Talk:Spherical conic

List of sources

Here is the full list of sources which I added here with the intention of incorporating in the future, but haven’t fully gotten around to yet (as you can see this is still a stub article). Where I got stuck was with making good figures (I need to write or repurpose some plotting software), and then started working on other projects inside and outside of Wikipedia. Since David Eppstein removed a bunch of them from the page (aggressively calling them "predatory" – let’s be polite please), let’s put them here so they don’t disappear.

Most if not all of those which were removed should be added back at some future point (some should clearly be added back immediately). This is a subject that is nowadays pretty obscure (to the point that a Wikipedia page didn’t previously exist; there are now only a few researchers working on it per se, apparently mostly in Austria), and tracking down sources old and new took a lot of effort. –jacobolus (t) 17:45, 3 November 2022 (UTC)

In chronological order:

• Fuss, Nicolas (1788). "De proprietatibus quibusdam ellipseos in superficie sphaerica descriptae" [On certain properties of ellipses described on a spherical surface]. Nova Acta academiae scientiarum imperialis Petropolitanae (in Latin). 3: 90–99.
• Gudermann, Christoph (1830). "Über die analytische Sphärik" [On Spherical Analysis]. Crelle's Journal (in German). 6: 244–254.
• Chasles, Michel (1831). Mémoire de géométrie sur les propriétés générales des coniqes sphériques (in French). L’Académie de Bruxelles. English edition:
  Chasles, Michel (1841). Two geometrical memoirs on the general properties of cones of the second degree, and on the spherical conics. Translated by Graves, Charles. Grant and Bolton.
• Davies, Thomas Stephens (1834). "XII. On the Equations of Loci traced upon the Surface of the Sphere, as expressed by Spherical Co-ordinates". Transactions of the Royal Society of Edinburgh. 12 (1): 259–362. doi:10.1017/S0080456800030611.
• Gudermann, Christoph (1835). "Integralia elliptica tertiae speciei reducendi methodus simplicior, quae simul ad ipsorum applicationem facillimam et computum numericum expeditum perducit. Sectionum conico–sphaericarum qudratura et rectification" [A simpler method of reducing elliptic integrals of the third kind, providing easy application and convenient numerical computation: Quadrature and rectification of conico-spherical sections]. Crelle's Journal. 14: 169–181.
• Booth, James (1844). "IV. On the rectification and quadrature of the spherical ellipse". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 25 (163): 18–38. doi:10.1080/14786444408644925.
• Booth, James (1851). The Theory of Elliptic Integrals: And the Properties of Surfaces of the Second Order, Applied to the Investigation of the Motion of a Body Round a Fixed Point. George Bell.
• Neumann, Carl (1859). "De problemate quodam mechanico, quod ad primam integralium ultraellipticorum classem revocatur" [On a problem in mechanics, whose integral is called ultraelliptical]. Crelle's Journal (in Latin). 56: 46–63. doi:10.1515/crll.1859.56.46.
• Chasles, Michel (1860). "Résumé d'une théorie des coniques sphériques homofocales" (PDF). Comptes Rendus des séances de l'Académie des Sciences. 50: 623–633.
• Serret, Paul Joseph (1860). Théorie nouvelle géométrique et mécanique des lignes a double courbure [New geometric and mechanical theory of lines with double curvature] (in French). Mallet-Bachelier.
• Mulcahy, John (1862) [1852]. Principles of Modern Geometry, with Numerous Applications to Plane and Spherical Figures; and an Appendix Containing Questions for Exercise (2nd ed.). Hodges and Smith.
• Sykes, Gerrit Smith (1877). "Spherical Conics". Proceedings of the American Academy of Arts and Sciences. 13: 375–395. doi:10.2307/25138501.
• Killing, Wilhelm (1885). "Die Mechanik in den Nicht-Euklidischen Raumformen". Crelle's Journal. 98: 1–48.
• Burstall, H. F. W. (1886). "Note on the Arc of a Sphero-Conic". Proceedings of the London Mathematical Society ser. 1. 18 (1): 58–60. doi:10.1112/plms/s1-18.1.58.
• Guyou, Émile (1887). "Nouveau système de projection de la sphère: Généralisation de la projection de Mercator" [New sphere projection system: Generalization of the Mercator projection]. Annales Hydrographiques, Ser. 2 (in French). 9: 16–35.
• Burnside, William (1891). "On the differential equation of confocal sphero-conics". Messenger of Mathematics. 20: 60–63.
• Huber, G. (1900). "Über den sphärischen Kegelschnitt und seine abwickelbare Tangentenfläche" [On the spherical conic and its developable tangent surface]. Zeitschrift für Mathematik und Physik (in German). 45: 86–118.
• Hill, George William (1901). "On the use of the sphero-conic in astronomy". The Astronomical Journal. 22 (511): 53–56.
• Liebmann, Heinrich (1902). "Die Kegelschnitte und die Planetenbewegung im nichteuklidischen Raum" [Conics and Planetary Motion in Non-Euclidean Space]. Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematisch–Physische Classe (in German). 54: 393–423.
• Adams, Oscar Sherman (1925). Elliptic functions applied to conformal world maps (PDF). US Government Printing Office. US Coast and Geodetic Survey Special Publication No. 112.
• Salmon, George (1927). "X. Cones and Sphero-Conics". A Treatise on the Analytic Geometry of Three Dimensions (7th ed.). Chelsea. pp. 249–267.
• Sommerville, Duncan MacLaren Young (1934). "§13.35–36". Analytic Geometry of Three Dimensions. Cambridge University Press. pp. 259–260.
• Cox, Jacques-François (1946). "The doubly equidistant projection". Bulletin Géodésique. 2 (1): 74–76. doi:10.1007/bf02521618.
• Razin, Sheldon (1967). "Explicit (Noniterative) Loran Solution". Navigation. 14 (3): 265–269. doi:10.1002/j.2161-4296.1967.tb02208.x.
• Lukáčs, I.; Smorodinskii, Yakov Abramovich (1973). "Separation of variables in a spheroconical coordinate system and the Schrödinger equation for a case of noncentral forces". Theoretical and Mathematical Physics. 14 (2): 125–131. doi:10.1007/BF01036350.
• Lukáčs, I. (1973). "A complete set of quantum-mechanical observables on a two-dimensional sphere". Theoretical and Mathematical Physics. 14 (3): 271–281. doi:10.1007/BF01029309.
• Freiesleben, Hans-Christian (1976). "Spherical hyperbolae and ellipses". The Journal of Navigation. 29 (2): 194–199. doi:10.1017/S0373463300030186.
• Higgs, Peter W. (1979). "Dynamical symmetries in a spherical geometry I". Journal of Physics A: Mathematical and General. 12 (3): 309–323. doi:10.1088/0305-4470/12/3/006.
• Veselov, Alexander Petrovich (1990). "Confocal surfaces and integrable billiards on the sphere and in the Lobachevsky space". Journal of Geometry and Physics. 7 (1): 81–107. doi:10.1016/0393-0440(90)90021-t.
• Kozlov, Valery Vasilevich; Harin, Alexander O. (1992). "Kepler's problem in constant curvature spaces". Celestial Mechanics and Dynamical Astronomy. 54 (4): 393–399. doi:10.1007/BF00049149.
• Izmest’ev, A. A.; Pogosyan, G. S.; Sissakian, A. N.; Winternitz, P. (1996). "Contractions of Lie algebras and separation of variables". Journal of Physics A: Mathematical and General. 29 (18): 5949–5962. doi:10.1088/0305-4470/29/18/024.
• Dirnböck, Hans (1999). "Absolute polarity on the sphere; conics; loxodrome, tractrix". Mathematical Communications. 4 (2): 225–240.
• Kozlov, Valery Vasilevich (2000). "Теоремы Ньютона и Айвори о притяжении в пространствах постоянной кривизны" [Newton's and Ivory's theorems on attraction in spaces of constant curvature]. Вестник Московского университета. Серия 1: Математика. Механика (in Russian). 2000 (5): 43–47.
• Stachel, Hellmuth; Wallner, Johannes (2004), "Ivory's theorem in hyperbolic spaces" (PDF), Siberian Mathematical Journal, 45 (4): 785–794
• Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano (2005). "Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S² and the hyperbolic plane H²". Journal of Mathematical Physics. 46 (5): 052702. doi:10.1063/1.1893214.
• Tranacher, Harald (2006). Sphärische Kegelschnitte – didaktisch aufbereitet [Spherical conics – didactically prepared] (PDF) (Thesis) (in German). Technischen Universität Wien.
• Arnold, Vladimir; Kozlov, Valery Vasilevich; Neishtadt, Anatoly I. (2007). Mathematical Aspects of Classical and Celestial Mechanics. doi:10.1007/978-3-540-48926-9.
• Schröcker, Hans-Peter (2008). "Double Tangent Circles and Focal Properties of Sphero-Conics" (PDF). Journal for Geometry and Graphics. 12 (2).
• Albouy, Alain (2013). "There is a projective dynamics" (PDF). European Mathematical Society Newsletter. 89: 37–43.
• Diacu, Florin (2013). "The curved N-body problem: risks and rewards" (PDF). Mathematical Intelligencer. 35 (3): 24–33.
• Altunkaya, Bülent; Yaylı, Yusuf; Hacısalihoğlu, H. Hilmi; Arslan, Fahrettin (2014). "One-Parameter Equations of Spherical Conics and Its Applications". Journal of Mathematics Research. 6 (4): 77–84. doi:10.5539/jmr.v6n4p77.
• Glaeser, Georg; Stachel, Hellmuth; Odehnal, Boris (2016). "10.1 Spherical conics". The Universe of Conics: From the ancient Greeks to 21st century developments. Springer. pp. 436–467. doi:10.1007/978-3-662-45450-3_10.
• Horváth, Ákos G. (2016). "Constructive curves in non-Euclidean planes". arXiv:1610.00473.{{cite arXiv}}: CS1 maint: missing class (link) A bot will complete this citation soon. Click here to jump the queue
• Langer, Joel C; Singer, David A. (2018). "On the geometric mean of a pair of oriented, meromorphic foliations, Part I". Complex Analysis and its Synergies. 4 (1): 1–18. doi:10.1186/s40627-018-0015-z.
• Albouy, Alain; Zhao, Lei (2019). "Lambert's theorem and projective dynamics". Philosophical Transactions of the Royal Society A. 377 (2158): 20180417. doi:10.1098/rsta.2018.0417.{{cite journal}}: CS1 maint: article number as page number (link)
• Akopyan, Arseniy; Izmestiev, Ivan (2019). "The Regge symmetry, confocal conics, and the Schläfli formula". Bulletin of the London Mathematical Society. 51 (5): 765–775. doi:10.1112/blms.12276.
• Izmestiev, Ivan (2019). "Spherical and hyperbolic conics". Eighteen Essays in Non-Euclidean Geometry. European Mathematical Society. pp. 262–320. arXiv:1702.06860. doi:10.4171/196-1/15.