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A121403
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Decimal expansion of the area of home plate (USA major league baseball) in square inches.
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2
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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, 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, 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
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OFFSET
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3,1
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COMMENTS
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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.]
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REFERENCES
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Kreutzer, P. and Kerley, T., Little League's Official How-to-Play Baseball Book. New York: Doubleday, 1990.
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LINKS
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EXAMPLE
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216.4995659709...
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MATHEMATICA
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RealDigits[17/4 (34+Sqrt[287]), 10, 120][[1]] (* Harvey P. Dale, May 24 2023 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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