%I #24 May 24 2023 16:12:49
%S 2,1,6,4,9,9,5,6,5,9,7,0,9,1,4,0,1,9,1,1,4,7,4,0,2,5,9,1,0,0,6,0,5,5,
%T 8,5,4,4,9,6,7,6,5,6,6,3,5,1,0,5,4,3,6,0,9,1,9,7,4,1,4,3,1,0,8,7,1,2,
%U 6,1,7,6,2,1,6,9,3,3,0,9,6,2,3,9,9,4,1,7,3,2,5,3,9,1,1,7,6,3,2,9,9,8,1,0,4
%N Decimal expansion of the area of home plate (USA major league baseball) in square inches.
%C The home plate in baseball is an irregular pentagon with edge lengths in inches (8.5, 17, 8.5, 12, 12), incorrectly shown in Kreutzer as having 3 right angles. The area of home plate in square inches is thus the area of the 8.5*17 rectangle plus the area of the (12,12,17) isosceles triangle. The latter is (17/2)*sqrt(12^2 - (17^2)/4)) = (17/4)*sqrt(287), which is a near-integer, 71.999565, because the angle is so close to a right angle. Hence the home plate area is approximately 216.49956 square inches, which is coincidentally close to (6^3) + 1/2. [High-precision calculation by _T. D. Noe_ from the exact solution in this comment.]
%D Kreutzer, P. and Kerley, T., Little League's Official How-to-Play Baseball Book. New York: Doubleday, 1990.
%H M. J. Bradley, <a href="http://www.jstor.org/stable/2691394">Building Home Plate: Field of Dreams or Reality?</a>, Math. Mag. 69, 44-45, 1996.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HomePlate.html">Home Plate</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IsoscelesTriangle.html">Isosceles Triangle</a>
%e 216.4995659709...
%t RealDigits[17/4 (34+Sqrt[287]),10,120][[1]] (* _Harvey P. Dale_, May 24 2023 *)
%K cons,easy,nonn
%O 3,1
%A _Jonathan Vos Post_, Sep 06 2006
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