A296794 Decimal expansion of the arc length of the Golden Spiral inscribed inside a Golden Rectangle with a unit width.

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

Table of n, a(n) for n=1..87.

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

Cf. A001622, A212224, A212225.

Sequence in context: A060196 A204169 A255331 * A119305 A198215 A062175

Adjacent sequences: A296791 A296792 A296793 * A296795 A296796 A296797

Keyword

nonn,cons

Author

Amiram Eldar, Dec 20 2017

Status

approved