A185260 Decimal expansion of sqrt(4*sqrt(3) - 3) - 1, the solution to the problem of dissecting an equilateral triangle into a square, with 3 cuts (Haberdasher's problem).

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

Offset

0,1

Comments

Dissecting the triangle, 2 hinges out of 3 are at the middle of 2 sides. The 3rd hinge is at a distance h(s)=(1/4)*(sqrt(4*sqrt(3)-3)-1)*s from the nearest vertex, 's' being the triangle side length. Getting rid of denominators with s=4, the base has to be cut in the ratio h(4):2:2-h(4), which is approximately 0.98197:2:1.01803.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Andrés Navas, La quadrature du triangle, Images des Mathématiques, CNRS, 2021 (in French). Gives (1 - (this constant))/4.

Eric Weisstein's World of Mathematics, Haberdasher's problem

Index entries for algebraic numbers, degree 4.

Formula

Minimal polynomial x^4+4*x^3+12*x^2+16*x-32. - R. J. Mathar, Jun 03 2026

Equals 2*(A298744-1). - R. J. Mathar, Jun 03 2026

Example

0.981969533135035144632455577645244577876506488298626128140435464629108917429...

Mathematica

Sqrt[4*Sqrt[3]-3]-1 // N[#, 100]& // RealDigits // First

Prog

(PARI) sqrt(4*sqrt(3) - 3) - 1 \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Sequence in context: A114864 A261025 A340207 * A275615 A385962 A249677

Adjacent sequences: A185257 A185258 A185259 * A185261 A185262 A185263

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 23 2013

Status

approved