Abstracts to the papers that appeared in Journal of Recreational Mathematics 37(3)
More Simple – But Little Known – Methods of Generating Pythagorean Triples
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?
Eastern Illinois University
Eastern Illinois University
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
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
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
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.