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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 (list; constant; graph; refs; listen; history; text; internal format)
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
Sequence in context: A060196 A204169 A255331 * A119305 A198215 A062175
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Dec 20 2017
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)