Descartes' theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Descartes' theorem" in English language version.

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32doi.org

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16jstor.org

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14ams.org

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8archive.org

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6arxiv.org

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2handle.net

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2web.archive.org

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1americanscientist.org

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1zbmath.org

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1koreascience.kr

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1hathitrust.org

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1bridgesmathart.org

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1davidhestenes.net

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americanscientist.org (Global: 7,231^st place; English: 5,635^th place)

Mackenzie, Dana (March–April 2023), "The princess and the philosopher", American Scientist, vol. 111, no. 2, pp. 80–84, ProQuest 2779946948

ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

Hogendijk, Jan P. (1986), "Arabic traces of lost works of Apollonius", Archive for History of Exact Sciences, 35 (3): 187–253, doi:10.1007/BF00357307, JSTOR 41133783, MR 0851067
Barnes, John (2012), "Soddy's hexlet", Gems of Geometry (2nd ed.), Heidelberg: Springer, pp. 173–177, doi:10.1007/978-3-642-30964-9_7, ISBN 978-3-642-30963-2, MR 2963305
Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R. (2002), "Beyond the Descartes circle theorem", The American Mathematical Monthly, 109 (4): 338–361, arXiv:math/0101066, doi:10.2307/2695498, JSTOR 2695498, MR 1903421
Levrie, Paul (2019), "A straightforward proof of Descartes's circle theorem", The Mathematical Intelligencer, 41 (3): 24–27, doi:10.1007/s00283-019-09883-x, hdl:10067/1621880151162165141, MR 3995314
Pedoe, Daniel (1967), "On a theorem in geometry", The American Mathematical Monthly, 74 (6): 627–640, doi:10.2307/2314247, JSTOR 2314247, MR 0215169
Bradford, Alden (2023), "An even more straightforward proof of Descartes's circle theorem", The Mathematical Intelligencer, 45 (3): 263–265, arXiv:2211.05539, doi:10.1007/s00283-022-10234-6, MR 4645170
Wilker, J. B. (1969), "Four proofs of a generalization of the Descartes circle theorem", The American Mathematical Monthly, 76 (3): 278–282, doi:10.2307/2316373, JSTOR 2316373, MR 0246207
Northshield, Sam (2014), "Complex Descartes circle theorem", The American Mathematical Monthly, 121 (10): 927–931, doi:10.4169/amer.math.monthly.121.10.927, hdl:1951/69912, JSTOR 10.4169/amer.math.monthly.121.10.927, MR 3295667
Tupan, Alexandru (2022), "On the complex Descartes circle theorem", The American Mathematical Monthly, 129 (9): 876–879, doi:10.1080/00029890.2022.2104084, MR 4499753
Dergiades, Nikolaos (2007), "The Soddy circles" (PDF), Forum Geometricorum, 7: 191–197, MR 2373402, archived from the original (PDF) on 2008-07-05
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H. (2003), "Apollonian circle packings: number theory", Journal of Number Theory, 100 (1): 1–45, arXiv:math/0009113, doi:10.1016/S0022-314X(03)00015-5, MR 1971245
McGonagle, Annmarie; Northshield, Sam (2014), "A new parameterization of Ford circles", Pi Mu Epsilon Journal, 13 (10): 637–643, JSTOR 24345283, MR 3235834
Coxeter, H. S. M. (1968), "Loxodromic sequences of tangent spheres", Aequationes Mathematicae, 1 (1–2): 104–121, doi:10.1007/BF01817563, MR 0235456
This concept of distance was called the "pseudo-chordal distance" for the complex unit disk as a model for the hyperbolic plane by Carathéodory, Constantin (1954) [1950], "§§1.3.86–88 Chordal and Pseudo-chordal Distance", Theory of Functions of a Complex Variable, vol. I, translated by Steinhardt, Fritz, Chelsea, pp. 81–86, MR 0060009

archive.org (Global: 6^th place; English: 6^th place)

Boyer, Carl B. (1956), "Chapter 5: Fermat and Descartes", History of Analytic Geometry, New York: Scripta Mathematica, pp. 74–102; Reprinted by Dover, 2004, ISBN 978-0-486-43832-0
Descartes, René (1901), Adam, Charles; Tannery, Paul (eds.), Oeuvres de Descartes (in French), vol. 4: Correspondance Juillet 1643 – Avril 1647, Paris: Léopold Cerf, "325. Descartes a Elisabeth", pp. 37–42; "328. Descartes a Elisabeth", pp. 45–50
Bos, Erik-Jan (2010), "Princess Elizabeth of Bohemia and Descartes' letters (1650–1665)", Historia Mathematica, 37 (3): 485–502, doi:10.1016/j.hm.2009.11.004
Steiner, Jakob (January 1826), "Fortsetzung der geometrischen Betrachtungen (Heft 2, S. 161)" [Continuation of the geometric considerations], Journal für die reine und angewandte Mathematik (in German), 1826 (1), pp. 252–288, fig. 2–25 taf. III, doi:10.1515/crll.1826.1.252
Lachlan, Robert (1886), "On Systems of Circles and Spheres", Philosophical Transactions of the Royal Society of London, 177, pp. 481–625, see "Spheres touching one another", pp. 585–587, JSTOR 109492
Weiss, Asia (1981), "On Coxeter's Loxodromic Sequences of Tangent Spheres", in Davis, Chandler; Grünbaum, Branko; Sherk, F.A. (eds.), The Geometric Vein: The Coxeter Festschrift, Springer, pp. 241–250, doi:10.1007/978-1-4612-5648-9_16, ISBN 978-1-4612-5650-2
Coolidge, Julian Lowell (1916), "X. The Oriented Circle", A Treatise on the Circle and the Sphere, Clarendon, pp. 351–407, also see p. 109, p. 408
Rigby, J. F. (1981), "The geometry of cycles, and generalized Laguerre inversion", in Davis, Chandler; Grünbaum, Branko; Sherk, F.A. (eds.), The Geometric Vein: The Coxeter Festschrift, Springer, pp. 355–378, doi:10.1007/978-1-4612-5648-9_26, ISBN 978-1-4612-5650-2
This concept of distance was called the "pseudo-chordal distance" for the complex unit disk as a model for the hyperbolic plane by Carathéodory, Constantin (1954) [1950], "§§1.3.86–88 Chordal and Pseudo-chordal Distance", Theory of Functions of a Complex Variable, vol. I, translated by Steinhardt, Fritz, Chelsea, pp. 81–86, MR 0060009

arxiv.org (Global: 69^th place; English: 59^th place)

Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R. (2002), "Beyond the Descartes circle theorem", The American Mathematical Monthly, 109 (4): 338–361, arXiv:math/0101066, doi:10.2307/2695498, JSTOR 2695498, MR 1903421
Bradford, Alden (2023), "An even more straightforward proof of Descartes's circle theorem", The Mathematical Intelligencer, 45 (3): 263–265, arXiv:2211.05539, doi:10.1007/s00283-022-10234-6, MR 4645170
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H. (2003), "Apollonian circle packings: number theory", Journal of Number Theory, 100 (1): 1–45, arXiv:math/0009113, doi:10.1016/S0022-314X(03)00015-5, MR 1971245
Garcia, Ronaldo; Reznik, Dan; Moses, Peter; Gheorghe, Liliana (2022), "Triads of conics associated with a triangle", KoG (26), Croatian Society for Geometry and Graphics: 16–32, arXiv:2112.15232, doi:10.31896/k.26.2
Kocik, Jerzy (2007), A theorem on circle configurations, arXiv:0706.0372
Kocik, Jerzy (2010), "Golden window" (PDF), Mathematics Magazine, 83 (5): 384–390, JSTOR 10.4169/002557010x529815, doi:10.4169/002557010x529815

Kocik, Jerzy (2019), Proof of Descartes circle formula and its generalization clarified, arXiv:1910.09174
Eriksson, Nicholas; Lagarias, Jeffrey C. (2007), "Apollonian Circle Packings: Number Theory II. Spherical and Hyperbolic Packings", The Ramanujan Journal, 14 (3): 437–469, arXiv:math/0403296, doi:10.1007/s11139-007-9052-6

bnf.fr (Global: 124^th place; English: 544^th place)

gallica.bnf.fr

Lemoine, Émile (1891), "Sur les triangles orthologiques et sur divers sujets de la géométrie du triangle" [On orthologic triangles and on various subjects of triangle geometry], Compte rendu de la 19me session de l'association française pour l'avancement des sciences, pt. 2, Congrès de Limoges 1890 (in French), Paris: Secrétariat de l'association, pp. 111–146, especially §4 "Sur les intersections deux a deux des coniques qui ont pour foyers-deux sommets d'un triangle et passent par le troisième" [On the intersections in pairs of the conics which have as foci two vertices of a triangle and pass through the third], pp. 128–144

bridgesmathart.org (Global: low place; English: low place)

archive.bridgesmathart.org

Hidetoshi, Fukagawa; Kazunori, Horibe (2014), "Sangaku – Japanese Mathematics and Art in the 18th, 19th and 20th Centuries", in Greenfield, Gary; Hart, George; Sarhangi, Reza (eds.), Bridges Seoul Conference Proceedings, Tessellations Publishing, pp. 111–118

davidhestenes.net (Global: low place; English: low place)

A definition of stereographic distance can be found in Li, Hongbo; Hestenes, David; Rockwood, Alyn (2001), "Spherical conformal geometry with geometric algebra" (PDF), Geometric Computing with Clifford Algebras, Springer, pp. 61–75, CiteSeerX 10.1.1.412.4949, doi:10.1007/978-3-662-04621-0_3, ISBN 978-3-642-07442-4

doi.org (Global: 2^nd place; English: 2^nd place)

Soddy, F. (June 1936), "The Kiss Precise", Nature, 137 (3477): 1021, doi:10.1038/1371021a0
Hogendijk, Jan P. (1986), "Arabic traces of lost works of Apollonius", Archive for History of Exact Sciences, 35 (3): 187–253, doi:10.1007/BF00357307, JSTOR 41133783, MR 0851067
Court, Nathan Altshiller (October 1961), "The problem of Apollonius", The Mathematics Teacher, 54 (6): 444–452, doi:10.5951/MT.54.6.0444, JSTOR 27956431
Descartes, René (1901), Adam, Charles; Tannery, Paul (eds.), Oeuvres de Descartes (in French), vol. 4: Correspondance Juillet 1643 – Avril 1647, Paris: Léopold Cerf, "325. Descartes a Elisabeth", pp. 37–42; "328. Descartes a Elisabeth", pp. 45–50
Bos, Erik-Jan (2010), "Princess Elizabeth of Bohemia and Descartes' letters (1650–1665)", Historia Mathematica, 37 (3): 485–502, doi:10.1016/j.hm.2009.11.004
Coxeter, H. S. M. (January 1968), "The problem of Apollonius", The American Mathematical Monthly, 75 (1): 5–15, doi:10.1080/00029890.1968.11970941, JSTOR 2315097
Michiwaki, Yoshimasa (2008), "Geometry in Japanese mathematics", in Selin, Helaine (ed.), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, Springer Netherlands, pp. 1018–1019, doi:10.1007/978-1-4020-4425-0_9133, ISBN 978-1-4020-4559-2
Rothman, Tony; Fugakawa, Hidetoshi (May 1998), "Japanese temple geometry", Scientific American, 278 (5): 84–91, doi:10.1038/scientificamerican0598-84, JSTOR 26057787; see top illustration, p. 86. Another tablet from 1822 (center, p. 88) concerns Soddy's hexlet, a configuration of three-dimensional tangent spheres.
Steiner, Jakob (January 1826), "Fortsetzung der geometrischen Betrachtungen (Heft 2, S. 161)" [Continuation of the geometric considerations], Journal für die reine und angewandte Mathematik (in German), 1826 (1), pp. 252–288, fig. 2–25 taf. III, doi:10.1515/crll.1826.1.252
Soddy, Frederick (December 1936), "The hexlet", Nature, 138 (3501): 958, doi:10.1038/138958a0
Barnes, John (2012), "Soddy's hexlet", Gems of Geometry (2nd ed.), Heidelberg: Springer, pp. 173–177, doi:10.1007/978-3-642-30964-9_7, ISBN 978-3-642-30963-2, MR 2963305
Gardner, Martin (May 1968), "Mathematical Games: Circles and spheres, and how they kiss and pack", Scientific American, 218 (5): 130–139, doi:10.1038/scientificamerican0568-130, JSTOR 24926234
"The Kiss Precise", Nature, 139 (3506): 62, January 1937, doi:10.1038/139062a0
Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R. (2002), "Beyond the Descartes circle theorem", The American Mathematical Monthly, 109 (4): 338–361, arXiv:math/0101066, doi:10.2307/2695498, JSTOR 2695498, MR 1903421
Mathews, Daniel V.; Zymaris, Orion (2025), "Spinors and the Descartes circle theorem", Journal of Geometry and Physics, 212 105458, doi:10.1016/j.geomphys.2025.105458
Levrie, Paul (2019), "A straightforward proof of Descartes's circle theorem", The Mathematical Intelligencer, 41 (3): 24–27, doi:10.1007/s00283-019-09883-x, hdl:10067/1621880151162165141, MR 3995314
Pedoe, Daniel (1967), "On a theorem in geometry", The American Mathematical Monthly, 74 (6): 627–640, doi:10.2307/2314247, JSTOR 2314247, MR 0215169
Bradford, Alden (2023), "An even more straightforward proof of Descartes's circle theorem", The Mathematical Intelligencer, 45 (3): 263–265, arXiv:2211.05539, doi:10.1007/s00283-022-10234-6, MR 4645170
Wilker, J. B. (1969), "Four proofs of a generalization of the Descartes circle theorem", The American Mathematical Monthly, 76 (3): 278–282, doi:10.2307/2316373, JSTOR 2316373, MR 0246207
Glaeser, Georg; Stachel, Hellmuth; Odehnal, Boris (2016), "The parabolic pencil – a common line element", The Universe of Conics, Springer, p. 327, doi:10.1007/978-3-662-45450-3_7, ISBN 978-3-662-45449-7
Northshield, Sam (2014), "Complex Descartes circle theorem", The American Mathematical Monthly, 121 (10): 927–931, doi:10.4169/amer.math.monthly.121.10.927, hdl:1951/69912, JSTOR 10.4169/amer.math.monthly.121.10.927, MR 3295667
Tupan, Alexandru (2022), "On the complex Descartes circle theorem", The American Mathematical Monthly, 129 (9): 876–879, doi:10.1080/00029890.2022.2104084, MR 4499753
This is a special case of a formula for the radii of circles in a Steiner chain with concentric inner and outer circles, given by Sheydvasser, Arseniy (2023), "3.1 Steiner's porism and 3.6 Steiner's porism revisited", Linear Fractional Transformations, Undergraduate Texts in Mathematics, Springer, pp. 75–81, 99–101, doi:10.1007/978-3-031-25002-6, ISBN 978-3-031-25001-9
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H. (2003), "Apollonian circle packings: number theory", Journal of Number Theory, 100 (1): 1–45, arXiv:math/0009113, doi:10.1016/S0022-314X(03)00015-5, MR 1971245
Bradley, Christopher J. (March 2003), "Heron triangles and touching circles", The Mathematical Gazette, 87 (508): 36–41, doi:10.1017/s0025557200172080, JSTOR 3620562
Coxeter, H. S. M. (1968), "Loxodromic sequences of tangent spheres", Aequationes Mathematicae, 1 (1–2): 104–121, doi:10.1007/BF01817563, MR 0235456
Weiss, Asia (1981), "On Coxeter's Loxodromic Sequences of Tangent Spheres", in Davis, Chandler; Grünbaum, Branko; Sherk, F.A. (eds.), The Geometric Vein: The Coxeter Festschrift, Springer, pp. 241–250, doi:10.1007/978-1-4612-5648-9_16, ISBN 978-1-4612-5650-2
Veldkamp, G. R. (1985), "The Isoperimetric Point and the Point(s) of Equal Detour in a Triangle", The American Mathematical Monthly, 92 (8): 546–558, doi:10.1080/00029890.1985.11971677, JSTOR 2323159
Garcia, Ronaldo; Reznik, Dan; Moses, Peter; Gheorghe, Liliana (2022), "Triads of conics associated with a triangle", KoG (26), Croatian Society for Geometry and Graphics: 16–32, arXiv:2112.15232, doi:10.31896/k.26.2
Mauldon, J. G. (1962), "Sets of equally inclined spheres", Canadian Journal of Mathematics, 14: 509–516, doi:10.4153/CJM-1962-042-6
Rigby, J. F. (1981), "The geometry of cycles, and generalized Laguerre inversion", in Davis, Chandler; Grünbaum, Branko; Sherk, F.A. (eds.), The Geometric Vein: The Coxeter Festschrift, Springer, pp. 355–378, doi:10.1007/978-1-4612-5648-9_26, ISBN 978-1-4612-5650-2
A definition of stereographic distance can be found in Li, Hongbo; Hestenes, David; Rockwood, Alyn (2001), "Spherical conformal geometry with geometric algebra" (PDF), Geometric Computing with Clifford Algebras, Springer, pp. 61–75, CiteSeerX 10.1.1.412.4949, doi:10.1007/978-3-662-04621-0_3, ISBN 978-3-642-07442-4
Eriksson, Nicholas; Lagarias, Jeffrey C. (2007), "Apollonian Circle Packings: Number Theory II. Spherical and Hyperbolic Packings", The Ramanujan Journal, 14 (3): 437–469, arXiv:math/0403296, doi:10.1007/s11139-007-9052-6

fau.edu (Global: 6,442^nd place; English: 4,551^st place)

forumgeom.fau.edu

Dergiades, Nikolaos (2007), "The Soddy circles" (PDF), Forum Geometricorum, 7: 191–197, MR 2373402, archived from the original (PDF) on 2008-07-05
Jackson, Frank M. (2013), "Soddyian Triangles" (PDF), Forum Geometricorum, 13: 1–6, archived from the original (PDF) on 2014-06-30

handle.net (Global: 102^nd place; English: 76^th place)

hdl.handle.net

Levrie, Paul (2019), "A straightforward proof of Descartes's circle theorem", The Mathematical Intelligencer, 41 (3): 24–27, doi:10.1007/s00283-019-09883-x, hdl:10067/1621880151162165141, MR 3995314
Northshield, Sam (2014), "Complex Descartes circle theorem", The American Mathematical Monthly, 121 (10): 927–931, doi:10.4169/amer.math.monthly.121.10.927, hdl:1951/69912, JSTOR 10.4169/amer.math.monthly.121.10.927, MR 3295667

hathitrust.org (Global: 441^st place; English: 311^th place)

babel.hathitrust.org

Beecroft, Philip (1842), "Properties of circles in mutual contact", The Lady's and Gentleman's Diary (139): 91–96

jstor.org (Global: 26^th place; English: 20^th place)

Hogendijk, Jan P. (1986), "Arabic traces of lost works of Apollonius", Archive for History of Exact Sciences, 35 (3): 187–253, doi:10.1007/BF00357307, JSTOR 41133783, MR 0851067
Court, Nathan Altshiller (October 1961), "The problem of Apollonius", The Mathematics Teacher, 54 (6): 444–452, doi:10.5951/MT.54.6.0444, JSTOR 27956431
Coxeter, H. S. M. (January 1968), "The problem of Apollonius", The American Mathematical Monthly, 75 (1): 5–15, doi:10.1080/00029890.1968.11970941, JSTOR 2315097
Rothman, Tony; Fugakawa, Hidetoshi (May 1998), "Japanese temple geometry", Scientific American, 278 (5): 84–91, doi:10.1038/scientificamerican0598-84, JSTOR 26057787; see top illustration, p. 86. Another tablet from 1822 (center, p. 88) concerns Soddy's hexlet, a configuration of three-dimensional tangent spheres.
Gardner, Martin (May 1968), "Mathematical Games: Circles and spheres, and how they kiss and pack", Scientific American, 218 (5): 130–139, doi:10.1038/scientificamerican0568-130, JSTOR 24926234
Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R. (2002), "Beyond the Descartes circle theorem", The American Mathematical Monthly, 109 (4): 338–361, arXiv:math/0101066, doi:10.2307/2695498, JSTOR 2695498, MR 1903421
Lachlan, Robert (1886), "On Systems of Circles and Spheres", Philosophical Transactions of the Royal Society of London, 177, pp. 481–625, see "Spheres touching one another", pp. 585–587, JSTOR 109492
Pedoe, Daniel (1967), "On a theorem in geometry", The American Mathematical Monthly, 74 (6): 627–640, doi:10.2307/2314247, JSTOR 2314247, MR 0215169
Mackenzie, Dana (January–February 2010), "A tisket, a tasket, an Apollonian gasket", Computing Science, American Scientist, vol. 98, no. 1, pp. 10–14, JSTOR 27859441, All of these reciprocals look a little bit extravagant, so the formula is usually simplified by writing it in terms of the curvatures or the bends of the circles.
Wilker, J. B. (1969), "Four proofs of a generalization of the Descartes circle theorem", The American Mathematical Monthly, 76 (3): 278–282, doi:10.2307/2316373, JSTOR 2316373, MR 0246207
Northshield, Sam (2014), "Complex Descartes circle theorem", The American Mathematical Monthly, 121 (10): 927–931, doi:10.4169/amer.math.monthly.121.10.927, hdl:1951/69912, JSTOR 10.4169/amer.math.monthly.121.10.927, MR 3295667
Hajja, Mowaffaq (2009), "93.33 on a Morsel of Ross Honsberger", The Mathematical Gazette, 93 (527): 309–312, JSTOR 40378744
Bradley, Christopher J. (March 2003), "Heron triangles and touching circles", The Mathematical Gazette, 87 (508): 36–41, doi:10.1017/s0025557200172080, JSTOR 3620562
McGonagle, Annmarie; Northshield, Sam (2014), "A new parameterization of Ford circles", Pi Mu Epsilon Journal, 13 (10): 637–643, JSTOR 24345283, MR 3235834
Veldkamp, G. R. (1985), "The Isoperimetric Point and the Point(s) of Equal Detour in a Triangle", The American Mathematical Monthly, 92 (8): 546–558, doi:10.1080/00029890.1985.11971677, JSTOR 2323159
Kocik, Jerzy (2007), A theorem on circle configurations, arXiv:0706.0372
Kocik, Jerzy (2010), "Golden window" (PDF), Mathematics Magazine, 83 (5): 384–390, JSTOR 10.4169/002557010x529815, doi:10.4169/002557010x529815

Kocik, Jerzy (2019), Proof of Descartes circle formula and its generalization clarified, arXiv:1910.09174

koreascience.kr (Global: low place; English: low place)

Takinami, Susumu; Michiwaki, Yoshimasa (1984), "On the Descartes circle theorem" (PDF), Journal for History of Mathematics, 1 (1), Korean Society for History of Mathematics: 1–8

proquest.com (Global: 206^th place; English: 124^th place)

Mackenzie, Dana (March–April 2023), "The princess and the philosopher", American Scientist, vol. 111, no. 2, pp. 80–84, ProQuest 2779946948

psu.edu (Global: 207^th place; English: 136^th place)

citeseerx.ist.psu.edu

A definition of stereographic distance can be found in Li, Hongbo; Hestenes, David; Rockwood, Alyn (2001), "Spherical conformal geometry with geometric algebra" (PDF), Geometric Computing with Clifford Algebras, Springer, pp. 61–75, CiteSeerX 10.1.1.412.4949, doi:10.1007/978-3-662-04621-0_3, ISBN 978-3-642-07442-4

siu.edu (Global: low place; English: 9,567^th place)

lagrange.math.siu.edu

Kocik, Jerzy (2007), A theorem on circle configurations, arXiv:0706.0372
Kocik, Jerzy (2010), "Golden window" (PDF), Mathematics Magazine, 83 (5): 384–390, JSTOR 10.4169/002557010x529815, doi:10.4169/002557010x529815

Kocik, Jerzy (2019), Proof of Descartes circle formula and its generalization clarified, arXiv:1910.09174

srce.hr (Global: 1,922^nd place; English: 1,922^nd place)

hrcak.srce.hr

Garcia, Ronaldo; Reznik, Dan; Moses, Peter; Gheorghe, Liliana (2022), "Triads of conics associated with a triangle", KoG (26), Croatian Society for Geometry and Graphics: 16–32, arXiv:2112.15232, doi:10.31896/k.26.2

tandfonline.com (Global: 507^th place; English: 429^th place)

Kocik, Jerzy (2007), A theorem on circle configurations, arXiv:0706.0372
Kocik, Jerzy (2010), "Golden window" (PDF), Mathematics Magazine, 83 (5): 384–390, JSTOR 10.4169/002557010x529815, doi:10.4169/002557010x529815

Kocik, Jerzy (2019), Proof of Descartes circle formula and its generalization clarified, arXiv:1910.09174

web.archive.org (Global: 1^st place; English: 1^st place)

Dergiades, Nikolaos (2007), "The Soddy circles" (PDF), Forum Geometricorum, 7: 191–197, MR 2373402, archived from the original (PDF) on 2008-07-05
Jackson, Frank M. (2013), "Soddyian Triangles" (PDF), Forum Geometricorum, 13: 1–6, archived from the original (PDF) on 2014-06-30

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)

Yanagihara, K. (1913), "On some geometrical propositions in Wasan, the Japanese native mathematics", Tohoku Mathematical Journal, 3: 87–95, JFM 44.0052.02

Descartes' theorem (English Wikipedia)

americanscientist.org (Global: 7,231st place; English: 5,635th place)

ams.org (Global: 451st place; English: 277th place)

mathscinet.ams.org

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 69th place; English: 59th place)

bnf.fr (Global: 124th place; English: 544th place)

gallica.bnf.fr

bridgesmathart.org (Global: low place; English: low place)

archive.bridgesmathart.org

davidhestenes.net (Global: low place; English: low place)

doi.org (Global: 2nd place; English: 2nd place)

fau.edu (Global: 6,442nd place; English: 4,551st place)

forumgeom.fau.edu

handle.net (Global: 102nd place; English: 76th place)

hdl.handle.net

hathitrust.org (Global: 441st place; English: 311th place)

babel.hathitrust.org

jstor.org (Global: 26th place; English: 20th place)

koreascience.kr (Global: low place; English: low place)

proquest.com (Global: 206th place; English: 124th place)

psu.edu (Global: 207th place; English: 136th place)

citeseerx.ist.psu.edu

siu.edu (Global: low place; English: 9,567th place)

lagrange.math.siu.edu

srce.hr (Global: 1,922nd place; English: 1,922nd place)

hrcak.srce.hr

tandfonline.com (Global: 507th place; English: 429th place)

web.archive.org (Global: 1st place; English: 1st place)

zbmath.org (Global: 1,923rd place; English: 1,068th place)

americanscientist.org (Global: 7,231^st place; English: 5,635^th place)

ams.org (Global: 451^st place; English: 277^th place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 69^th place; English: 59^th place)

bnf.fr (Global: 124^th place; English: 544^th place)

doi.org (Global: 2^nd place; English: 2^nd place)

fau.edu (Global: 6,442^nd place; English: 4,551^st place)

handle.net (Global: 102^nd place; English: 76^th place)

hathitrust.org (Global: 441^st place; English: 311^th place)

jstor.org (Global: 26^th place; English: 20^th place)

proquest.com (Global: 206^th place; English: 124^th place)

psu.edu (Global: 207^th place; English: 136^th place)

siu.edu (Global: low place; English: 9,567^th place)

srce.hr (Global: 1,922^nd place; English: 1,922^nd place)

tandfonline.com (Global: 507^th place; English: 429^th place)

web.archive.org (Global: 1^st place; English: 1^st place)

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)