چندوجهی (Persian Wikipedia)

Analysis of information sources in references of the Wikipedia article "چندوجهی" in Persian language version.

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ams.org

Lakatos, Imre (2015) [1976], Worrall, John; Zahar, Elie (eds.), Proofs and Refutations: The logic of mathematical discovery, Cambridge Philosophy Classics, Cambridge: Cambridge University Press, p. 16, doi:10.1017/CBO9781316286425, ISBN 978-1-107-53405-6, MR 3469698, definitions are frequently proposed and argued about.
Grünbaum, Branko (1999), "Acoptic polyhedra", Advances in discrete and computational geometry (South Hadley, MA, 1996) (PDF), Contemporary Mathematics, vol. 223, Providence, Rhode Island: American Mathematical Society, pp. 163–199, doi:10.1090/conm/223/03137, ISBN 978-0-8218-0674-6, MR 1661382, archived from the original (PDF) on 31 March 2021, retrieved 5 June 2021.
Bokowski, J.; Guedes de Oliveira, A. (2000), "On the generation of oriented matroids", Discrete and Computational Geometry, 24 (2–3): 197–208, doi:10.1007/s004540010027, MR 1756651.
Burgiel, H.; Stanton, D. (2000), "Realizations of regular abstract polyhedra of types {3,6} and {6,3}", Discrete and Computational Geometry, 24 (2–3): 241–255, doi:10.1007/s004540010030, MR 1758047.
(Grünbaum 2003), pp. 468–469. Grünbaum, Branko (2003), "Are your polyhedra the same as my polyhedra?" (PDF), in Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (eds.), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics (به انگلیسی), vol. 25, Berlin: Springer, pp. 461–488, CiteSeerX 10.1.1.102.755, doi:10.1007/978-3-642-55566-4_21, ISBN 978-3-642-62442-1, MR 2038487.
Grünbaum, Branko (2003), Convex Polytopes, Graduate Texts in Mathematics, vol. 221 (2nd ed.), New York: Springer-Verlag, p. 26, doi:10.1007/978-1-4613-0019-9, ISBN 978-0-387-00424-2, MR 1976856.
Bruns, Winfried; Gubeladze, Joseph (2009), "Definition 1.1", Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer, p. 5, CiteSeerX 10.1.1.693.2630, doi:10.1007/b105283, ISBN 978-0-387-76355-2, MR 2508056.
Shephard, G. C. (1975), "Convex polytopes with convex nets", Mathematical Proceedings of the Cambridge Philosophical Society, 78 (3): 389–403, Bibcode:1975MPCPS..78..389S, doi:10.1017/s0305004100051860, MR 0390915
(Richeson 2008), p. 157. Richeson, David S. (2008), Euler's Gem: The polyhedron formula and the birth of topology (به انگلیسی), Princeton, NJ: Princeton University Press, ISBN 978-0-691-12677-7, MR 2440945.
(Richeson 2008), p. 180. Richeson, David S. (2008), Euler's Gem: The polyhedron formula and the birth of topology (به انگلیسی), Princeton, NJ: Princeton University Press, ISBN 978-0-691-12677-7, MR 2440945.
(Whiteley 1979); (Stewart 1980), p. 15. Whiteley, Walter (1979), "Realizability of polyhedra" (PDF), Structural Topology (به انگلیسی) (1), MR 0621628. Stewart, B. M. (1980), Adventures Among the Toroids: A Study of Orientable Polyhedra with Regular Faces (به انگلیسی) (2nd ed.), B. M. Stewart, ISBN 978-0-686-11936-4
Webber, William T. (1997), "Monohedral idemvalent polyhedra that are toroids", Geometriae Dedicata, 67 (1): 31–44, doi:10.1023/A:1004997029852, MR 1468859, S2CID 117884274.
Whiteley, Walter (1979), "Realizability of polyhedra" (PDF), Structural Topology (1): 46–58, 73, MR 0621628.
Sydler, J. -P. (1965), "Conditions nécessaires et suffisantes pour l'équivalence des polyèdres de l'espace euclidien à trois dimensions", Comment. Math. Helv. (به فرانسوی), 40: 43–80, doi:10.1007/bf02564364, MR 0192407, S2CID 123317371
Debrunner, Hans E. (1980), "Über Zerlegungsgleichheit von Pflasterpolyedern mit Würfeln", Archiv der Mathematik (به آلمانی), 35 (6): 583–587, doi:10.1007/BF01235384, MR 0604258, S2CID 121301319.
Cundy, H. Martyn; Rollett, A.P. (1961), "3.2 Duality", Mathematical models (2nd ed.), Oxford: Clarendon Press, pp. 78–79, MR 0124167.
Grünbaum, B.; Shephard, G.C. (1969), "Convex polytopes" (PDF), Bulletin of the London Mathematical Society, 1 (3): 257–300, doi:10.1112/blms/1.3.257, MR 0250188, archived from the original (PDF) on 2017-02-22, retrieved 2017-02-21. See in particular the bottom of page 260.
(Grünbaum 2009). Grünbaum, Branko (2009), "An enduring error", Elemente der Mathematik (به انگلیسی), 64 (3): 89–101, doi:10.4171/EM/120, MR 2520469. Reprinted in Pitici, Mircea, ed. (2011), The Best Writing on Mathematics 2010 (به انگلیسی), Princeton University Press, pp. 18–31.
Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954). "Uniform polyhedra" (PDF). Philosophical Transactions of the Royal Society A. 246 (916): 401–450. doi:10.1098/rsta.1954.0003. ISSN 0080-4614. JSTOR 91532. MR 0062446.
Alexandrov (2010). Alexandrov, Victor (2010), "The Dehn invariants of the Bricard octahedra", Journal of Geometry (به انگلیسی), 99 (1–2), arXiv:0901.2989, doi:10.1007/s00022-011-0061-7, MR 2823098.
Gaĭfullin & Ignashchenko (2018). Gaĭfullin, A. A.; Ignashchenko, L. S. (2018), "Dehn invariant and scissors congruence of flexible polyhedra", Trudy Matematicheskogo Instituta Imeni V. A. Steklova (به انگلیسی), 302 (Topologiya i Fizika): 143–160, doi:10.1134/S0371968518030068, ISBN 5-7846-0147-4, MR 3894642.
Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954). "Uniform polyhedra". Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences. The Royal Society. 246 (916): 401–450. Bibcode:1954RSPTA.246..401C. doi:10.1098/rsta.1954.0003. ISSN 0080-4614. JSTOR 91532. MR 0062446. S2CID 202575183.

archive.org

Pottmann 2007, p. 74. Pottmann, Helmut (2007). Architectural geometry (به انگلیسی). Exton, Pa: Bentley Institute Press. ISBN 978-1-934493-04-5. OCLC 180177477.
Pottmann 2007, p. 72. Pottmann, Helmut (2007). Architectural geometry (به انگلیسی). Exton, Pa: Bentley Institute Press. ISBN 978-1-934493-04-5. OCLC 180177477.
Sherk et al. 1995, papers 22,23 and 24. Sherk, F. Arthur; McMullen, Peter; Thompson, Anthony C.; Weiss, Asia Ivic, eds. (1995). Kaleidoscopes: Selected Writings of H.S.M. Coxeter (به انگلیسی). Wiley. ISBN 978-0-471-01003-6.
- Pottmann 2007, p. 75. Pottmann, Helmut (2007). Architectural geometry (به انگلیسی). Exton, Pa: Bentley Institute Press. ISBN 978-1-934493-04-5. OCLC 180177477.
- Pottmann 2007, p. 76. Pottmann, Helmut (2007). Architectural geometry (به انگلیسی). Exton, Pa: Bentley Institute Press. ISBN 978-1-934493-04-5. OCLC 180177477.
- Pottmann et al. 2007‏:‎81 Pottmann, Helmut; Asperl, Andreas; Hofer, Michael; Kilian, Axel; Bentley, Daril (2007). Architectural geometry (به انگلیسی). Bentley Institute Press. ISBN 1-934493-04-X. OCLC 180177477.
- Johnson, Norman W. (1966). "Convex Solids with Regular Faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. ISSN 0008-414X. Zbl 0132.14603. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
- Gardner 1987‏:‎17 Gardner, Martin (1987). "Chapter 1: The Five Platonic Solids". The 2nd Scientific American book of mathematical puzzles & diversions (به انگلیسی). Chicago: University of Chicago Press. ISBN 0-226-28253-8. OCLC 15550017.
- Gardner 1987‏:‎13 Gardner, Martin (1987). "Chapter 1: The Five Platonic Solids". The 2nd Scientific American book of mathematical puzzles & diversions (به انگلیسی). Chicago: University of Chicago Press. ISBN 0-226-28253-8. OCLC 15550017.
- Coxeter, H. S. M. (2013). "Regular and semiregular polyhedra". In Senechal, Marjorie (ed.). Shaping Space: Exploring Polyhedra in Nature, Art, and the Geomtrical Imagination (2nd ed.). Springer. pp. 41–52. See in particular p. 42.

arxiv.org

Alexandrov (2010). Alexandrov, Victor (2010), "The Dehn invariants of the Bricard octahedra", Journal of Geometry (به انگلیسی), 99 (1–2), arXiv:0901.2989, doi:10.1007/s00022-011-0061-7, MR 2823098.
Sparavigna, Amelia Carolina (2012), An Etruscan dodecahedron, arXiv:1205.0706

bbc.co.uk

news.bbc.co.uk

Pollard, Lawrence (2004-09-09). "Sudan's past uncovered". BBC News. Retrieved 2010-04-12.

books.google.com

Bruns, Winfried; Gubeladze, Joseph (2009), "Definition 1.1", Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer, p. 5, CiteSeerX 10.1.1.693.2630, doi:10.1007/b105283, ISBN 978-0-387-76355-2, MR 2508056.
Crystallography of Quasicrystals: Concepts, Methods and Structures by Walter Steurer, Sofia Deloudi, (2009) pp. 18–20 and 51–53
French 2014‏:‎96 French, K.L. (2014). The Hidden Geometry of Life: The Science and Spirituality of Nature. Gateway series (به انگلیسی). Watkins Media Limited. ISBN 978-1-78028-845-1. Archived from the original on 16 December 2018. Retrieved 2018-11-12.
French 2014‏:‎96 French, K.L. (2014). The Hidden Geometry of Life: The Science and Spirituality of Nature. Gateway series (به انگلیسی). Watkins Media Limited. ISBN 978-1-78028-845-1. Archived from the original on 16 December 2018. Retrieved 2018-11-12.
Haeckel 2012, PLATE 1 Haeckel, E. (2012). Art Forms in Nature. Dover Pictorial Archive (به انگلیسی). Dover Publications. ISBN 978-0-486-15532-6. Archived from the original on 16 December 2018. Retrieved 2018-11-12.
Katz, 364 Katz, E. A. (2006). "Fullerene Thin Films as Photovoltaic Material". In Sōga, Tetsuo (ed.). Nanostructured materials for solar energy conversion (به انگلیسی). Elsevier. pp. 361–443. ISBN 978-0-444-52844-5.
Mark Lehner (2008). The Complete Pyramids: Solving the Ancient Mysteries. Thames & Hudson. p. 34. ISBN 978-0-500-28547-3.

britannica.com

Encyclopedia Britannica ""Platonic solid - MATHEMATICS"". Encyclopedia Britannica (به انگلیسی). Archived from the original on 16 December 2018. Retrieved 2018-09-06.

doi.org

Lakatos, Imre (2015) [1976], Worrall, John; Zahar, Elie (eds.), Proofs and Refutations: The logic of mathematical discovery, Cambridge Philosophy Classics, Cambridge: Cambridge University Press, p. 16, doi:10.1017/CBO9781316286425, ISBN 978-1-107-53405-6, MR 3469698, definitions are frequently proposed and argued about.
O'Rourke, Joseph (1993), "Computational Geometry in C", Computers in Physics, 9 (1): 113–116, Bibcode:1995ComPh...9...55O, doi:10.1063/1.4823371.
Grünbaum, Branko (1999), "Acoptic polyhedra", Advances in discrete and computational geometry (South Hadley, MA, 1996) (PDF), Contemporary Mathematics, vol. 223, Providence, Rhode Island: American Mathematical Society, pp. 163–199, doi:10.1090/conm/223/03137, ISBN 978-0-8218-0674-6, MR 1661382, archived from the original (PDF) on 31 March 2021, retrieved 5 June 2021.
Bokowski, J.; Guedes de Oliveira, A. (2000), "On the generation of oriented matroids", Discrete and Computational Geometry, 24 (2–3): 197–208, doi:10.1007/s004540010027, MR 1756651.
Burgiel, H.; Stanton, D. (2000), "Realizations of regular abstract polyhedra of types {3,6} and {6,3}", Discrete and Computational Geometry, 24 (2–3): 241–255, doi:10.1007/s004540010030, MR 1758047.
(Grünbaum 2003), pp. 468–469. Grünbaum, Branko (2003), "Are your polyhedra the same as my polyhedra?" (PDF), in Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (eds.), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics (به انگلیسی), vol. 25, Berlin: Springer, pp. 461–488, CiteSeerX 10.1.1.102.755, doi:10.1007/978-3-642-55566-4_21, ISBN 978-3-642-62442-1, MR 2038487.
Grünbaum, Branko (2003), Convex Polytopes, Graduate Texts in Mathematics, vol. 221 (2nd ed.), New York: Springer-Verlag, p. 26, doi:10.1007/978-1-4613-0019-9, ISBN 978-0-387-00424-2, MR 1976856.
Bruns, Winfried; Gubeladze, Joseph (2009), "Definition 1.1", Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer, p. 5, CiteSeerX 10.1.1.693.2630, doi:10.1007/b105283, ISBN 978-0-387-76355-2, MR 2508056.
Shephard, G. C. (1975), "Convex polytopes with convex nets", Mathematical Proceedings of the Cambridge Philosophical Society, 78 (3): 389–403, Bibcode:1975MPCPS..78..389S, doi:10.1017/s0305004100051860, MR 0390915
Ghomi, Mohammad (2018-01-01), "Dürer's Unfolding Problem for Convex Polyhedra", Notices of the American Mathematical Society, 65 (1): 25–27, doi:10.1090/noti1609
Webber, William T. (1997), "Monohedral idemvalent polyhedra that are toroids", Geometriae Dedicata, 67 (1): 31–44, doi:10.1023/A:1004997029852, MR 1468859, S2CID 117884274.
Sydler, J. -P. (1965), "Conditions nécessaires et suffisantes pour l'équivalence des polyèdres de l'espace euclidien à trois dimensions", Comment. Math. Helv. (به فرانسوی), 40: 43–80, doi:10.1007/bf02564364, MR 0192407, S2CID 123317371
Debrunner, Hans E. (1980), "Über Zerlegungsgleichheit von Pflasterpolyedern mit Würfeln", Archiv der Mathematik (به آلمانی), 35 (6): 583–587, doi:10.1007/BF01235384, MR 0604258, S2CID 121301319.
Grünbaum, B.; Shephard, G.C. (1969), "Convex polytopes" (PDF), Bulletin of the London Mathematical Society, 1 (3): 257–300, doi:10.1112/blms/1.3.257, MR 0250188, archived from the original (PDF) on 2017-02-22, retrieved 2017-02-21. See in particular the bottom of page 260.
Al-Sammarraie, Ahmed T.; Vafai, Kambiz (2017). "Heat transfer augmentation through convergence angles in a pipe". Numerical Heat Transfer, Part A: Applications. 72 (3): 197−214. doi:10.1080/10407782.2017.1372670. S2CID 125509773.
(Grünbaum 2009). Grünbaum, Branko (2009), "An enduring error", Elemente der Mathematik (به انگلیسی), 64 (3): 89–101, doi:10.4171/EM/120, MR 2520469. Reprinted in Pitici, Mircea, ed. (2011), The Best Writing on Mathematics 2010 (به انگلیسی), Princeton University Press, pp. 18–31.
Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954). "Uniform polyhedra" (PDF). Philosophical Transactions of the Royal Society A. 246 (916): 401–450. doi:10.1098/rsta.1954.0003. ISSN 0080-4614. JSTOR 91532. MR 0062446.
Johnson, Norman W. (1966). "Convex Solids with Regular Faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. ISSN 0008-414X. Zbl 0132.14603. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
Trigg, Charles W. (1978), "An Infinite Class of Deltahedra", Mathematics Magazine, 51 (1): 55–57, doi:10.1080/0025570X.1978.11976675, JSTOR 2689647.
Alexandrov (2010). Alexandrov, Victor (2010), "The Dehn invariants of the Bricard octahedra", Journal of Geometry (به انگلیسی), 99 (1–2), arXiv:0901.2989, doi:10.1007/s00022-011-0061-7, MR 2823098.
Gaĭfullin & Ignashchenko (2018). Gaĭfullin, A. A.; Ignashchenko, L. S. (2018), "Dehn invariant and scissors congruence of flexible polyhedra", Trudy Matematicheskogo Instituta Imeni V. A. Steklova (به انگلیسی), 302 (Topologiya i Fizika): 143–160, doi:10.1134/S0371968518030068, ISBN 5-7846-0147-4, MR 3894642.
Mettenleiter TC, Klupp BG, Granzow H (2006). "Herpesvirus assembly: a tale of two membranes". Curr. Opin. Microbiol. 9 (4): 423–9. doi:10.1016/j.mib.2006.06.013. PMID 16814597.
Kotschick, Dieter (2006). "The Topology and Combinatorics of Soccer Balls". American Scientist. 94 (4): 350–357. doi:10.1511/2006.60.350.
Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954). "Uniform polyhedra". Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences. The Royal Society. 246 (916): 401–450. Bibcode:1954RSPTA.246..401C. doi:10.1098/rsta.1954.0003. ISSN 0080-4614. JSTOR 91532. MR 0062446. S2CID 202575183.
Sarhangi 2008‏:‎511–523 Sarhangi, Reza (2008). "Illustrating Abu al-Wafā' Būzjānī: Flat Images, Spherical Constructions". Iranian Studies (به انگلیسی). Informa UK Limited. 41 (4): 511–523. doi:10.1080/00210860802246184. ISSN 0021-0862.

encyclopediaofmath.org

Matveev, S.V. (2001) [1994], "Polyhedron, abstract", Encyclopedia of Mathematics, EMS Press
Hazewinkel, M. (2001) [1994], "Dehn invariant", Encyclopedia of Mathematics, EMS Press

eudml.org

Sherk et al. 1995, papers 22,23 and 24. Sherk, F. Arthur; McMullen, Peter; Thompson, Anthony C.; Weiss, Asia Ivic, eds. (1995). Kaleidoscopes: Selected Writings of H.S.M. Coxeter (به انگلیسی). Wiley. ISBN 978-0-471-01003-6.
- Sydler, J. -P. (1965), "Conditions nécessaires et suffisantes pour l'équivalence des polyèdres de l'espace euclidien à trois dimensions", Comment. Math. Helv. (به فرانسوی), 40: 43–80, doi:10.1007/bf02564364, MR 0192407, S2CID 123317371

harvard.edu

ui.adsabs.harvard.edu

O'Rourke, Joseph (1993), "Computational Geometry in C", Computers in Physics, 9 (1): 113–116, Bibcode:1995ComPh...9...55O, doi:10.1063/1.4823371.
Shephard, G. C. (1975), "Convex polytopes with convex nets", Mathematical Proceedings of the Cambridge Philosophical Society, 78 (3): 389–403, Bibcode:1975MPCPS..78..389S, doi:10.1017/s0305004100051860, MR 0390915
Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954). "Uniform polyhedra". Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences. The Royal Society. 246 (916): 401–450. Bibcode:1954RSPTA.246..401C. doi:10.1098/rsta.1954.0003. ISSN 0080-4614. JSTOR 91532. MR 0062446. S2CID 202575183.

jst.go.jp

jstage.jst.go.jp

Goldberg, Michael (1937). "A class of multi-symmetric polyhedra". Tohoku Mathematical Journal.

jstor.org

Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954). "Uniform polyhedra" (PDF). Philosophical Transactions of the Royal Society A. 246 (916): 401–450. doi:10.1098/rsta.1954.0003. ISSN 0080-4614. JSTOR 91532. MR 0062446.
Trigg, Charles W. (1978), "An Infinite Class of Deltahedra", Mathematics Magazine, 51 (1): 55–57, doi:10.1080/0025570X.1978.11976675, JSTOR 2689647.
Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954). "Uniform polyhedra". Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences. The Royal Society. 246 (916): 401–450. Bibcode:1954RSPTA.246..401C. doi:10.1098/rsta.1954.0003. ISSN 0080-4614. JSTOR 91532. MR 0062446. S2CID 202575183.

keu92.org

التسلسل التاریخی لاستخدام الحدید فی المبانی | إتحاد مهندسی کوردستان بایگانی‌شده در ۴ مارس ۲۰۱۶ توسط Wayback Machine

latinamericanstudies.org

"The Enigma of Aztec Sacrifice". Natural History, April 1977. Vol. 86, No. 4, pages 46–51.

mathmos.net

polyhedra.mathmos.net

Vertex Symbol Robert Whittaker

nih.gov

pubmed.ncbi.nlm.nih.gov

Mettenleiter TC, Klupp BG, Granzow H (2006). "Herpesvirus assembly: a tale of two membranes". Curr. Opin. Microbiol. 9 (4): 423–9. doi:10.1016/j.mib.2006.06.013. PMID 16814597.

noormags.ir

هاشمی ۱۳۹۱‏:‎۲۶–۳۱ هاشمی، غلامرضا (۱۳۹۱). «نظری به جایگه هندسه و نقوش هندسی در آرا متفکران یونانی و مسلمان». کتاب ماه هنر (۱۶۵): ۲۶–۳۱. بایگانی‌شده از اصلی در ۱۶ دسامبر ۲۰۱۸. دریافت‌شده در ۲۰۱۸-۰۹-۱۶.

nytimes.com

Slackman, Michael (17 November 2008). "In the Shadow of a Long Past, Patiently Awaiting the Future". The New York Times. Retrieved 1 May 2010.
Slackman, Michael (16 November 2007). "In the Shadow of a Long Past, Patiently Awaiting the Future". The New York Times. Retrieved 17 November 2008. Deep below the Egyptian desert, archaeologists have found evidence of yet another pyramid, this one constructed 4,300 years ago to store the remains of a pharaoh’s mother. That makes 138 pyramids discovered here so far, and officials say they expect to find more.

openproblemgarden.org

Moskovich, D. (June 4, 2012), "Dürer's conjecture", Open Problem Garden

orchidpalms.com

"cupolas". www.orchidpalms.com. Retrieved 21 April 2018.

psu.edu

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