|
| |
|
|
A352453
|
|
Decimal expansion of the area of intersection of 4 unit-radius circles that have the vertices of a unit-side square as centers.
|
|
4
|
|
|
|
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, 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, 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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
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.)
The perimeter of the shape formed by the intersection is 2*Pi/3 (A019693).
The solution to the three-dimensional version of this problem is A352454.
|
|
|
LINKS
|
Donald L. Chambers, Problem 3684, School Science and Mathematics, Vol. 77, No. 5 (1977), p. 443; Solution by J. Philip Smith, ibid., Vol. 78, No. 4 (1978), pp. 354-355.
Bruce Shawyer, Problem 6, APICS 1999 Mathematics Competition, The Academy Corner, Crux Mathematicorum, Vol. 25, No. 8, 1999, p. 453; Solutions by Richard Tod and Catherine Shevlin, Vol. 26, No. 4, 2000, pp. 193-194.
Charles W. Trigg, Problem 686, Crux Mathematicorum, Vol. 7, No. 9, 1981, p. 275; Solution by Jordan Dou, Vol. 8, No. 9, 1982, p. 294.
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
0.31514674362772045262676811958729526112291787931465...
|
|
|
MATHEMATICA
|
RealDigits[1 + Pi/3 - Sqrt[3], 10, 100][[1]]
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
