

A121403


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


2



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

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 nearinteger, 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. [Highprecision calculation by T. D. Noe from the exact solution in this comment.]


REFERENCES

Kreutzer, P. and Kerley, T., Little League's Official HowtoPlay 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, 4445, 1996.
Eric Weisstein's World of Mathematics, Home Plate
Eric Weisstein's World of Mathematics, Isosceles Triangle


EXAMPLE

216.4995659709...


CROSSREFS

Sequence in context: A021466 A286259 A257134 * A155550 A268754 A005299
Adjacent sequences: A121400 A121401 A121402 * A121404 A121405 A121406


KEYWORD

cons,easy,nonn


AUTHOR

Jonathan Vos Post, Sep 06 2006


STATUS

approved



