|
%I #7 Dec 27 2017 01:30:57
%S 4,1,0,7,0,3,8,0,4,9,4,4,0,1,0,2,3,8,1,2,8,3,1,2,9,9,5,1,5,8,0,8,7,2,
%T 8,1,4,3,8,1,5,8,8,9,9,2,4,5,5,3,1,9,2,0,6,5,4,3,6,2,1,7,3,4,4,0,4,5,
%U 1,8,0,7,1,4,0,7,4,6,8,4,8,4,9,3,1,3,0
%N Decimal expansion of the arc length of the Golden Spiral inscribed inside a Golden Rectangle with a unit width.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenSpiral.html">Golden Spiral</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRectangle.html">Golden Rectangle</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LogarithmicSpiral.html">Logarithmic Spiral</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_spiral">Golden spiral</a>.
%F sqrt(1+1/sqrt(5))*sqrt(1+b^2)/b, where b=2*log(phi)/Pi, and phi=(1+sqrt(5))/2.
%e 4.10703804944010238128...
%t b=2*Log[GoldenRatio]/Pi; RealDigits[Sqrt[1+1/Sqrt[5]]*Sqrt[1 + b^2]/b, 10, 120][[1]]
%o (PARI) phi = (1+sqrt(5))/2; b = 2*log(phi)/Pi; sqrt(1+1/sqrt(5))*sqrt(1+b^2)/b \\ _Michel Marcus_, Dec 23 2017
%Y Cf. A001622, A212224, A212225.
%K nonn,cons
%O 1,1
%A _Amiram Eldar_, Dec 20 2017
|
