Kepler triangle (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Kepler triangle" in English language version.

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mathscinet.ams.org

Herz-Fischler, Roger (2000). The Shape of the Great Pyramid. Waterloo, Ontario: Wilfrid Laurier University Press. ISBN 0-88920-324-5. MR 1788996. The entire book 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.
Høyrup, Jens (2002). "Review of The shape of the Great Pyramid by Roger Herz-Fischler" (PDF). Mathematical Reviews. MR 1788996. Archived (PDF) from the original on 2022-02-23. Retrieved 2022-02-23.
Hughes, Barnabas, ed. (2008). Fibonacci's De Practica Geometrie. Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. pp. 130–131. doi:10.1007/978-0-387-72931-2. ISBN 978-0-387-72930-5. MR 2364574.
Anglin, W. S. (1994). "Great pyramid nonsense". Mathematics: a concise history and philosophy. Undergraduate Texts in Mathematics. New York: Springer-Verlag. p. 4. doi:10.1007/978-1-4612-0875-4. ISBN 0-387-94280-7. MR 1301327.
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. MR 1896969.
Bruce, Ian (1994). "Another instance of the golden right triangle" (PDF). Fibonacci Quarterly. 32 (3): 232–233. doi:10.1080/00150517.1994.12429219. MR 1285752. Archived (PDF) from the original on 2022-01-29. Retrieved 2022-01-29.
DeTemple, Duane W. (1992). "The triangle of smallest perimeter which circumscribes a semicircle" (PDF). Fibonacci Quarterly. 30 (3): 274. doi:10.1080/00150517.1992.12429354. MR 1175315. Archived (PDF) from the original on 2022-01-20. Retrieved 2022-01-29.

archive.org

Fink, Karl (1903). A Brief History of Mathematics: An Authorized Translation of Dr. Karl Fink's Geschichte der Elementar-Mathematik. Translated by Beman, Wooster Woodruff; Smith, David Eugene (2nd ed.). Chicago: Open Court Publishing Company. p. 223.
Ghyka, Matila Costiescu (1946). The Geometry of Art and Life. New York: Sheed and Ward. p. 22.

arxiv.org

Kocik, Jerzy (January 2019). "A note on unbounded Apollonian disk packings". arXiv:1910.05924 [math.MG].

books.google.com

Huffman, Carl (2005). "Archytas and the history of means". Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King. Cambridge University Press. pp. 170–177. ISBN 978-1-139-44407-1. Archived from the original on 2022-01-22. Retrieved 2022-01-22.

dal.ca

mathstat.dal.ca

Bruce, Ian (1994). "Another instance of the golden right triangle" (PDF). Fibonacci Quarterly. 32 (3): 232–233. doi:10.1080/00150517.1994.12429219. MR 1285752. Archived (PDF) from the original on 2022-01-29. Retrieved 2022-01-29.

doi.org

Busard, Hubert L. L. (April–June 1968). "L'algèbre au Moyen Âge : le "Liber mensurationum" d'Abû Bekr". Journal des Savants (in French and Latin). 1968 (2): 65–124. doi:10.3406/jds.1968.1175. Archived from the original on 2022-01-12. Retrieved 2022-01-12. See problem 51, reproduced on p. 98
Hughes, Barnabas, ed. (2008). Fibonacci's De Practica Geometrie. Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. pp. 130–131. doi:10.1007/978-0-387-72931-2. ISBN 978-0-387-72930-5. MR 2364574.
Bartlett, Christopher (May 2014). "The Design of The Great Pyramid of Khufu". Nexus Network Journal. 16 (2): 299–311. doi:10.1007/s00004-014-0193-9. S2CID 122021107.
Fischler, R. (1979). "What did Herodotus really say? or how to build (a theory of) the Great Pyramid". Environment and Planning B: Planning and Design. 6 (1): 89–93. Bibcode:1979EnPlB...6...89F. doi:10.1068/b060089. S2CID 62210630.
Anglin, W. S. (1994). "Great pyramid nonsense". Mathematics: a concise history and philosophy. Undergraduate Texts in Mathematics. New York: Springer-Verlag. p. 4. doi:10.1007/978-1-4612-0875-4. ISBN 0-387-94280-7. MR 1301327.
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. MR 1896969.
Markowsky, George (January 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. Archived (PDF) from the original on 2020-12-11. Retrieved 2012-06-29. It does not appear that the Egyptians even knew of the existence of $\varphi$ much less incorporated it in their buildings
Bruce, Ian (1994). "Another instance of the golden right triangle" (PDF). Fibonacci Quarterly. 32 (3): 232–233. doi:10.1080/00150517.1994.12429219. MR 1285752. Archived (PDF) from the original on 2022-01-29. Retrieved 2022-01-29.
Di Domenico, Angelo (July 2005). "89.41 The golden ratio—the right triangle—and the arithmetic, geometric, and harmonic means". The Mathematical Gazette. 89 (515): 261. doi:10.1017/s0025557200177769. JSTOR 3621234. S2CID 123738769.
Halleck, Ezra (March 2012). "Teaching tip: Consider a circular cow". The College Mathematics Journal. 43 (2): 133. doi:10.4169/college.math.j.43.2.133. JSTOR 10.4169/college.math.j.43.2.133. S2CID 123891402.
DeTemple, Duane W. (1992). "The triangle of smallest perimeter which circumscribes a semicircle" (PDF). Fibonacci Quarterly. 30 (3): 274. doi:10.1080/00150517.1992.12429354. MR 1175315. Archived (PDF) from the original on 2022-01-20. Retrieved 2022-01-29.

handle.net

hdl.handle.net

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. MR 1896969.

harvard.edu

ui.adsabs.harvard.edu

Fischler, R. (1979). "What did Herodotus really say? or how to build (a theory of) the Great Pyramid". Environment and Planning B: Planning and Design. 6 (1): 89–93. Bibcode:1979EnPlB...6...89F. doi:10.1068/b060089. S2CID 62210630.

jstor.org

Markowsky, George (January 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. Archived (PDF) from the original on 2020-12-11. Retrieved 2012-06-29. It does not appear that the Egyptians even knew of the existence of $\varphi$ much less incorporated it in their buildings
Di Domenico, Angelo (July 2005). "89.41 The golden ratio—the right triangle—and the arithmetic, geometric, and harmonic means". The Mathematical Gazette. 89 (515): 261. doi:10.1017/s0025557200177769. JSTOR 3621234. S2CID 123738769.
Halleck, Ezra (March 2012). "Teaching tip: Consider a circular cow". The College Mathematics Journal. 43 (2): 133. doi:10.4169/college.math.j.43.2.133. JSTOR 10.4169/college.math.j.43.2.133. S2CID 123891402.

maine.edu

umcs.maine.edu

Markowsky, George (January 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. Archived (PDF) from the original on 2020-12-11. Retrieved 2012-06-29. It does not appear that the Egyptians even knew of the existence of $\varphi$ much less incorporated it in their buildings

math.ca

fq.math.ca

DeTemple, Duane W. (1992). "The triangle of smallest perimeter which circumscribes a semicircle" (PDF). Fibonacci Quarterly. 30 (3): 274. doi:10.1080/00150517.1992.12429354. MR 1175315. Archived (PDF) from the original on 2022-01-20. Retrieved 2022-01-29.

persee.fr

Busard, Hubert L. L. (April–June 1968). "L'algèbre au Moyen Âge : le "Liber mensurationum" d'Abû Bekr". Journal des Savants (in French and Latin). 1968 (2): 65–124. doi:10.3406/jds.1968.1175. Archived from the original on 2022-01-12. Retrieved 2022-01-12. See problem 51, reproduced on p. 98

ruc.dk

webhotel4.ruc.dk

Høyrup, Jens (2002). "Review of The shape of the Great Pyramid by Roger Herz-Fischler" (PDF). Mathematical Reviews. MR 1788996. Archived (PDF) from the original on 2022-02-23. Retrieved 2022-02-23.

semanticscholar.org

api.semanticscholar.org

Bartlett, Christopher (May 2014). "The Design of The Great Pyramid of Khufu". Nexus Network Journal. 16 (2): 299–311. doi:10.1007/s00004-014-0193-9. S2CID 122021107.
Fischler, R. (1979). "What did Herodotus really say? or how to build (a theory of) the Great Pyramid". Environment and Planning B: Planning and Design. 6 (1): 89–93. Bibcode:1979EnPlB...6...89F. doi:10.1068/b060089. S2CID 62210630.
Di Domenico, Angelo (July 2005). "89.41 The golden ratio—the right triangle—and the arithmetic, geometric, and harmonic means". The Mathematical Gazette. 89 (515): 261. doi:10.1017/s0025557200177769. JSTOR 3621234. S2CID 123738769.
Halleck, Ezra (March 2012). "Teaching tip: Consider a circular cow". The College Mathematics Journal. 43 (2): 133. doi:10.4169/college.math.j.43.2.133. JSTOR 10.4169/college.math.j.43.2.133. S2CID 123891402.

web.archive.org

Høyrup, Jens (2002). "Review of The shape of the Great Pyramid by Roger Herz-Fischler" (PDF). Mathematical Reviews. MR 1788996. Archived (PDF) from the original on 2022-02-23. Retrieved 2022-02-23.
Busard, Hubert L. L. (April–June 1968). "L'algèbre au Moyen Âge : le "Liber mensurationum" d'Abû Bekr". Journal des Savants (in French and Latin). 1968 (2): 65–124. doi:10.3406/jds.1968.1175. Archived from the original on 2022-01-12. Retrieved 2022-01-12. See problem 51, reproduced on p. 98
Markowsky, George (January 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. Archived (PDF) from the original on 2020-12-11. Retrieved 2012-06-29. It does not appear that the Egyptians even knew of the existence of $\varphi$ much less incorporated it in their buildings
Bruce, Ian (1994). "Another instance of the golden right triangle" (PDF). Fibonacci Quarterly. 32 (3): 232–233. doi:10.1080/00150517.1994.12429219. MR 1285752. Archived (PDF) from the original on 2022-01-29. Retrieved 2022-01-29.
Huffman, Carl (2005). "Archytas and the history of means". Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King. Cambridge University Press. pp. 170–177. ISBN 978-1-139-44407-1. Archived from the original on 2022-01-22. Retrieved 2022-01-22.
DeTemple, Duane W. (1992). "The triangle of smallest perimeter which circumscribes a semicircle" (PDF). Fibonacci Quarterly. 30 (3): 274. doi:10.1080/00150517.1992.12429354. MR 1175315. Archived (PDF) from the original on 2022-01-20. Retrieved 2022-01-29.