Geodesic
The history of hyperbolic functions research and some applications
Matematičeskoe obrazovanie, Tome 88 (2018) no. 4, pp. 18-29.

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

On the history of discovering and research the hyperbolic functions.
Keywords: hyperbolic functions, hyperbolic sine, hyperbolic cosine
Mots-clés : chain line. 
@article{MO_2018_88_4_a3,
     author = {V. Yu. Bodryakov and A. A. Bykov},
     title = {The history of hyperbolic functions  research and some applications},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {18--29},
     publisher = {mathdoc},
     volume = {88},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2018_88_4_a3/}
}
TY  - JOUR
AU  - V. Yu. Bodryakov
AU  - A. A. Bykov
TI  - The history of hyperbolic functions  research and some applications
JO  - Matematičeskoe obrazovanie
PY  - 2018
SP  - 18
EP  - 29
VL  - 88
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MO_2018_88_4_a3/
LA  - ru
ID  - MO_2018_88_4_a3
ER  - 
%0 Journal Article
%A V. Yu. Bodryakov
%A A. A. Bykov
%T The history of hyperbolic functions  research and some applications
%J Matematičeskoe obrazovanie
%D 2018
%P 18-29
%V 88
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MO_2018_88_4_a3/
%G ru
%F MO_2018_88_4_a3
V. Yu. Bodryakov; A. A. Bykov. The history of hyperbolic functions  research and some applications. Matematičeskoe obrazovanie, Tome 88 (2018) no. 4, pp. 18-29. http://geodesic.mathdoc.fr/item/MO_2018_88_4_a3/

[1] Bernoulli Jakob, “Analysis problematis antehac propositi, de inventione lineae descensus a corpore gravi percurrendae uniformiter, sic ut temporibus aequalibus aequales altitudines eme tiantur: et alterius cujusdam problematis proposition”, Acta Eruditorum. - Lipsia, 1690, May, 217–219

[2] Mencke O., “Solutions of the problem proposed by J.B.”, Acta Eruditorum. - Lipsia, 1691, June, 273.

[3] Bernoulli Johannis, “Solutio problematic funicularii”, Acta Eruditorum, 277, June (1691), 274–276

[4] Leibniz G.W., “Solutio problematic catenarii”, Acta Eruditorum, 277, June (1691), 277–281 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=987432'>987432</ext-link>

[5] Huygens Christiani, “Dynaste Zulichemii, solutio problematis funicularii”, Acta Eruditorum, 277, June (1691), 281–282

[6] Euler Leonhard, Introductio in Analysin Infinitorum, v. 2, Apud Marcum-Michaelem Bousquet & Socios, Lausannæ, 1748, 398 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1841793'>1841793</ext-link>

[7] Riccati Vincenzo, Opuscula physico-mathematica. Ad res., Physicas & Mathematicas pertinentium, v. 1, Apud Lae lium a Vulpe Inftituti Scientiarium Typographum, Boboniae, 1757, 173 pp.

[8] Lambert Johann H., “Observations trigonométriques”, Mem. Acad. Sci., 24 (1770), 327–354, Berlin

[9] Lambert J.H., “Mémoire sur quelques propriétés remarquables des quantités transcendantes circulaires et logarithmiques”, Histoire de l'Académie de Berlin 1761, 1768, 265–322; Vgl. Hierzu Alfred Pringsheim, “Uber die ersten Beweise der Irrationalität von $e$ und $\pi$”, Sitzungsb., d. math.-phys. Kl. dk bayer. -Akad. d. Wiss., 28 (1898), 325–337

[10] Gudermann C., Theorie der Potenzial-oder cyclisch-hyperbolischen Funktionen, Gedruckt und verlegt bei G. Reimer, Berlin, 1833, 354 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1577789'>1577789</ext-link>

[11] Galilei G., Besedy i matematicheskie dokazatelstva, kasayuschiesya dvukh novykh otraslei nauki, otnosyaschikhsya k mekhanike i mestnomu dvizheniyu sinora Galileo Galileya Lincheo, filosofa i pervogo matematika svetleishego velikogo gertsoga Toskanskogo. S prilozheniem o tsentrakh tyazhesti razlichnykh tel, Gosudarstvennoe tekhniko-teoreticheskoe izdatelstvo, M.-L., 1934, 273–274

[12] Shtaerman I.Ya., Giperbolicheskie funktsii, Ob'edinennoe nauchno-tekhnicheskoe izdatelstvo NKTP SSSR, M., 1935, 55 pp.

[13] Yates R.C., “Catenary”, A Handbook on Curves and Their Properties, J.W. Edwards, Ann Arbor, MI, 1952, 12–14 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=23075'>23075</ext-link>

[14] Shervatov V.G., Giperbolicheskie funktsii, Gosudarstvennoe izdatelstvo tekhniko-teoreticheskoi literatury, M., 1954, 55 pp.

[15] Smith D.E., History of Mathematics, v. 2, Special Topics of Elementary Mathematics, Dover, New York, 1958, 327 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=91897'>91897</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0081.00411'>0081.00411</ext-link>

[16] Yanpolskii A.R., Giperbolicheskie funktsii, Gosudarstvennoe izdatelstvo fiziko-matematicheskoi literatury, M., 1960, 194 pp.

[17] Lawrence J.D., A Catalog of Special Plane Curves, Dover, New York, 1972, 195, 199–200 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1572089'>1572089</ext-link>

[18] MacTutor History of Mathematics archive, (data obrascheniya: 21.05.2018) <ext-link ext-link-type='uri' href='http://www-history.mcs.st-and.ac.uk/'>http://www-history.mcs.st-and.ac.uk/</ext-link>

[19] Giperbolicheskie funktsii, (data obrascheniya: 21.05.2018) <ext-link ext-link-type='uri' href='https://ru.wikipedia.org/wiki/'>https://ru.wikipedia.org/wiki/</ext-link>

[20] Merkin D.R., Vvedenie v mekhaniku gibkoi niti, Nauka, M., 1980, 240 pp. (data obrascheniya: 21.05.2018) <ext-link ext-link-type='uri' href='http://www.twirpx.com/file/357235'>http://www.twirpx.com/file/357235</ext-link>

[21] Pappas T., “The Catenary & the Parabolic Curves”, The Joy of Mathematics, Wide World Publ. / Tetra, San Carlos, CA, 1989, 34

[22] Denzler J., Hinz A.M., “Catenaria vera — the true catenary”, Expositiones Mathematicae, 17 (1999), 117–142 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1690419'>1690419</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0943.49001'>0943.49001</ext-link>

[23] Nedev S., “The catenary — an ancient problem on the computer screen”, European Journal of Physics, 21: 5 (2000), 451–457 <ext-link ext-link-type='doi' href='https://doi.org/10.1088/0143-0807/21/5/311'>10.1088/0143-0807/21/5/311</ext-link>

[24] Barnett J.H., “Enter, stage center: the early drama of the hyperbolic functions”, Mathematics Magazine, 77:1, February (2004), 15–30 <ext-link ext-link-type='doi' href='https://doi.org/10.1080/0025570X.2004.11953223'>10.1080/0025570X.2004.11953223</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2087222'>2087222</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1051.01006'>1051.01006</ext-link>

[25] Mareno A., English L.Q., “The stability of the catenary shapes for a hanging cable of unspecified length”, European Journal of Physics, 30:1 (2008), 97–108 <ext-link ext-link-type='doi' href='https://doi.org/10.1088/0143-0807/30/1/010'>10.1088/0143-0807/30/1/010</ext-link>

[26] Bukowski J., “Christiaan Huygens and the problem of the hanging chain”, The College Mathematical Journal, 39, January (2008), 2–11 <ext-link ext-link-type='doi' href='https://doi.org/10.1080/07468342.2008.11922269'>10.1080/07468342.2008.11922269</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2378201'>2378201</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1293.97071'>1293.97071</ext-link>

[27] Sobbich E.M., “Kurva Catenary Dan Aproksimasi Parabola, Evaluasi Perbedaan Titik Koordinat Dan Panjang Busur [English: Catenary Curve and Parabolic Approximation, Evaluation of Coordinate Point Difference and Arc Length]”, Journal Mat Stat, 9 (2009), 2

[28] Jwa Y., Sohn G., “A piecewise catenary curve model growing for 3D power line reconstruction”, Photogrammetric Engineering & Remote Sensing, 78:12 (2012), 1227–1240 <ext-link ext-link-type='doi' href='https://doi.org/10.14358/PERS.78.11.1227'>10.14358/PERS.78.11.1227</ext-link>

[29] Wang C.Y., Wang C.M., “Analytical Solutions for Catenary Domes”, Journal of Engineering Mechanics, 141:2 (2015), 06014019 <ext-link ext-link-type='doi' href='https://doi.org/10.1061/(ASCE)EM.1943-7889.0000896'>10.1061/(ASCE)EM.1943-7889.0000896</ext-link>

[30] Ben-Abu Y., Eshach H., Yizhaq H., “Interweaving the Principle of Least Potential Energy in School and Introductory University Physics Courses”, Symmetry, 9:3 (2017), 45, 12 pp. <ext-link ext-link-type='doi' href='https://doi.org/10.3390/sym9030045'>10.3390/sym9030045</ext-link>

[31] Carlson S.C., “Catenary mathematics”, ENCYCLOPÆDIA BRITANNICA <ext-link ext-link-type='uri' href='https://www.britannica.com/science/catenary'>https://www.britannica.com/science/catenary</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=53831'>53831</ext-link>

[32] Fedoseev V.M., “Laboratornye raboty po matematike s razvitiem temy”, Matematika v Shkole, 2010, no. 6, 62–69

[33] Nicol Imperi, The determination of the equation of the catenary by Huygens, Leibniz and Bernoulli, PhD in Mathematics, University of Rome, Rome, 2015, 55 pp.

[34] Starova O.A., “Tsepnaya liniya”, Matematika. Vsë dlya uchitelya, 2015, no. 12, 31–33

[35] Saranin V.A., “K zadache o visyachei tsepochke”, Uchebnaya fizika, 2016, no. 3, 30–33

[36] Ochkov V.F., Tsurikov G.N., Chudova Yu.V., “Ostorozhno: Tsepnaya funktsiya”, Informatika v shkole, 2017, no. 4(127), 58–62

[37] Aksenova O.V., Bodryakov V.Yu., “Sistema raznourovnevykh laboratornykh rabot po matematike s primeneniem IKT kak instrument frontalnogo formirovaniya uchebno-issledovatelskikh i tvorcheskikh umenii obuchayuschikhsya”, Sb. materialov XXVIII Mezhdunarodnoi konferentsii “Sovremennye informatsionnye tekhnologii v obrazovanii” (Moskva–Troitsk: Fond “BAITIK”, 27 iyunya 2017 g.), 460–462, 602 pp. (data obrascheniya: 06.05.2018) <ext-link ext-link-type='uri' href='http://ito.bytic.ru/uploads/files/conf_2017.pdf'>http://ito.bytic.ru/uploads/files/conf_2017.pdf</ext-link>

[38] Ochkov V.F., “Tsepnaya liniya = fizika + matematika + informatika”, Informatika v shkole, 2018, no. 3, 56–63 <ext-link ext-link-type='uri' href='http://twt.mpei.ac.ru/ochkov/catenary.pdf'>http://twt.mpei.ac.ru/ochkov/catenary.pdf</ext-link>

[39] Aksenova O.V., Bodryakov V.Yu., “Laboratornye raboty po matematike s primeneniem IKT kak instrument formirovaniya issledovatelskikh umenii studentov pedagogicheskogo vuza”, Sb. dokladov i nauchnykh statei Vserossiiskoi nauchno-prakticheskoi konferentsii “Sostoyanie i perspektivy razvitiya IT-obrazovaniya”, posvyaschennoi 50-letiyu Chuvashskogo gosudarstvennogo universiteta im. I.N. Ulyanova (Cheboksary, 16–18 noyabrya 2017 g.), Izd-vo Chuvashskogo gos. un-ta, Cheboksary, 2018, 175–181, 520 pp.

[40] Aksenova O.V., Bodryakov V.Yu., Bykov A.A., Toporova N.V., “Optimizatsionnaya zadacha o provisanii tsepnoi linii”, Aktualnye voprosy prepodavaniya matematiki, informatiki i informatsionnykh tekhnologii, mezhvuzovskii sbornik nauchnykh rabot, Ural. gos. ped. un-t., Ekaterinburg, 2018, 123–130, 314 pp.

[41] Aksenova O.V., Bodryakov V.Yu., “Naturnyi eksperiment s primeneniem sredstv IKT i mobilnykh ustroistv kak instrument formirovaniya issledovatelskikh umenii studentov”, Vestnik Rossiiskogo universiteta druzhby narodov, Informatizatsiya obrazovaniya, 15, no. 4, 2018