cp's OEIS Frontend

A352453 Decimal expansion of the area of intersection of 4 unit-radius circles that have the vertices of a unit-side square as centers.

%I A352453 #16 Mar 17 2022 05:49:56
%S A352453 3,1,5,1,4,6,7,4,3,6,2,7,7,2,0,4,5,2,6,2,6,7,6,8,1,1,9,5,8,7,2,9,5,2,
%T A352453 6,1,1,2,2,9,1,7,8,7,9,3,1,4,6,5,4,6,4,5,6,0,2,5,0,7,8,8,4,6,5,0,6,7,
%U A352453 2,4,5,1,8,5,3,2,6,9,6,2,9,1,2,8,1,9,8,7,5,5,0,2,3,4,5,7,1,1,3,6,5,1,7,5,6
%N A352453 Decimal expansion of the area of intersection of 4 unit-radius circles that have the vertices of a unit-side square as centers.
%C A352453 The solution to a problem in Jones (1932): "At each corner of a garden, surrounded by a wall n yards square, a goat is tied with a rope n yards long. Find the area of the part of the garden common to the four goats." (When the square is taken to be of unit size, the common area is this constant.)
%C A352453 The perimeter of the shape formed by the intersection is 2*Pi/3 (A019693).
%C A352453 The solution to the three-dimensional version of this problem is A352454.
%H A352453 Donald L. Chambers, <a href="https://doi.org/10.1111/j.1949-8594.1977.tb09283.x">Problem 3684</a>, School Science and Mathematics, Vol. 77, No. 5 (1977), p. 443; <a href="https://doi.org/10.1111/j.1949-8594.1978.tb09373.x">Solution</a> by J. Philip Smith, ibid., Vol. 78, No. 4 (1978), pp. 354-355.
%H A352453 Amiram Eldar, <a href="/A352453/a352453.jpg">Illustration</a>.
%H A352453 Samuel Isaac Jones, <a href="https://archive.org/details/MathematicalNuts/page/n155/mode/2up">Mathematical Nuts: For Lovers of Mathematics</a>, 1932, Problems 9 and 10, pp. 86, 301-302.
%H A352453 Missouri State University, <a href="http://people.missouristate.edu/lesreid/Adv08.html">Problem #8, Finding the Area (resp. Volume) of Overlapping Circles (resp. Spheres)</a>, Advanced Problem Archive,; <a href="http://people.missouristate.edu/lesreid/AdvSol08.html">Solution to Problem #8</a>, by Raymond Roan.
%H A352453 Bruce Shawyer, <a href="https://cms.math.ca/publications/crux/issue?volume=25&amp;issue=8">Problem 6</a>, APICS 1999 Mathematics Competition, The Academy Corner, Crux Mathematicorum, Vol. 25, No. 8, 1999, p. 453; <a href="https://cms.math.ca/publications/crux/issue?volume=26&amp;issue=4">Solutions</a> by Richard Tod and Catherine Shevlin, Vol. 26, No. 4, 2000, pp. 193-194.
%H A352453 Charles W. Trigg, <a href="https://cms.math.ca/publications/crux/issue?volume=7&amp;issue=9">Problem 686</a>, Crux Mathematicorum, Vol. 7, No. 9, 1981, p. 275; <a href="https://cms.math.ca/publications/crux/issue?volume=8&amp;issue=9">Solution</a> by Jordan Dou, Vol. 8, No. 9, 1982, p. 294.
%F A352453 Equals 1 + Pi/3 - sqrt(3) = 1 + A019670 - A002194.
%e A352453 0.31514674362772045262676811958729526112291787931465...
%t A352453 RealDigits[1 + Pi/3 - Sqrt[3], 10, 100][[1]]
%Y A352453 Cf. A002194, A019670, A019693.
%Y A352453 Cf. A075838, A133731, A192930, A352454.
%K A352453 nonn,cons
%O A352453 0,1
%A A352453 _Amiram Eldar_, Mar 16 2022