Hyperbolic spiral (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Hyperbolic spiral" in English language version.

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ams.org

mathscinet.ams.org

Mumford, David; Series, Caroline; Wright, David (2002), "Inversions and the Riemann sphere", Indra's Pearls: The Vision of Felix Klein, Cambridge University Press, p. 54, ISBN 9781107717190, MR 3558870

archive.org

Waud, Samuel Wilkes (1835), A Treatise on Algebraical Geometry, Baldwin and Cradock, p. 194
Maxwell, James Clerk (1849), "XXXV.—On the theory of rolling curves", Transactions of the Royal Society of Edinburgh, 16 (5): 519–540, doi:10.1017/s008045680002247x, Zenodo: 2250749
Bowser, Edward Albert (1882), "The reciprocal or hyperbolic spiral", An Elementary Treatise on Analytic Geometry: Embracing Plane Geometry and an Introduction to Geometry of Three Dimensions (4th ed.), D. Van Nostrand, p. 232
Ganguli, Surendramohan (1926), "289: The hyperbolic spiral", The Theory of Plane Curves, vol. II (2nd ed.), University of Calcutta, pp. 364–365

arxiv.org

Ringermacher, Harry I.; Mead, Lawrence R. (July 2009), "A new formula describing the scaffold structure of spiral galaxies", Monthly Notices of the Royal Astronomical Society, 397 (1): 164–171, arXiv:0908.0892, Bibcode:2009MNRAS.397..164R, doi:10.1111/j.1365-2966.2009.14950.x
Savchenko, S. S.; Reshetnikov, V. P. (September 2013), "Pitch angle variations in spiral galaxies", Monthly Notices of the Royal Astronomical Society, 436 (2): 1074–1083, arXiv:1309.4308, doi:10.1093/mnras/stt1627

books.google.com

Varignon, Pierre (1704), "Nouvelle formation de Spirales – exemple II", Mémoires de l'Académie des sciences de l'Institut de France: 94–103
Cotesium, Rogerum (1722), Smith, Robertus (ed.), Harmonia Mensurarum, Sive Analysis & Synthesis per Rationum & Angulorum Mensuras (in Latin), Cambridge. For the Cotes spirals, see pp. 30–35; the hyperbolic spiral is case 4, p. 34. Hammer dates this material to 1714, but it was not published until after Cotes's death.
Nicholson, Peter (1825), A Popular Course of Pure and Mixed Mathematics for the Use of Schools and Students, G. B. Whittaker, p. 436
Morris, Christopher G., ed. (1992), "Hyperbolic spiral", Academic Press Dictionary of Science and Technology, Academic Press, p. 1068
Shikin, Eugene V. (2014), "Hyperbolic spiral (reciprocal spiral)", Handbook and Atlas of Curves, CRC Press, pp. 222–223, ISBN 9781498710671
Mumford, David; Series, Caroline; Wright, David (2002), "Inversions and the Riemann sphere", Indra's Pearls: The Vision of Felix Klein, Cambridge University Press, p. 54, ISBN 9781107717190, MR 3558870
Rutter, J.W. (2018), "Theorem 7.11", Geometry of Curves, CRC Press, p. 143, ISBN 9781482285673

bridgesmathart.org

archive.bridgesmathart.org

Dunham, Douglas (2003), "Hyperbolic spirals and spiral patterns", in Barrallo, Javier; Friedman, Nathaniel; Maldonado, Juan Antonio; Martínez-Aroza, José; Sarhangi, Reza; Séquin, Carlo (eds.), Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings, Granada, Spain: University of Granada, pp. 521–528, ISBN 84-930669-1-5

doi.org

Maxwell, James Clerk (1849), "XXXV.—On the theory of rolling curves", Transactions of the Royal Society of Edinburgh, 16 (5): 519–540, doi:10.1017/s008045680002247x, Zenodo: 2250749
Drábek, Karel (1994), "Plane curves and constructions", in Rektorys, Karel (ed.), Survey of Applicable Mathematics, Mathematics and Its Applications, vol. 280–281, Springer Netherlands, pp. 112–166, doi:10.1007/978-94-015-8308-4_4, ISBN 9789401583084; see p. 138
Hammer, Øyvind (2016), "15: The case of the staircase", The Perfect Shape: Spiral Stories, Springer International Publishing, pp. 65–68, doi:10.1007/978-3-319-47373-4_15
Guicciardini, Niccolò (1995), "Johann Bernoulli, John Keill and the inverse problem of central forces", Annals of Science, 52 (6): 537–575, doi:10.1080/00033799500200401
Haines, C. R. (December 1977), "Old curves in a new setting", The Mathematical Gazette, 61 (418): 262–266, doi:10.2307/3617399, JSTOR 3617399, S2CID 189050097
Ringermacher, Harry I.; Mead, Lawrence R. (July 2009), "A new formula describing the scaffold structure of spiral galaxies", Monthly Notices of the Royal Astronomical Society, 397 (1): 164–171, arXiv:0908.0892, Bibcode:2009MNRAS.397..164R, doi:10.1111/j.1365-2966.2009.14950.x
Kennicutt, R. C. Jr. (December 1981), "The shapes of spiral arms along the Hubble sequence", The Astronomical Journal, 86, American Astronomical Society: 1847, Bibcode:1981AJ.....86.1847K, doi:10.1086/113064
Savchenko, S. S.; Reshetnikov, V. P. (September 2013), "Pitch angle variations in spiral galaxies", Monthly Notices of the Royal Astronomical Society, 436 (2): 1074–1083, arXiv:1309.4308, doi:10.1093/mnras/stt1627
Scott, Thomas R.; Noland, J. H. (1965), "Some stimulus dimensions of rotating spirals", Psychological Review, 72 (5): 344–357, doi:10.1037/h0022204, PMID 5318086, ProQuest 614277135
Polezhaev, Andrey (2019), "Spirals, their types and peculiarities", in Tsuji, Kinko; Müller, Stefan C. (eds.), Spirals and Vortices: In Culture, Nature, and Science, The Frontiers Collection, Springer International Publishing, pp. 91–112, doi:10.1007/978-3-030-05798-5_4, ISBN 9783030057985, S2CID 150149152; see especially Section 2.2, Hyperbolic spiral, p. 96
Loria, Gino; Roever, W. H. (February 1919), "On certain constructions of descriptive geometry", The American Mathematical Monthly, 26 (2): 45–53, doi:10.1080/00029890.1919.11998485, JSTOR 2973138; for the central projection of a helix, see p. 51
Kepr, Bořivoj (1994), "Differential geometry", in Rektorys, Karel (ed.), Survey of Applicable Mathematics, Mathematics and Its Applications, vol. 280–281, Springer Netherlands, pp. 260–335, doi:10.1007/978-94-015-8308-4_9, ISBN 9789401583084. For an equivalent formula for the direction angle (the complementary angle to the pitch angle) see Section 9.9, Theorem 1, p. 300

harvard.edu

ui.adsabs.harvard.edu

Ringermacher, Harry I.; Mead, Lawrence R. (July 2009), "A new formula describing the scaffold structure of spiral galaxies", Monthly Notices of the Royal Astronomical Society, 397 (1): 164–171, arXiv:0908.0892, Bibcode:2009MNRAS.397..164R, doi:10.1111/j.1365-2966.2009.14950.x
Kennicutt, R. C. Jr. (December 1981), "The shapes of spiral arms along the Hubble sequence", The Astronomical Journal, 86, American Astronomical Society: 1847, Bibcode:1981AJ.....86.1847K, doi:10.1086/113064

jstor.org

Haines, C. R. (December 1977), "Old curves in a new setting", The Mathematical Gazette, 61 (418): 262–266, doi:10.2307/3617399, JSTOR 3617399, S2CID 189050097
Loria, Gino; Roever, W. H. (February 1919), "On certain constructions of descriptive geometry", The American Mathematical Monthly, 26 (2): 45–53, doi:10.1080/00029890.1919.11998485, JSTOR 2973138; for the central projection of a helix, see p. 51

nih.gov

pubmed.ncbi.nlm.nih.gov

Scott, Thomas R.; Noland, J. H. (1965), "Some stimulus dimensions of rotating spirals", Psychological Review, 72 (5): 344–357, doi:10.1037/h0022204, PMID 5318086, ProQuest 614277135

proquest.com

search.proquest.com

Scott, Thomas R.; Noland, J. H. (1965), "Some stimulus dimensions of rotating spirals", Psychological Review, 72 (5): 344–357, doi:10.1037/h0022204, PMID 5318086, ProQuest 614277135

semanticscholar.org

api.semanticscholar.org

Haines, C. R. (December 1977), "Old curves in a new setting", The Mathematical Gazette, 61 (418): 262–266, doi:10.2307/3617399, JSTOR 3617399, S2CID 189050097
Polezhaev, Andrey (2019), "Spirals, their types and peculiarities", in Tsuji, Kinko; Müller, Stefan C. (eds.), Spirals and Vortices: In Culture, Nature, and Science, The Frontiers Collection, Springer International Publishing, pp. 91–112, doi:10.1007/978-3-030-05798-5_4, ISBN 9783030057985, S2CID 150149152; see especially Section 2.2, Hyperbolic spiral, p. 96

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

"Curves: Hyperbolic Spiral", MacTutor History of Mathematics Archive, University of St Andrews

zenodo.org

Maxwell, James Clerk (1849), "XXXV.—On the theory of rolling curves", Transactions of the Royal Society of Edinburgh, 16 (5): 519–540, doi:10.1017/s008045680002247x, Zenodo: 2250749