cp's OEIS Frontend

A309282 Decimal expansion of the circumference of a golden ellipse with a unit semi-major axis.

%I A309282 #33 Jan 05 2025 19:51:41
%S A309282 5,1,5,4,2,7,3,1,7,8,0,2,5,8,7,9,9,6,2,4,9,2,8,3,5,5,3,9,1,1,3,3,4,1,
%T A309282 9,5,5,2,8,7,9,7,2,2,3,5,7,0,8,6,6,1,8,2,0,7,2,9,7,2,0,0,0,2,0,5,3,9,
%U A309282 4,3,8,1,1,3,6,1,1,0,4,6,2,2,8,4,7,8,5
%N A309282 Decimal expansion of the circumference of a golden ellipse with a unit semi-major axis.
%C A309282 A golden ellipse is an ellipse inscribed in a golden rectangle. The concept of a golden ellipse was introduced by H. E. Huntley in 1970.
%C A309282 The aesthetic preferences of rectangles and ellipses with relation to the golden ratio were studied by Gustav Fechner in 1876. His results for ellipses were published by Witmer in 1893.
%C A309282 A golden ellipse with a semi-major axis 1 has a minor semi-axis 1/phi and an eccentricity 1/sqrt(phi), where phi is the golden ratio (A001622).
%H A309282 H. E. Huntley, <a href="https://archive.org/details/divineproportion0000hunt">The Divine Proportion: A Study in Mathematical Beauty</a>, Dover, New York, 1970, page 65.
%H A309282 H. E. Huntley, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/12-1/huntley1.pdf">The Golden Ellipse</a>, The Fibonacci Quarterly, Vol. 12, No. 1 (1974), pp. 38-40.
%H A309282 Thomas Koshy, <a href="https://doi.org/10.1002/9781118033067.ch26">The Golden Ellipse and Hyperbola</a>, in the book Fibonacci and Lucas Numbers with Applications, Wiley, 2001, chapter 26.
%H A309282 M. C. Monzingo, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/14-5/monzingo1.pdf">A Note on the Golden Ellipse</a>, The Fibonacci Quarterly, Vol. 14, No. 5 (1974), p. 388.
%H A309282 A. D. Rawlins, <a href="http://www.jstor.org/stable/3620006">A Note on the Golden Ratio</a>, The Mathematical Gazette, Vol. 79, No. 484 (1995), p. 104.
%H A309282 Stanislav Sýkora, <a href="http://dx.doi.org/10.3247/SL2Math08.001">Mathematical Constants</a>, Stan's Library, Vol.II.
%H A309282 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ellipse.html">Ellipse</a>.
%H A309282 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ellipse#Circumference">Ellipse</a>.
%H A309282 Lightner Witmer, <a href="http://echo.mpiwg-berlin.mpg.de/MPIWG:BBE1NSH8">Zur experimentellen Aesthetik einfacher räumlicher Formverhältnisse</a>, Philosophische Studien, Vol. 9 (1893), pp. 96-144.
%F A309282 Equals 4*E(1/phi), where E(x) is the complete elliptic integral of the second kind.
%e A309282 5.154273178025879962492835539113341955287972235708661...
%t A309282 RealDigits[4 * EllipticE[1/GoldenRatio], 10, 100][[1]]
%Y A309282 Cf. A001622 (phi), A094881 (area of the golden ellipse), A197762 (eccentricity of the golden ellipse).
%Y A309282 Similar sequences: A138500, A274014.
%K A309282 nonn,cons
%O A309282 1,1
%A A309282 _Amiram Eldar_, Jul 05 2020