OFFSET
3,1
COMMENTS
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.]
REFERENCES
Kreutzer, P. and Kerley, T., Little League's Official How-to-Play Baseball Book. New York: Doubleday, 1990.
LINKS
M. J. Bradley, Building Home Plate: Field of Dreams or Reality?, Math. Mag. 69, 44-45, 1996.
Eric Weisstein's World of Mathematics, Home Plate
Eric Weisstein's World of Mathematics, Isosceles Triangle
FORMULA
Equals (17/4)*(34+sqrt(287)). - Jason Yuen, Sep 14 2024
EXAMPLE
216.4995659709...
MATHEMATICA
RealDigits[17/4 (34+Sqrt[287]), 10, 120][[1]] (* Harvey P. Dale, May 24 2023 *)
CROSSREFS
KEYWORD
AUTHOR
Jonathan Vos Post, Sep 06 2006
STATUS
approved