On the knowledge in the XIII--XVI centuries of the relationship of Fibonacci numbers with the golden ratio
Matematičeskoe obrazovanie, Tome 92 (2019) no. 4, pp. 63-75.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is suggested that the use of Divine Proportion (Golden Ratio) by artists and architects, starting from the 13th century, could lead to the calculation of suitable fractions for the Phidia number, and, as a consequence, to the discovery of its connection with Fibonacci numbers.
Keywords: Fibonacci numbers, Phidias number, golden ratio
Mots-clés : triangulation, Cassini formula.
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A. N. Kovalev. On the knowledge in the XIII--XVI centuries of the relationship of Fibonacci numbers with the golden ratio. Matematičeskoe obrazovanie, Tome 92 (2019) no. 4, pp. 63-75. http://geodesic.mathdoc.fr/item/MO_2019_92_4_a6/

[1] Herz-Fischler R., “The Fibonacci Quarterly”, Letter to the editor, 24:4 (1986), 382 <ext-link ext-link-type='uri' href='http://www.fq.math.ca/Scanned/34-4/letter2.pdf'>http://www.fq.math.ca/Scanned/34-4/letter2.pdf</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=863061'>863061</ext-link>

[2] Herz-Fischler R., “A Mathematical History of Division in Extreme and Mean Ratio”, Golden Number Studies J., 1987, Wilfred Laurier University Press, Waterloo, Ontario <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=907871'>907871</ext-link>

[3] Scott T.C., Marketos P. ., “On the origin of the Fibonacci Sequence”, MacTutor History of Mathematics, 2014, Scotland <ext-link ext-link-type='uri' href='http://www-history.mcs.st-ndrews.ac.uk/Publications/fibonacci.pdf'>http://www-history.mcs.st-ndrews.ac.uk/Publications/fibonacci.pdf</ext-link>

[4] Sigler L.E., Fibonacci's Liber Abaci, Leonardo Pisano Book of Calculations, Springer, NewYork, 2002, 644 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1923794'>1923794</ext-link>

[5] Voloshinov A.V., Matematika i iskusstvo, Prosveschenie, M., 2000, 399 pp.

[6] Клавдий Птолемей Almagest ili matematicheskoe sochinenie v trinadtsati knigakh, perevod I.N. Veselovskogo, Nauka, M., 1998.

[7] Kovalev A.N., “Bozhestvennaya proportsiya v poiskakh epokhi Vozrozhdeniya, Ch. II”, Kultura kultury, 2019, no. 4 <ext-link ext-link-type='uri' href='http://cult-cult.ru/divine-proportion-in-search-of-the-renaissance1/'>http://cult-cult.ru/divine-proportion-in-search-of-the-renaissance1/</ext-link>

[8] Kympan F., Istoriya chisla $\pi $, Nauka, M., 1971, 216 s. pp.

[9] Yushkevich A.P. (red.), Istoriya matematiki v trekh tomakh, v. 1, Nauka, M., 1970.

[10] S.N. Bernshtein (red.), O kvadrature kruga. S prilozheniem teorii voprosa, GTTI, M.–L., 1934

[11] Zverkina G.A., “Algoritm Evklida kak vychislitelnoe sredstvo antichnoi matematiki”, Istoriko-matematicheskie-issledovaniya, vtoraya seriya, 2000, no. 5(40), 232–243, Yanus-K, M.

[12] Zverkina G.A., Sufiyarova I.I., “O metodakh priblizheniya dliny okruzhnosti perimetrami pravilnykh mnogougolnikov matematiki”, Istoriko-matematicheskie-issledovaniya, vtoraya seriya, 1997, no. 2(37), 237–261, Yanus-K, M.

[13] Belyi Yu.A., Iogann Myuller (Regiomontan). 1436—1476, Nauka, M., 1985, 128 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=824982'>824982</ext-link>

[14] Gardner L., Chasha Graalya i potomki Iisusa Khrista, M., 2001, 496 pp.

[15] Zaitsev E.A., “Kvadratura kruga i infinitezimalnye metody Nikolaya Kuzanskogo”, Istoriko-matematicheskie-issledovaniya, vtoraya seriya, 2007, no. 12(47), 275–289, Yanus-K, M.

[16] Lure S.Ya., Arkhimed, Iz-vo AN SSSR, M.–L., 1945.

[17] Zhukov A.V., Vezdesuschee chislo $\pi $, Editorial URSS, M., 2004.

[18] Mikhailova E.N., “Zabytye imena evropeiskoi lingvistiki: Sharl de Bovel (1479–1566)”, Yazyk v sotsiokulturnom prostranstve i vremeni, Vserossiiskaya konferentsiya (g. Astrakhan, 13–14 oktyabrya 2011 g.), 2011 <ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1230.93002'>1230.93002</ext-link>

[19] Schetnikov A.I., “Luka Pacholi i ego traktat «O bozhestvennoi proportsii» Prilozhenie k repritnomu izdaniyu 1509 g.”, Matematicheskoe obrazovanie, 2007, no. 1(41)

[20] Pacholi Luka, O bozhestvennoi proportsii, Reprint izd. 1509. S prilozheniem perevoda A.I. Schetnikova, Fond «Russkii avangard», M., 2007

[21] Ieits F., Rozenkreitserskoe Prosveschenie, Perevod A. Kavtaskina pod red. T. Baskakovoi, Aleteia, Enigma, M., 1999, 496 pp. <ext-link ext-link-type='uri' href='http://psylib.org.ua/books/yates01/index.htm'>http://psylib.org.ua/books/yates01/index.htm</ext-link>

[22] Kovalev A.N., “Bozhestvennaya proportsiya v poiskakh epokhi Vozrozhdeniya, Ch. I”, Kultura kultury, 2019, no. 3 <ext-link ext-link-type='uri' href='http://cult-cult.ru/divine-proportion-in-search-of-the-renaissance/'>http://cult-cult.ru/divine-proportion-in-search-of-the-renaissance/</ext-link>

[23] Kovalev A.N., V poiskakh pyatogo poryadka, 2019 <ext-link ext-link-type='uri' href='http://kovalevandrey.ihostfull.com/Books/Book_1'>http://kovalevandrey.ihostfull.com/Books/Book_1</ext-link>