A121403 Decimal expansion of the area of home plate (USA major league baseball) in square inches.

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

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

Table of n, a(n) for n=3..107.

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

Sequence in context: A021466 A286259 A257134 * A155550 A355642 A268754

Adjacent sequences: A121400 A121401 A121402 * A121404 A121405 A121406

Keyword

cons,easy,nonn

Author

Jonathan Vos Post, Sep 06 2006

Status

approved