Merrimack College
Merrimack ScholarWorks
Mathematics Faculty Publications
Mathematics
2-1996
Building Home Plate: Field of Dreams or Reality?
Michael J. Bradley
Merrimack College, [email protected]
Follow this and additional works at: http://scholarworks.merrimack.edu/mth_facpub
Part of the Mathematics Commons
Repository Citation
Bradley, M. J. (1996). Building Home Plate: Field of Dreams or Reality?. Mathematics Magazine, 69(1), 44-45.
Available at: http://scholarworks.merrimack.edu/mth_facpub/11
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44
MATHEMATICSMAGAZINE
REFERENCES
1. JamesGleick,Genius: The Life and Scienceof RichardFeynman,PantheonBooks, New York 1992,
page 47.
2. E. C. Anderson,Morrie'slaw and experimental
mathematics,
to appear,J.of RecreationalMathematics.
-W. A. BEYER ANDJ. D. LOUCK
Los ALAMOS NATIONAL LABORATORY
Los ALAMOS,
NM 87545
-D.
ZEILBERGER
TEMPLE UNIVERSITY
PHILADELPHIA,
PA 19122
BuildingHome Plate:FieldofDreamsor Reality?
MICHAEL J. BRADLEY
MerrimackCollege
NorthAndover,MA 01845
In the movie Field of Dreams, Kevin Costner'scharacter,Ray Kinsella,considers
buildinga baseball park in the middleof his cornfield."If you build it, theywill
come," encouragesa voice fromthe past. As an assistantcoach formynine-year-old
son's baseballteam,I was interestedto read in the officialleague rulesthe following
forhomeplate:
specifications
"Home base shallbe markedby a five-sidedslab ofwhitenedrubber.It
shall be a 12-inchsquarewithtwoofthecornersfilledin so thatone edge
is 17 incheslong, two are 8 1/2 inchesand two are 12 inches."([1],
p. 160)
An accompanying
diagramshowsthe finishedproduct:
17
81/2
81/2
FIGURE 1
I wondered not whetherwe should build it, but
Ponderingthese instructions,
whetherwe cotuldbuildit. Is such a homeplatepossible?
The "correct"answeris "No." The figureimpliesthe existenceof a rightisosceles
trianglewithsides 12, 12 and 17. But (12,12,17) is not (quite) a Pythagorean
triple:
122 + 122 = 288; 172 = 289. Thus, these specificationsseem to give new meaning to a
"Field of Dreams."
45
VOL. 69, NO. 1, FEBRUARY 1996
On the otherhand,if one interprets
the values 12 and 17 as measurednumbers,
accurateto two significant
digits,thenhomeplate can be built,since,to thatdegree
of accuracy,(12,12,17) is a Pythagorean
triple.
We can buildit! Let themcome.
-REFERENCE
1. Peter Kreutzerand Ted Kerley,LittleLeague's OfficialHow-to-PlayBaseball Book, Doubleday,New
York,1990.
The Pythagorean
Proposition:
A Proof
byMeansofCalculus
MIKE STARING
Hogeschool
Katholieke
Leergangen
5022 DN Tilburg,
TheNetherlands
E. S. Loomis,in [1], arguesthattherecan be no trigonometric
proofnor anyproof
based on analytical
or calculusforthePythagorean
geometry
proposition
because each
of these subjects "accepts the truthof geometryas established,and therefore
furnishes
no new proof."His argumentseemsvalid in so faras functions
of two(or
more)variablesare involvedin such a 'proof.'Since calculusof one variablecan be
developedwithoutusingthePythagorean
theorem,circularreasoningmaybe avoided.
The following
is a proofof the proposition
usingcalculus.
Let ABC be a trianglewithits rightangleat A. Keep AB fixedand let AB = b.
Denote AC by thevariablex, so that BC is a function
of x, f(x). See FIGURE 1. If
AC increasesby an amountA x, then BC willincreasebyAf. Fromsimilartriangles,
Jf S>
Ax
CP
CD >CD
x
CA=
CB f(x)
A
D
b
FIGURE 1