A343487 Decimal expansion of the perimeter of the convex hull around the terdragon fractal.

2, 8, 1, 8, 8, 1, 4, 9, 2, 4, 8, 7, 0, 0, 6, 8, 8, 2, 0, 4, 6, 9, 7, 1, 6, 6, 8, 3, 1, 6, 1, 1, 2, 4, 6, 6, 3, 2, 4, 0, 3, 3, 0, 5, 3, 8, 2, 1, 8, 7, 2, 7, 1, 2, 6, 0, 9, 3, 1, 1, 1, 7, 4, 9, 1, 8, 6, 0, 2, 7, 5, 4, 4, 5, 9, 8, 4, 8, 5, 0, 5, 5, 4, 1, 7, 6, 5, 5, 3, 1, 5, 8, 0, 8, 4, 9, 5, 0, 1, 7, 1, 0, 3, 3, 3

Offset: 1

Author

Kevin Ryde, Apr 17 2021

Keywords

• cons
• easy
• nonn

Comments

The convex hull around the terdragon fractal has 14 sides and with unit length from curve start to end their lengths are four sqrt(3)/24 and two each 1/24, 1/8, sqrt(3)/8, 3/8, sqrt(37)/12. Their total is the perimeter.

Examples

			2.8188149248700688204697166831611246...
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..10000
• Kevin Ryde, Iterations of the Terdragon Curve, see index "HBf".

Crossrefs

Cf. A343486 (terdragon hull area), A341030 (dragon hull perimeter).

Programs

Mathematica

RealDigits[(13+5*Sqrt[3]+2*Sqrt[37])/12,10,120][[1]] (* Harvey P. Dale, Dec 25 2021 *)

PARI

my(c=223+20*quadgen(3*37*4)); a_vector(len) = my(s=10^(len-1)); digits((13*s + sqrtint(floor(c*s^2))) \12);

Formula

Equals (13 + 5*sqrt(3) + 2*sqrt(37)) / 12.

Equals (13 + sqrt(223 + 20*sqrt(3*37))) / 12.

Largest root of ((12*x - 13)^2 - 223)^2 - 44400 = 0 (all its roots are real).