Abstracts
to the papers that appeared in Journal of Recreational Mathematics 37(3)
More
Simple – But Little Known – Methods of Generating Pythagorean Triples
Owen O’Shea
Ireland
Abstract
Pythagorean
triples are three positive integers a, b and c that can form the sides of a
right triangle. In other words a*a + b*b = c*c. This paper contains some simple
formulas for generating Pythagorean triples with the additional restriction
that the hypotenuse is only one unit longer than the longest leg.
Tic-Tac-Toe
on Topological Surfaces: Does O Always Win?
Ira Rosenholtz
Eastern Illinois University
Keith Wolcott
Eastern Illinois University
Abstract
Among the
various versions of Tic-Tac-Toe, we address the version that is played on an m ×
n board where X plays first, followed by O with play alternating and the first
player that gets three in a row loses (three in a row winning is trivial on
larger boards.) We consider boards which are a plane, cylinder, Möbius band,
torus, Klein bottle, and projective plane. O draws and loses on all 3 × 3
boards, but we prove that O wins on all larger boards up through 6 × 6 and
prove that O wins on many infinite classes of larger boards. We conjecture that
O wins on all larger boards.
BABE: The Sultan of
Pitching Stats?
Matthew H. LoRusso and Paul M. Sommers
Middlebury College
psommers@middlebury.edu
Abstract
The BABE, a
baseball metric, adds the number of total bases a pitcher gives up to the
number of walks allowed and divides this sum by the number of batters
faced. The lower the BABE, the better
the pitcher’s performance. In this
paper, the authors examine the BABEs of all 369 World Series games played
between 1946 and 2009, grouping winners and losers by league and by length of
the series, both before and after free agency (1976). Of the 63 World Series, the eventual series
winner had significantly lower BABEs, both before and after free agency. Individual game winners had the lower BABE
over 83 percent (or 307/369) of the
time.
Racer Swimsuits Fit to a t
Jay Li and Paul M. Sommers
Middlebury College
psommers@middlebury.edu
Abstract
Collegiate
swimmers were allowed to wear high-tech racer suits in 2009. The authors examine the impact of the
high-tech suits on men and women in the New England Small College Athletic
Conference (NESCAC) championships in 2009 relative to the same swimmers’
winning times in sprint and endurance events in 2010 (the first year of their
ban) and 2008 (one year before their introduction to collegiate swimming). Drop times (that is, the difference between a
swimmer’s best in-season time and best time at the championships) in four
different free style events are compared.
Men seemingly benefited more in 2009 from the high-tech swimwear than
did women swimmers.
Is
There a Road-Ice Advantage in NHL Shootouts?
Alexandra A. Fox, Tucker P. Donahoe, John M. Yanchek,
and Paul M. Sommers
Middlebury College
psommers@middlebury.edu
Abstract
Following the
National Hockey League’s 2004-2005 lockout, the NHL adopted shootouts at the
end of a tie overtime game to determine a winner. The authors examine the box scores of 184
shootouts in the 2009-2010 NHL regular season to gauge the importance of
scoring last late in regulation to tie the game (and force an overtime period
and ultimately a shootout). There is no
evidence of a home-ice advantage to a shootout victory. But, given the eventual shootout winner did
score last in the final five minutes of regulation, 62.5 percent of the time
the shootout winner (and hence the winner of the game) is the visiting team.
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