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A296794
Decimal expansion of the arc length of the Golden Spiral inscribed inside a Golden Rectangle with a unit width.
1
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, 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, 1, 8, 0, 7, 1, 4, 0, 7, 4, 6, 8, 4, 8, 4, 9, 3, 1, 3, 0
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Golden Spiral.
Eric Weisstein's World of Mathematics, Golden Rectangle.
Eric Weisstein's World of Mathematics, Logarithmic Spiral.
Wikipedia, Golden spiral.
FORMULA
sqrt(1+1/sqrt(5))*sqrt(1+b^2)/b, where b=2*log(phi)/Pi, and phi=(1+sqrt(5))/2.
EXAMPLE
4.10703804944010238128...
MATHEMATICA
b=2*Log[GoldenRatio]/Pi; RealDigits[Sqrt[1+1/Sqrt[5]]*Sqrt[1 + b^2]/b, 10, 120][[1]]
PROG
(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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Dec 20 2017
STATUS
approved