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%I #29 Jul 07 2023 14:35:48
%S 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,
%T 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,
%U 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
%N 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).
%C 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.
%H Vincenzo Librandi, <a href="/A185260/b185260.txt">Table of n, a(n) for n = 0..1000</a>
%H Andrés Navas, <a href="http://images.math.cnrs.fr/La-quadrature-du-triangle.html">La quadrature du triangle</a>, Images des Mathématiques, CNRS, 2021 (in French). Gives (1 - (this constant))/4.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HaberdashersProblem.html">Haberdasher's problem</a>
%e 0.981969533135035144632455577645244577876506488298626128140435464629108917429...
%t Sqrt[4*Sqrt[3]-3]-1 // N[#, 100]& // RealDigits // First
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Apr 23 2013
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