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
EXAMPLE
0.981969533135035144632455577645244577876506488298626128140435464629108917429...
MATHEMATICA
Sqrt[4*Sqrt[3]-3]-1 // N[#, 100]& // RealDigits // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Apr 23 2013
STATUS
approved