Ellipse (English Wikipedia)

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

refsWebsite

Global rank English rank

10doi.org

2^nd place

4books.google.com

3^rd place

4semanticscholar.org

11^th place

8^th place

3worldcat.org

5^th place

2loc.gov

70^th place

63^rd place

2jstor.org

26^th place

20^th place

2archive.org

6^th place

2arxiv.org

69^th place

59^th place

2johndcook.com

low place

1wolfram.com

513^th place

537^th place

1encyclopediaofmath.org

3,863^rd place

2,637^th place

1tu-darmstadt.de

low place

1nist.gov

355^th place

454^th place

1ams.org

451^st place

277^th place

1harvard.edu

18^th place

17^th place

1sirinudi.org

low place

1uga.edu

2,385^th place

1,626^th place

1rp-photonics.com

low place

9,678^th place

1web.archive.org

1^st place

1cymer.com

low place

ams.org

mathscinet.ams.org

Carlson, B. C. (2010), "Elliptic Integrals", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.

archive.org

From Περί παραδόξων μηχανημάτων [Concerning Wondrous Machines]: "If, then, we stretch a string surrounding the points A, B tightly around the first point from which the rays are to be reflected, the line will be drawn which is part of the so-called ellipse, with respect to which the surface of the mirror must be situated."
Huxley, G. L. (1959). Anthemius of Tralles: A Study in Later Greek Geometry. Cambridge, MA. pp. 8–9. LCCN 59-14700.{{cite book}}: CS1 maint: location missing publisher (link)
Linderholm, Carl E.; Segal, Arthur C. (June 1995). "An Overlooked Series for the Elliptic Perimeter". Mathematics Magazine. 68 (3): 216–220. doi:10.1080/0025570X.1995.11996318. which cites to Kummer, Ernst Eduard (1836). "Uber die Hypergeometrische Reihe" [About the hypergeometric series]. Journal für die Reine und Angewandte Mathematik (in German). 15 (1, 2): 39–83, 127–172. doi:10.1515/crll.1836.15.39.

arxiv.org

Bessel, F. W. (2010). "The calculation of longitude and latitude from geodesic measurements (1825)". Astron. Nachr. 331 (8): 852–861. arXiv:0908.1824. Bibcode:2010AN....331..852K. doi:10.1002/asna.201011352. S2CID 118760590. English translation of Bessel, F. W. (1825). "Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermesssungen". Astron. Nachr. (in German). 4 (16): 241–254. arXiv:0908.1823. Bibcode:1825AN......4..241B. doi:10.1002/asna.18260041601. S2CID 118630614.
Villarino, Mark B. (20 June 2005). "Ramanujan's Perimeter of an Ellipse". arXiv:math.CA/0506384. We present a detailed analysis of Ramanujan's most accurate approximation to the perimeter of an ellipse. In particular, the second equation underestimates the circumference by $\pi (a+b)h^{5}\theta (h),$ where $22.888\cdot 10^{-6}<3\cdot 2^{-17}<\theta (h)\leq 4\left(1-{\frac {7\pi }{22}}\right)<1.60935\cdot 10^{-3}$ is an increasing function of $0\leq h\leq 1.$

books.google.com

Larson, Ron; Hostetler, Robert P.; Falvo, David C. (2006). "Chapter 10". Precalculus with Limits. Cengage Learning. p. 767. ISBN 978-0-618-66089-6.
Young, Cynthia Y. (2010). "Chapter 9". Precalculus. John Wiley and Sons. p. 831. ISBN 978-0-471-75684-2.
Ivory, J. (1798). "A new series for the rectification of the ellipsis". Transactions of the Royal Society of Edinburgh. 4 (2): 177–190. doi:10.1017/s0080456800030817. S2CID 251572677.
Grant, George B. (1906). A treatise on gear wheels. Philadelphia Gear Works. p. 72.

cymer.com

"Cymer - EUV Plasma Chamber Detail Category Home Page". Archived from the original on 2013-05-17. Retrieved 2013-06-20.

doi.org

Blake, E. M. (1900). "The Ellipsograph of Proclus". American Journal of Mathematics. 22 (2): 146–153. doi:10.2307/2369752. JSTOR 2369752.
Ivory, J. (1798). "A new series for the rectification of the ellipsis". Transactions of the Royal Society of Edinburgh. 4 (2): 177–190. doi:10.1017/s0080456800030817. S2CID 251572677.
Bessel, F. W. (2010). "The calculation of longitude and latitude from geodesic measurements (1825)". Astron. Nachr. 331 (8): 852–861. arXiv:0908.1824. Bibcode:2010AN....331..852K. doi:10.1002/asna.201011352. S2CID 118760590. English translation of Bessel, F. W. (1825). "Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermesssungen". Astron. Nachr. (in German). 4 (16): 241–254. arXiv:0908.1823. Bibcode:1825AN......4..241B. doi:10.1002/asna.18260041601. S2CID 118630614.
Linderholm, Carl E.; Segal, Arthur C. (June 1995). "An Overlooked Series for the Elliptic Perimeter". Mathematics Magazine. 68 (3): 216–220. doi:10.1080/0025570X.1995.11996318. which cites to Kummer, Ernst Eduard (1836). "Uber die Hypergeometrische Reihe" [About the hypergeometric series]. Journal für die Reine und Angewandte Mathematik (in German). 15 (1, 2): 39–83, 127–172. doi:10.1515/crll.1836.15.39.
Jameson, G.J.O. (2014). "Inequalities for the perimeter of an ellipse". Mathematical Gazette. 98 (542): 227–234. doi:10.1017/S002555720000125X. S2CID 125063457.
Chamberlain, G. (February 1983). "A characterization of the distributions that imply mean—Variance utility functions". Journal of Economic Theory. 29 (1): 185–201. doi:10.1016/0022-0531(83)90129-1.
Owen, J.; Rabinovitch, R. (June 1983). "On the class of elliptical distributions and their applications to the theory of portfolio choice". Journal of Finance. 38 (3): 745–752. doi:10.1111/j.1540-6261.1983.tb02499.x. JSTOR 2328079.
Pitteway, M.L.V. (1967). "Algorithm for drawing ellipses or hyperbolae with a digital plotter". The Computer Journal. 10 (3): 282–9. doi:10.1093/comjnl/10.3.282.
Van Aken, J.R. (September 1984). "An Efficient Ellipse-Drawing Algorithm". IEEE Computer Graphics and Applications. 4 (9): 24–35. doi:10.1109/MCG.1984.275994. S2CID 18995215.
Smith, L.B. (1971). "Drawing ellipses, hyperbolae or parabolae with a fixed number of points". The Computer Journal. 14 (1): 81–86. doi:10.1093/comjnl/14.1.81.

encyclopediaofmath.org

Encyclopedia of Mathematics, Springer, URL: http://encyclopediaofmath.org/index.php?title=Apollonius_theorem&oldid=17516 .

harvard.edu

ui.adsabs.harvard.edu

Bessel, F. W. (2010). "The calculation of longitude and latitude from geodesic measurements (1825)". Astron. Nachr. 331 (8): 852–861. arXiv:0908.1824. Bibcode:2010AN....331..852K. doi:10.1002/asna.201011352. S2CID 118760590. English translation of Bessel, F. W. (1825). "Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermesssungen". Astron. Nachr. (in German). 4 (16): 241–254. arXiv:0908.1823. Bibcode:1825AN......4..241B. doi:10.1002/asna.18260041601. S2CID 118630614.

johndcook.com

Cook, John D. (28 May 2023). "Comparing approximations for ellipse perimeter". John D. Cook Consulting blog. Retrieved 2024-09-16.
Cook, John D. (22 September 2024). "Error in Ramanujan's approximation for ellipse perimeter". John D. Cook Consulting blog. Retrieved 2024-12-01. the relative error when $b = 1$ and $a$ varies ... is bound by $4/ π - 14/11 = 0.00051227\dots$ .

jstor.org

Blake, E. M. (1900). "The Ellipsograph of Proclus". American Journal of Mathematics. 22 (2): 146–153. doi:10.2307/2369752. JSTOR 2369752.
Owen, J.; Rabinovitch, R. (June 1983). "On the class of elliptical distributions and their applications to the theory of portfolio choice". Journal of Finance. 38 (3): 745–752. doi:10.1111/j.1540-6261.1983.tb02499.x. JSTOR 2328079.

loc.gov

lccn.loc.gov

Protter & Morrey (1970, pp. 304, APP-28) Protter, Murray H.; Morrey, Charles B. Jr. (1970), College Calculus with Analytic Geometry (2nd ed.), Reading: Addison-Wesley, LCCN 76087042
From Περί παραδόξων μηχανημάτων [Concerning Wondrous Machines]: "If, then, we stretch a string surrounding the points A, B tightly around the first point from which the rays are to be reflected, the line will be drawn which is part of the so-called ellipse, with respect to which the surface of the mirror must be situated."
Huxley, G. L. (1959). Anthemius of Tralles: A Study in Later Greek Geometry. Cambridge, MA. pp. 8–9. LCCN 59-14700.{{cite book}}: CS1 maint: location missing publisher (link)

nist.gov

dlmf.nist.gov

Carlson, B. C. (2010), "Elliptic Integrals", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.

rp-photonics.com

Encyclopedia of Laser Physics and Technology - lamp-pumped lasers, arc lamps, flash lamps, high-power, Nd:YAG laser

semanticscholar.org

api.semanticscholar.org

Ivory, J. (1798). "A new series for the rectification of the ellipsis". Transactions of the Royal Society of Edinburgh. 4 (2): 177–190. doi:10.1017/s0080456800030817. S2CID 251572677.
Bessel, F. W. (2010). "The calculation of longitude and latitude from geodesic measurements (1825)". Astron. Nachr. 331 (8): 852–861. arXiv:0908.1824. Bibcode:2010AN....331..852K. doi:10.1002/asna.201011352. S2CID 118760590. English translation of Bessel, F. W. (1825). "Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermesssungen". Astron. Nachr. (in German). 4 (16): 241–254. arXiv:0908.1823. Bibcode:1825AN......4..241B. doi:10.1002/asna.18260041601. S2CID 118630614.
Jameson, G.J.O. (2014). "Inequalities for the perimeter of an ellipse". Mathematical Gazette. 98 (542): 227–234. doi:10.1017/S002555720000125X. S2CID 125063457.
Van Aken, J.R. (September 1984). "An Efficient Ellipse-Drawing Algorithm". IEEE Computer Graphics and Applications. 4 (9): 24–35. doi:10.1109/MCG.1984.275994. S2CID 18995215.

sirinudi.org

ramanujan.sirinudi.org

Ramanujan, Srinivasa (1914). "Modular Equations and Approximations to π" (PDF). Quart. J. Pure App. Math. 45: 350–372. ISBN 978-0-8218-2076-6. {{cite journal}}: ISBN / Date incompatibility (help)

tu-darmstadt.de

mathematik.tu-darmstadt.de

E. Hartmann: Lecture Note 'Planar Circle Geometries', an Introduction to Möbius-, Laguerre- and Minkowski Planes, p. 55

uga.edu

jwilson.coe.uga.edu

David Drew. "Elliptical Gears". [1]

web.archive.org

"Cymer - EUV Plasma Chamber Detail Category Home Page". Archived from the original on 2013-05-17. Retrieved 2013-06-20.

wolfram.com

mathworld.wolfram.com

"Ellipse - from Wolfram MathWorld". Mathworld.wolfram.com. 2020-09-10. Retrieved 2020-09-10.

worldcat.org

search.worldcat.org

Strubecker, K. (1967). Vorlesungen über Darstellende Geometrie. Göttingen: Vandenhoeck & Ruprecht. p. 26. OCLC 4886184.
Archimedes. (1897). The works of Archimedes. Heath, Thomas Little, Sir, 1861-1940. Mineola, N.Y.: Dover Publications. p. 115. ISBN 0-486-42084-1. OCLC 48876646. {{cite book}}: ISBN / Date incompatibility (help)

worldcat.org

Archimedes. (1897). The works of Archimedes. Heath, Thomas Little, Sir, 1861-1940. Mineola, N.Y.: Dover Publications. p. 115. ISBN 0-486-42084-1. OCLC 48876646. {{cite book}}: ISBN / Date incompatibility (help)