. 122. Jarvis, Daniel; Naested, Irene (2012). Exploring the Math and Art Connection: Teaching and Learning Between the Lines. Brush Education. ISBN 978-1-55059-398-3. Simonson, Shai (2011). Rediscovering Mathematics: You Do the Math. Mathematical Association of America. ISBN 978-0-88385-912-4.
Petrucci, Harwood & Herring (2002), p. 414. Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey (2002). General Chemistry: Principles and Modern Applications. Vol. 1. Prentice Hall. ISBN 978-0-13-014329-7.
Emeléus (1969), p. 13. Emeléus, H. J. (1969). The Chemistry of Fluorine and Its Compounds. Academic Press. ISBN 978-1-4832-7304-4.
Rajwade (2001), pp. 84–89. See Table 12.3, where $P_{n}$ denotes the $n$ -sided prism and $A_{n}$ denotes the $n$ -sided antiprism. Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Hindustan Book Agency. doi:10.1007/978-93-86279-06-4. ISBN 978-93-86279-06-4.

doi.org

Johnson (1966). Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603.
Larcombe (1929), p. 177; Perry & Perry (1981), pp. 145–146. Larcombe, H. J. (1929). Cambridge Intermediate Mathematics: Geometry Part II. Cambridge University Press. Perry, O. W.; Perry, J. (1981). Mathematics. Springer. doi:10.1007/978-1-349-05230-1. ISBN 978-1-349-05230-1.
Wagner (1979). Wagner, Donald Blackmore (1979). "An early Chinese derivation of the volume of a pyramid: Liu Hui, third century A.D.". Historia Mathematica. 6 (2): 164–188. doi:10.1016/0315-0860(79)90076-4.
Uehara (2020), p. 62. Uehara, Ryuhei (2020). Introduction to Computational Origami: The World of New Computational Geometry. Springer. doi:10.1007/978-981-15-4470-5. ISBN 978-981-15-4470-5. S2CID 220150682.
Simonson (2011), p. 123; Berman (1971), see table IV, line 21. Simonson, Shai (2011). Rediscovering Mathematics: You Do the Math. Mathematical Association of America. ISBN 978-0-88385-912-4. Berman, Martin (1971). "Regular-faced convex polyhedra". Journal of the Franklin Institute. 291 (5): 329–352. doi:10.1016/0016-0032(71)90071-8. MR 0290245.
Pisanski & Servatius (2013), p. 21. Pisanski, Tomaž; Servatius, Brigitte (2013). Configuration from a Graphical Viewpoint. Springer. doi:10.1007/978-0-8176-8364-1. ISBN 978-0-8176-8363-4.
Wohlleben (2019), p. 485–486. Wohlleben, Eva (2019). "Duality in Non-Polyhedral Bodies Part I: Polyliner". In Cocchiarella, Luigi (ed.). ICGG 2018 – Proceedings of the 18th International Conference on Geometry and Graphics: 40th Anniversary – Milan, Italy, August 3–7, 2018. International Conference on Geometry and Graphics. Springer. doi:10.1007/978-3-319-95588-9. ISBN 978-3-319-95588-9.
Hartshorne (2000), p. 464; Johnson (1966). Hartshorne, Robin (2000). Geometry: Euclid and Beyond. Undergraduate Texts in Mathematics. Springer-Verlag. ISBN 9780387986500. Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603.
Herz-Fischler (2000) surveys many alternative theories for this pyramid's shape. See Chapter 11, "Kepler triangle theory", pp. 80–91, for material specific to the Kepler triangle, and p. 166 for the conclusion that the Kepler triangle theory can be eliminated by the principle that "A theory must correspond to a level of mathematics consistent with what was known to the ancient Egyptians." See note 3, p. 229, for the history of Kepler's work with this triangle. See Rossi (2004), pp. 67–68, quoting that "there is no direct evidence in any ancient Egyptian written mathematical source of any arithmetic calculation or geometrical construction which could be classified as the Golden Section ... convergence to $\varphi$ , and $\varphi$ itself as a number, do not fit with the extant Middle Kingdom mathematical sources"; see also extensive discussion of multiple alternative theories for the shape of the pyramid and other Egyptian architecture, pp. 7–56. See also Rossi & Tout (2002) and Markowsky (1992). Herz-Fischler, Roger (2000). The Shape of the Great Pyramid. Wilfrid Laurier University Press. ISBN 0-88920-324-5. Rossi, Corinna (2004). Architecture and Mathematics in Ancient Egypt. Cambridge University Press. pp. 67–68. Rossi, Corinna; Tout, Christopher A. (2002). "Were the Fibonacci series and the Golden Section known in ancient Egypt?". Historia Mathematica. 29 (2): 101–113. doi:10.1006/hmat.2001.2334. hdl:11311/997099. Markowsky, George (1992). "Misconceptions about the Golden Ratio" (PDF). The College Mathematics Journal. 23 (1). Mathematical Association of America: 2–19. doi:10.2307/2686193. JSTOR 2686193. Retrieved 29 June 2012.
Demey & Smessaert (2017). Demey, Lorenz; Smessaert, Hans (2017). "Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation". Symmetry. 9 (10): 204. Bibcode:2017Symm....9..204D. doi:10.3390/sym9100204.
Rajwade (2001), pp. 84–89. See Table 12.3, where $P_{n}$ denotes the $n$ -sided prism and $A_{n}$ denotes the $n$ -sided antiprism. Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Hindustan Book Agency. doi:10.1007/978-93-86279-06-4. ISBN 978-93-86279-06-4.

handle.net

hdl.handle.net

Herz-Fischler (2000) surveys many alternative theories for this pyramid's shape. See Chapter 11, "Kepler triangle theory", pp. 80–91, for material specific to the Kepler triangle, and p. 166 for the conclusion that the Kepler triangle theory can be eliminated by the principle that "A theory must correspond to a level of mathematics consistent with what was known to the ancient Egyptians." See note 3, p. 229, for the history of Kepler's work with this triangle. See Rossi (2004), pp. 67–68, quoting that "there is no direct evidence in any ancient Egyptian written mathematical source of any arithmetic calculation or geometrical construction which could be classified as the Golden Section ... convergence to $\varphi$ , and $\varphi$ itself as a number, do not fit with the extant Middle Kingdom mathematical sources"; see also extensive discussion of multiple alternative theories for the shape of the pyramid and other Egyptian architecture, pp. 7–56. See also Rossi & Tout (2002) and Markowsky (1992). Herz-Fischler, Roger (2000). The Shape of the Great Pyramid. Wilfrid Laurier University Press. ISBN 0-88920-324-5. Rossi, Corinna (2004). Architecture and Mathematics in Ancient Egypt. Cambridge University Press. pp. 67–68. Rossi, Corinna; Tout, Christopher A. (2002). "Were the Fibonacci series and the Golden Section known in ancient Egypt?". Historia Mathematica. 29 (2): 101–113. doi:10.1006/hmat.2001.2334. hdl:11311/997099. Markowsky, George (1992). "Misconceptions about the Golden Ratio" (PDF). The College Mathematics Journal. 23 (1). Mathematical Association of America: 2–19. doi:10.2307/2686193. JSTOR 2686193. Retrieved 29 June 2012.

harvard.edu

ui.adsabs.harvard.edu

Demey & Smessaert (2017). Demey, Lorenz; Smessaert, Hans (2017). "Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation". Symmetry. 9 (10): 204. Bibcode:2017Symm....9..204D. doi:10.3390/sym9100204.

heldermann-verlag.de

Slobodan, Obradović & Ðukanović (2015). Slobodan, Mišić; Obradović, Marija; Ðukanović, Gordana (2015). "Composite Concave Cupolae as Geometric and Architectural Forms" (PDF). Journal for Geometry and Graphics. 19 (1): 79–91.

jstor.org

Herz-Fischler (2000) surveys many alternative theories for this pyramid's shape. See Chapter 11, "Kepler triangle theory", pp. 80–91, for material specific to the Kepler triangle, and p. 166 for the conclusion that the Kepler triangle theory can be eliminated by the principle that "A theory must correspond to a level of mathematics consistent with what was known to the ancient Egyptians." See note 3, p. 229, for the history of Kepler's work with this triangle. See Rossi (2004), pp. 67–68, quoting that "there is no direct evidence in any ancient Egyptian written mathematical source of any arithmetic calculation or geometrical construction which could be classified as the Golden Section ... convergence to $\varphi$ , and $\varphi$ itself as a number, do not fit with the extant Middle Kingdom mathematical sources"; see also extensive discussion of multiple alternative theories for the shape of the pyramid and other Egyptian architecture, pp. 7–56. See also Rossi & Tout (2002) and Markowsky (1992). Herz-Fischler, Roger (2000). The Shape of the Great Pyramid. Wilfrid Laurier University Press. ISBN 0-88920-324-5. Rossi, Corinna (2004). Architecture and Mathematics in Ancient Egypt. Cambridge University Press. pp. 67–68. Rossi, Corinna; Tout, Christopher A. (2002). "Were the Fibonacci series and the Golden Section known in ancient Egypt?". Historia Mathematica. 29 (2): 101–113. doi:10.1006/hmat.2001.2334. hdl:11311/997099. Markowsky, George (1992). "Misconceptions about the Golden Ratio" (PDF). The College Mathematics Journal. 23 (1). Mathematical Association of America: 2–19. doi:10.2307/2686193. JSTOR 2686193. Retrieved 29 June 2012.

maine.edu

umcs.maine.edu

Herz-Fischler (2000) surveys many alternative theories for this pyramid's shape. See Chapter 11, "Kepler triangle theory", pp. 80–91, for material specific to the Kepler triangle, and p. 166 for the conclusion that the Kepler triangle theory can be eliminated by the principle that "A theory must correspond to a level of mathematics consistent with what was known to the ancient Egyptians." See note 3, p. 229, for the history of Kepler's work with this triangle. See Rossi (2004), pp. 67–68, quoting that "there is no direct evidence in any ancient Egyptian written mathematical source of any arithmetic calculation or geometrical construction which could be classified as the Golden Section ... convergence to $\varphi$ , and $\varphi$ itself as a number, do not fit with the extant Middle Kingdom mathematical sources"; see also extensive discussion of multiple alternative theories for the shape of the pyramid and other Egyptian architecture, pp. 7–56. See also Rossi & Tout (2002) and Markowsky (1992). Herz-Fischler, Roger (2000). The Shape of the Great Pyramid. Wilfrid Laurier University Press. ISBN 0-88920-324-5. Rossi, Corinna (2004). Architecture and Mathematics in Ancient Egypt. Cambridge University Press. pp. 67–68. Rossi, Corinna; Tout, Christopher A. (2002). "Were the Fibonacci series and the Golden Section known in ancient Egypt?". Historia Mathematica. 29 (2): 101–113. doi:10.1006/hmat.2001.2334. hdl:11311/997099. Markowsky, George (1992). "Misconceptions about the Golden Ratio" (PDF). The College Mathematics Journal. 23 (1). Mathematical Association of America: 2–19. doi:10.2307/2686193. JSTOR 2686193. Retrieved 29 June 2012.

semanticscholar.org

api.semanticscholar.org

Johnson (1966). Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603.
Uehara (2020), p. 62. Uehara, Ryuhei (2020). Introduction to Computational Origami: The World of New Computational Geometry. Springer. doi:10.1007/978-981-15-4470-5. ISBN 978-981-15-4470-5. S2CID 220150682.
Hartshorne (2000), p. 464; Johnson (1966). Hartshorne, Robin (2000). Geometry: Euclid and Beyond. Undergraduate Texts in Mathematics. Springer-Verlag. ISBN 9780387986500. Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603.

zbmath.org

Johnson (1966). Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603.
Hartshorne (2000), p. 464; Johnson (1966). Hartshorne, Robin (2000). Geometry: Euclid and Beyond. Undergraduate Texts in Mathematics. Springer-Verlag. ISBN 9780387986500. Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603.