Convex curve (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Convex curve" in English language version.

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mathscinet.ams.org

Fenchel, W. (1983), "Convexity through the ages", in Gruber, Peter M.; Wills, Jörg M. (eds.), Convexity and its Applications, Basel: Birkhäuser, pp. 120–130, doi:10.1007/978-3-0348-5858-8_6, MR 0731109
Dwilewicz, Roman J. (2009), "A short history of convexity" (PDF), Differential Geometry—Dynamical Systems, 11: 112–129, MR 2533649
Strantzen, John; Brooks, Jeff (1992), "A chord-stretching map of a convex loop is an isometry", Geometriae Dedicata, 41 (1): 51–62, doi:10.1007/BF00181542, MR 1147501, S2CID 121294001
Moore, Robert L. (1920), "Concerning simple continuous curves", Transactions of the American Mathematical Society, 21 (3): 333–347, doi:10.2307/1988935, JSTOR 1988935, MR 1501148
Bourbaki, Nicolas (2004), Functions of a Real Variable: Elementary Theory, Elements of Mathematics, translated by Spain, Philip, Berlin: Springer-Verlag, p. 29, doi:10.1007/978-3-642-59315-4, ISBN 3-540-65340-6, MR 2013000
Rademacher, Hans; Toeplitz, Otto (1994), The Enjoyment of Math, Princeton Science Library, Princeton, New Jersey: Princeton University Press, p. 164, ISBN 0-691-02351-4, MR 1300411
Ciesielski, Krzysztof Chris (2022), "Continuous maps admitting no tangent lines: a centennial of Besicovitch functions", The American Mathematical Monthly, 129 (7): 647–659, doi:10.1080/00029890.2022.2071562, MR 4457737, S2CID 249140750
Hug, Daniel; Weil, Wolfgang (2020), Lectures on Convex Geometry, Graduate Texts in Mathematics, vol. 286, Cham: Springer, doi:10.1007/978-3-030-50180-8, ISBN 978-3-030-50180-8, MR 4180684, S2CID 226548863; see in particular Theorem 1.16 (support theorem), p. 27, and exercise 16, p. 60
Polster, Burkard; Steinke, Günter (2001), "2.2.1 Convex curves, arcs, and ovals", Geometries on surfaces, Encyclopedia of Mathematics and its Applications, vol. 84, Cambridge University Press, pp. 31–34, doi:10.1017/CBO9780511549656, ISBN 0-521-66058-0, MR 1889925
Maehara, Hiroshi (2015), "Circle lattice point problem, revisited", Discrete Mathematics, 338 (3): 164–167, doi:10.1016/j.disc.2014.11.004, MR 3291879
Hartmann, Erich; Feng, Yu Yu (1993), "On the convexity of functional splines", Computer Aided Geometric Design, 10 (2): 127–142, doi:10.1016/0167-8396(93)90016-V, MR 1213308
Ha, Truong Xuan Duc; Jahn, Johannes (2019), "Characterizations of strictly convex sets by the uniqueness of support points", Optimization, 68 (7): 1321–1335, doi:10.1080/02331934.2018.1476513, MR 3985200, S2CID 126177709
Garibaldi, Julia; Iosevich, Alex; Senger, Steven (2011), The Erdős Distance Problem, Student Mathematical Library, vol. 56, Providence, Rhode Island: American Mathematical Society, p. 51, doi:10.1090/stml/056, ISBN 978-0-8218-5281-1, MR 2721878
Ricci, Fulvio; Travaglini, Giancarlo (2001), "Convex curves, Radon transforms and convolution operators defined by singular measures", Proceedings of the American Mathematical Society, 129 (6): 1739–1744, doi:10.1090/S0002-9939-00-05751-8, MR 1814105
Umehara, Masaaki; Yamada, Kotaro (2017), "Chapter 4: Geometry of spirals", Differential Geometry of Curves and Surfaces, Hackensack, New Jersey: World Scientific Publishing, pp. 40–49, doi:10.1142/9901, ISBN 978-981-4740-23-4, MR 3676571
Johnson, Harold H.; Vogt, Andrew (1980), "A geometric method for approximating convex arcs", SIAM Journal on Applied Mathematics, 38 (2): 317–325, doi:10.1137/0138027, MR 0564017
Arnold, V. I. (1989), "Topological proof of the transcendence of the abelian integrals in Newton's Principia", Istoriko-Matematicheskie Issledovaniya (31): 7–17, ISSN 0136-0949, MR 0993175
Swinnerton-Dyer, H. P. F. (1974), "The number of lattice points on a convex curve", Journal of Number Theory, 6 (2): 128–135, Bibcode:1974JNT.....6..128S, doi:10.1016/0022-314X(74)90051-1, MR 0337857
Martinez-Maure, Yves (2001), "A fractal projective hedgehog", Demonstratio Mathematica, 34 (1): 59–63, doi:10.1515/dema-2001-0108, MR 1823083, S2CID 118211962
Cieślak, Waldemar; Zając, Józef (1986), "The rosettes", Mathematica Scandinavica, 58 (1): 114–118, doi:10.7146/math.scand.a-12133, JSTOR 24491607, MR 0845490
Helton, J. William; Nie, Jiawang (2010), "Semidefinite representation of convex sets", Mathematical Programming, 122 (1, Ser. A): 21–64, arXiv:0705.4068, doi:10.1007/s10107-008-0240-y, MR 2533752, S2CID 1352703
Chen, Bang-Yen (2000), "Riemannian submanifolds", in Dillen, Franki J. E.; Verstraelen, Leopold C. A. (eds.), Handbook of differential geometry, Vol. I, Amsterdam: North-Holland, pp. 187–418, doi:10.1016/S1874-5741(00)80006-0, MR 1736854; see in particular p. 360
Gruber, Peter M. (2007), "2.2: Alexandrov's theorem in second-order differentiability", Convex and Discrete Geometry, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 336, Berlin: Springer, pp. 27–32, ISBN 978-3-540-71132-2, MR 2335496
Milnor, J. W. (1950), "On the total curvature of knots", Annals of Mathematics, Second Series, 52 (2): 248–257, doi:10.2307/1969467, JSTOR 1969467, MR 0037509; see discussion following Theorem 3.4 (Fenchel's theorem), p. 254
Stromquist, Walter (1989), "Inscribed squares and square-like quadrilaterals in closed curves", Mathematika, 36 (2): 187–197, doi:10.1112/S0025579300013061, MR 1045781
Akopyan, Arseniy; Avvakumov, Sergey (2018), "Any cyclic quadrilateral can be inscribed in any closed convex smooth curve", Forum of Mathematics, 6: Paper No. e7, 9, arXiv:1712.10205, doi:10.1017/fms.2018.7, MR 3810027, S2CID 111377310
Matschke, Benjamin (2021), "Quadrilaterals inscribed in convex curves", Transactions of the American Mathematical Society, 374 (8): 5719–5738, arXiv:1801.01945, doi:10.1090/tran/8359, MR 4293786, S2CID 119174856
Jerrard, R. P. (1961), "Inscribed squares in plane curves", Transactions of the American Mathematical Society, 98 (2): 234–241, doi:10.1090/s0002-9947-1961-0120604-3, MR 0120604, S2CID 54091952

ams.org

DeTurck, Dennis; Gluck, Herman; Pomerleano, Daniel; Vick, David Shea (2007), "The four vertex theorem and its converse" (PDF), Notices of the American Mathematical Society, 54 (2): 9268, arXiv:math/0609268

archive.org

Schwartzman, Steven (1994), The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, MAA Spectrum, Mathematical Association of America, p. 156, ISBN 9780883855119

arxiv.org

DeTurck, Dennis; Gluck, Herman; Pomerleano, Daniel; Vick, David Shea (2007), "The four vertex theorem and its converse" (PDF), Notices of the American Mathematical Society, 54 (2): 9268, arXiv:math/0609268
Helton, J. William; Nie, Jiawang (2010), "Semidefinite representation of convex sets", Mathematical Programming, 122 (1, Ser. A): 21–64, arXiv:0705.4068, doi:10.1007/s10107-008-0240-y, MR 2533752, S2CID 1352703
Akopyan, Arseniy; Avvakumov, Sergey (2018), "Any cyclic quadrilateral can be inscribed in any closed convex smooth curve", Forum of Mathematics, 6: Paper No. e7, 9, arXiv:1712.10205, doi:10.1017/fms.2018.7, MR 3810027, S2CID 111377310
Matschke, Benjamin (2021), "Quadrilaterals inscribed in convex curves", Transactions of the American Mathematical Society, 374 (8): 5719–5738, arXiv:1801.01945, doi:10.1090/tran/8359, MR 4293786, S2CID 119174856

books.google.com

Gruber, Peter M. (1993), "History of convexity", in Gruber, Peter M. (ed.), Handbook of Convex Geometry, Volume A, Amsterdam: North-Holland, pp. 1–15, ISBN 0-444-89598-1
Veblen, Oswald (1931), The Cambridge Colloquium, 1916, Part. II: Analysis Situs, Colloquium Lectures, vol. 5, Providence, Rhode Island: American Mathematical Society, p. 3
Bourbaki, Nicolas (2004), Functions of a Real Variable: Elementary Theory, Elements of Mathematics, translated by Spain, Philip, Berlin: Springer-Verlag, p. 29, doi:10.1007/978-3-642-59315-4, ISBN 3-540-65340-6, MR 2013000
Rademacher, Hans; Toeplitz, Otto (1994), The Enjoyment of Math, Princeton Science Library, Princeton, New Jersey: Princeton University Press, p. 164, ISBN 0-691-02351-4, MR 1300411
Epstein, Charles L. (2008), Introduction to the Mathematics of Medical Imaging (2nd ed.), Society for Industrial and Applied Mathematics, p. 17, ISBN 978-0-89871-779-2
Polster, Burkard; Steinke, Günter (2001), "2.2.1 Convex curves, arcs, and ovals", Geometries on surfaces, Encyclopedia of Mathematics and its Applications, vol. 84, Cambridge University Press, pp. 31–34, doi:10.1017/CBO9780511549656, ISBN 0-521-66058-0, MR 1889925
Garibaldi, Julia; Iosevich, Alex; Senger, Steven (2011), The Erdős Distance Problem, Student Mathematical Library, vol. 56, Providence, Rhode Island: American Mathematical Society, p. 51, doi:10.1090/stml/056, ISBN 978-0-8218-5281-1, MR 2721878
Umehara, Masaaki; Yamada, Kotaro (2017), "Chapter 4: Geometry of spirals", Differential Geometry of Curves and Surfaces, Hackensack, New Jersey: World Scientific Publishing, pp. 40–49, doi:10.1142/9901, ISBN 978-981-4740-23-4, MR 3676571
Yurinsky, Vadim Vladimirovich (1995), "1.4.4 Piecewise-linear functions and polytopes", Sums and Gaussian Vectors, Lecture Notes in Mathematics, vol. 1617, Berlin & Heidelberg: Springer, pp. 24–27, doi:10.1007/bfb0092599, ISBN 978-3-540-60311-5
Higgins, Peter M. (2008), Number Story: From Counting to Cryptography, London: Springer, p. 179, doi:10.1007/978-1-84800-001-8, ISBN 978-1-84800-000-1
Chen, Bang-Yen (2000), "Riemannian submanifolds", in Dillen, Franki J. E.; Verstraelen, Leopold C. A. (eds.), Handbook of differential geometry, Vol. I, Amsterdam: North-Holland, pp. 187–418, doi:10.1016/S1874-5741(00)80006-0, MR 1736854; see in particular p. 360

doi.org

Fenchel, W. (1983), "Convexity through the ages", in Gruber, Peter M.; Wills, Jörg M. (eds.), Convexity and its Applications, Basel: Birkhäuser, pp. 120–130, doi:10.1007/978-3-0348-5858-8_6, MR 0731109
Strantzen, John; Brooks, Jeff (1992), "A chord-stretching map of a convex loop is an isometry", Geometriae Dedicata, 41 (1): 51–62, doi:10.1007/BF00181542, MR 1147501, S2CID 121294001
Moore, Robert L. (1920), "Concerning simple continuous curves", Transactions of the American Mathematical Society, 21 (3): 333–347, doi:10.2307/1988935, JSTOR 1988935, MR 1501148
Toponogov, Victor A. (2006), "1.5 Problems: convex plane curves", in Rovenski, Vladimir Y (ed.), Differential Geometry of Curves and Surfaces: A Concise Guide, Birkhäuser, pp. 15–19, doi:10.1007/b137116, ISBN 978-0-8176-4402-4
Latecki, Longin Jan; Rosenfeld, Azriel (March 1998), "Supportedness and tameness differentialless geometry of plane curves" (PDF), Pattern Recognition, 31 (5): 607–622, Bibcode:1998PatRe..31..607L, doi:10.1016/s0031-3203(97)00071-x
Bourbaki, Nicolas (2004), Functions of a Real Variable: Elementary Theory, Elements of Mathematics, translated by Spain, Philip, Berlin: Springer-Verlag, p. 29, doi:10.1007/978-3-642-59315-4, ISBN 3-540-65340-6, MR 2013000
Ciesielski, Krzysztof Chris (2022), "Continuous maps admitting no tangent lines: a centennial of Besicovitch functions", The American Mathematical Monthly, 129 (7): 647–659, doi:10.1080/00029890.2022.2071562, MR 4457737, S2CID 249140750
Preparata, Franco P.; Shamos, Michael Ian (1985), "2.2.2.1 The slab method", Computational Geometry: An Introduction, New York: Springer, pp. 45–48, doi:10.1007/978-1-4612-1098-6, ISBN 978-1-4612-7010-2, S2CID 206656565
Latecki, Longin Jan (1998), "Basic Definitions and Propositions", Discrete Representation of Spatial Objects in Computer Vision, Computational Imaging and Vision, vol. 11, Springer Netherlands, pp. 33–43, doi:10.1007/978-94-015-9002-0_2
Brinkhuis, Jan (2020), "Convex functions: basic properties", Convex Analysis for Optimization, Graduate Texts in Operations Research, Springer International Publishing, pp. 123–149, doi:10.1007/978-3-030-41804-5_5, ISBN 978-3-030-41804-5, S2CID 218921797
Hug, Daniel; Weil, Wolfgang (2020), Lectures on Convex Geometry, Graduate Texts in Mathematics, vol. 286, Cham: Springer, doi:10.1007/978-3-030-50180-8, ISBN 978-3-030-50180-8, MR 4180684, S2CID 226548863; see in particular Theorem 1.16 (support theorem), p. 27, and exercise 16, p. 60
Polster, Burkard; Steinke, Günter (2001), "2.2.1 Convex curves, arcs, and ovals", Geometries on surfaces, Encyclopedia of Mathematics and its Applications, vol. 84, Cambridge University Press, pp. 31–34, doi:10.1017/CBO9780511549656, ISBN 0-521-66058-0, MR 1889925
Maehara, Hiroshi (2015), "Circle lattice point problem, revisited", Discrete Mathematics, 338 (3): 164–167, doi:10.1016/j.disc.2014.11.004, MR 3291879
Hartmann, Erich; Feng, Yu Yu (1993), "On the convexity of functional splines", Computer Aided Geometric Design, 10 (2): 127–142, doi:10.1016/0167-8396(93)90016-V, MR 1213308
Ha, Truong Xuan Duc; Jahn, Johannes (2019), "Characterizations of strictly convex sets by the uniqueness of support points", Optimization, 68 (7): 1321–1335, doi:10.1080/02331934.2018.1476513, MR 3985200, S2CID 126177709
Garibaldi, Julia; Iosevich, Alex; Senger, Steven (2011), The Erdős Distance Problem, Student Mathematical Library, vol. 56, Providence, Rhode Island: American Mathematical Society, p. 51, doi:10.1090/stml/056, ISBN 978-0-8218-5281-1, MR 2721878
Ricci, Fulvio; Travaglini, Giancarlo (2001), "Convex curves, Radon transforms and convolution operators defined by singular measures", Proceedings of the American Mathematical Society, 129 (6): 1739–1744, doi:10.1090/S0002-9939-00-05751-8, MR 1814105
Umehara, Masaaki; Yamada, Kotaro (2017), "Chapter 4: Geometry of spirals", Differential Geometry of Curves and Surfaces, Hackensack, New Jersey: World Scientific Publishing, pp. 40–49, doi:10.1142/9901, ISBN 978-981-4740-23-4, MR 3676571
Yurinsky, Vadim Vladimirovich (1995), "1.4.4 Piecewise-linear functions and polytopes", Sums and Gaussian Vectors, Lecture Notes in Mathematics, vol. 1617, Berlin & Heidelberg: Springer, pp. 24–27, doi:10.1007/bfb0092599, ISBN 978-3-540-60311-5
Johnson, Harold H.; Vogt, Andrew (1980), "A geometric method for approximating convex arcs", SIAM Journal on Applied Mathematics, 38 (2): 317–325, doi:10.1137/0138027, MR 0564017
Swinnerton-Dyer, H. P. F. (1974), "The number of lattice points on a convex curve", Journal of Number Theory, 6 (2): 128–135, Bibcode:1974JNT.....6..128S, doi:10.1016/0022-314X(74)90051-1, MR 0337857
Martinez-Maure, Yves (2001), "A fractal projective hedgehog", Demonstratio Mathematica, 34 (1): 59–63, doi:10.1515/dema-2001-0108, MR 1823083, S2CID 118211962
Higgins, Peter M. (2008), Number Story: From Counting to Cryptography, London: Springer, p. 179, doi:10.1007/978-1-84800-001-8, ISBN 978-1-84800-000-1
Cieślak, Waldemar; Zając, Józef (1986), "The rosettes", Mathematica Scandinavica, 58 (1): 114–118, doi:10.7146/math.scand.a-12133, JSTOR 24491607, MR 0845490
Helton, J. William; Nie, Jiawang (2010), "Semidefinite representation of convex sets", Mathematical Programming, 122 (1, Ser. A): 21–64, arXiv:0705.4068, doi:10.1007/s10107-008-0240-y, MR 2533752, S2CID 1352703
Chen, Bang-Yen (2000), "Riemannian submanifolds", in Dillen, Franki J. E.; Verstraelen, Leopold C. A. (eds.), Handbook of differential geometry, Vol. I, Amsterdam: North-Holland, pp. 187–418, doi:10.1016/S1874-5741(00)80006-0, MR 1736854; see in particular p. 360
Milnor, J. W. (1950), "On the total curvature of knots", Annals of Mathematics, Second Series, 52 (2): 248–257, doi:10.2307/1969467, JSTOR 1969467, MR 0037509; see discussion following Theorem 3.4 (Fenchel's theorem), p. 254
Stromquist, Walter (1989), "Inscribed squares and square-like quadrilaterals in closed curves", Mathematika, 36 (2): 187–197, doi:10.1112/S0025579300013061, MR 1045781
Akopyan, Arseniy; Avvakumov, Sergey (2018), "Any cyclic quadrilateral can be inscribed in any closed convex smooth curve", Forum of Mathematics, 6: Paper No. e7, 9, arXiv:1712.10205, doi:10.1017/fms.2018.7, MR 3810027, S2CID 111377310
Matschke, Benjamin (2021), "Quadrilaterals inscribed in convex curves", Transactions of the American Mathematical Society, 374 (8): 5719–5738, arXiv:1801.01945, doi:10.1090/tran/8359, MR 4293786, S2CID 119174856
Jerrard, R. P. (1961), "Inscribed squares in plane curves", Transactions of the American Mathematical Society, 98 (2): 234–241, doi:10.1090/s0002-9947-1961-0120604-3, MR 0120604, S2CID 54091952

harvard.edu

ui.adsabs.harvard.edu

Latecki, Longin Jan; Rosenfeld, Azriel (March 1998), "Supportedness and tameness differentialless geometry of plane curves" (PDF), Pattern Recognition, 31 (5): 607–622, Bibcode:1998PatRe..31..607L, doi:10.1016/s0031-3203(97)00071-x
Swinnerton-Dyer, H. P. F. (1974), "The number of lattice points on a convex curve", Journal of Number Theory, 6 (2): 128–135, Bibcode:1974JNT.....6..128S, doi:10.1016/0022-314X(74)90051-1, MR 0337857

jst.go.jp

jstage.jst.go.jp

Kakeya, Sōichi (1915), "On some properties of convex curves and surfaces.", Tohoku Mathematical Journal, 8: 218–221, JFM 45.1348.02

jstor.org

Moore, Robert L. (1920), "Concerning simple continuous curves", Transactions of the American Mathematical Society, 21 (3): 333–347, doi:10.2307/1988935, JSTOR 1988935, MR 1501148
Cieślak, Waldemar; Zając, Józef (1986), "The rosettes", Mathematica Scandinavica, 58 (1): 114–118, doi:10.7146/math.scand.a-12133, JSTOR 24491607, MR 0845490
Milnor, J. W. (1950), "On the total curvature of knots", Annals of Mathematics, Second Series, 52 (2): 248–257, doi:10.2307/1969467, JSTOR 1969467, MR 0037509; see discussion following Theorem 3.4 (Fenchel's theorem), p. 254

openstax.org

Abramson, Jay (2014), "3.1 Defining the derivative", Precalculus, OpenStax

pub.ro

mathem.pub.ro

Dwilewicz, Roman J. (2009), "A short history of convexity" (PDF), Differential Geometry—Dynamical Systems, 11: 112–129, MR 2533649

semanticscholar.org

api.semanticscholar.org

Strantzen, John; Brooks, Jeff (1992), "A chord-stretching map of a convex loop is an isometry", Geometriae Dedicata, 41 (1): 51–62, doi:10.1007/BF00181542, MR 1147501, S2CID 121294001
Ciesielski, Krzysztof Chris (2022), "Continuous maps admitting no tangent lines: a centennial of Besicovitch functions", The American Mathematical Monthly, 129 (7): 647–659, doi:10.1080/00029890.2022.2071562, MR 4457737, S2CID 249140750
Preparata, Franco P.; Shamos, Michael Ian (1985), "2.2.2.1 The slab method", Computational Geometry: An Introduction, New York: Springer, pp. 45–48, doi:10.1007/978-1-4612-1098-6, ISBN 978-1-4612-7010-2, S2CID 206656565
Brinkhuis, Jan (2020), "Convex functions: basic properties", Convex Analysis for Optimization, Graduate Texts in Operations Research, Springer International Publishing, pp. 123–149, doi:10.1007/978-3-030-41804-5_5, ISBN 978-3-030-41804-5, S2CID 218921797
Hug, Daniel; Weil, Wolfgang (2020), Lectures on Convex Geometry, Graduate Texts in Mathematics, vol. 286, Cham: Springer, doi:10.1007/978-3-030-50180-8, ISBN 978-3-030-50180-8, MR 4180684, S2CID 226548863; see in particular Theorem 1.16 (support theorem), p. 27, and exercise 16, p. 60
Ha, Truong Xuan Duc; Jahn, Johannes (2019), "Characterizations of strictly convex sets by the uniqueness of support points", Optimization, 68 (7): 1321–1335, doi:10.1080/02331934.2018.1476513, MR 3985200, S2CID 126177709
Martinez-Maure, Yves (2001), "A fractal projective hedgehog", Demonstratio Mathematica, 34 (1): 59–63, doi:10.1515/dema-2001-0108, MR 1823083, S2CID 118211962
Helton, J. William; Nie, Jiawang (2010), "Semidefinite representation of convex sets", Mathematical Programming, 122 (1, Ser. A): 21–64, arXiv:0705.4068, doi:10.1007/s10107-008-0240-y, MR 2533752, S2CID 1352703
Akopyan, Arseniy; Avvakumov, Sergey (2018), "Any cyclic quadrilateral can be inscribed in any closed convex smooth curve", Forum of Mathematics, 6: Paper No. e7, 9, arXiv:1712.10205, doi:10.1017/fms.2018.7, MR 3810027, S2CID 111377310
Matschke, Benjamin (2021), "Quadrilaterals inscribed in convex curves", Transactions of the American Mathematical Society, 374 (8): 5719–5738, arXiv:1801.01945, doi:10.1090/tran/8359, MR 4293786, S2CID 119174856
Jerrard, R. P. (1961), "Inscribed squares in plane curves", Transactions of the American Mathematical Society, 98 (2): 234–241, doi:10.1090/s0002-9947-1961-0120604-3, MR 0120604, S2CID 54091952

temple.edu

cis.temple.edu

Latecki, Longin Jan; Rosenfeld, Azriel (March 1998), "Supportedness and tameness differentialless geometry of plane curves" (PDF), Pattern Recognition, 31 (5): 607–622, Bibcode:1998PatRe..31..607L, doi:10.1016/s0031-3203(97)00071-x

worldcat.org

search.worldcat.org

Arnold, V. I. (1989), "Topological proof of the transcendence of the abelian integrals in Newton's Principia", Istoriko-Matematicheskie Issledovaniya (31): 7–17, ISSN 0136-0949, MR 0993175

zbmath.org

Kakeya, Sōichi (1915), "On some properties of convex curves and surfaces.", Tohoku Mathematical Journal, 8: 218–221, JFM 45.1348.02