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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).
1
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
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
Sequence in context: A114864 A261025 A340207 * A275615 A249677 A094135
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved