Abstracts to the papers that appeared in Journal of Recreational
Mathematics 36(1)
A Numerological Mini Tour of Manhattan
Owen O’Shea
Ireland
Abstract
In
this paper the imaginary Professor Richard Stein is in Manhattan in New York
City entertaining a small group of Japanese mathematicians. Being schooled in
many of the properties of numbers, Professor Stein includes many numerical
facts and properties of the landmarks as the group moves through the city.
Curious Numbers in the King James Bible
Owen O’Shea
Ireland
Abstract
The
imaginary Professor Richard Stein has just completed a vacation in Germany
where he met with a group of Protestant fundamentalists. At their urging, the
professor gave a speech on some of the number curiosities that appear in the
King James version of the Christian bible and those facts are given in a letter
to the author.
Consecutive Cubes with Perfect Square Sums
Steven Kahan
Queens College CUNY
Abstract
Starting with the observation that 23^3 + 24^3
+ 25^3 = 204^2, the author conducts a search for additional solutions where the
first number in the sequence is 2 or greater.
Does Shooting Efficiency
Matter in Explaining NBA Salaries?
Paul M. Sommers
Middlebury College
psommers@middlebury.edu
Abstract
Three different measures of a National Basketball
Association (NBA) player’s performance are used in regressions to help explain
variation in 2007-08 NBA salaries. The 269 NBA players included in the sample
have at least two years of pro experience and appeared in at least 20 games in
the 2006-07 season. After accounting for an NBA player’s years as
a pro and binary variables that control for black, East European, and other
foreign-born players, the results show
that the measure that uses only points, rebounds, steals, and turnovers explains
variation in NBA salaries as well as the two other measures that use additional
facets of a player’s performance.
Do New Ballparks Affect
the Home-Field Advantage?
Paul
M. Sommers
Middlebury College
psommers@middlebury.edu
Abstract
Five major
league baseball teams (Baltimore Orioles, Cleveland Indians, Texas Rangers ,
Colorado Rockies, and Atlanta Braves) played in a new ballpark between 1992 and
1997. For each team, the author uses a
series of chi-squared tests to examine the relationship between winning and
home site. When the home records one
season (or three seasons) before the move are compared to the home records one
season after the move, there is no discernible added home-field advantage. There is not even a home-field advantage through
the first two months in new ballparks compared to the rest of the season.
Probabilistic
Polyforms
Mark J. Lockwood
Dale K. Hathaway
Olivet Nazarene University
hathaway@olivet.edu
Abstract
There are three
regular shapes that tile the plane, the square, equilateral triangle and hexagon.
Polyforms are the figures created by putting together multiple copies of one of
the regular shapes in an edge-to-edge manner. When the next shape is to be
attached, there are several locations where it can be placed.
In this paper
the decision for where to place the next shape in the construction of the
polyform is made in a random manner and some of the consequences of this tactic
are examined.
Retrolife Generation of the Twelve Pentominoes©
Charles Ashbacher
Abstract
The
“Game of Life” was invented by John Horton Conway in the early 1970s and it has
fascinated people ever since. It is played on a two-dimensional checkerboard
and starts with an initial pattern of cells that are “alive” or “dead.” The
game iterates using simple rules regarding what cells come “alive”, stay “alive”
or “die.”
Retrolife is the examination of configurations
that will create a specific configuration using one iteration of the rules of
the game. This paper presents initial configurations that will lead to the generation
of each of the 12 pentominoes after one iteration.
Nimrod
James M. Henle
Emma L. Schlatter
Smith College
Abstract
We
present a new Nim-type game. The description is simple but the strategy is
complex. There is a well-defined core outside of which the game is neatly structured.
Inside the core the game appears chaotic. We have partial results for the core,
a strategy outside the core, and an overall strategy that might be described as
“promising.”
What’s the Radius
Steven Kahan
Queens College
Abstract
Problem solver extraordinaire Dick Hess posed
the simple question to the author.
“If chords WZ, XY and YZ in circle O
measure 7, 2 and 2, respectively, as shown in the figure, what is the radius of
the circle?”
A
generalized version of this problem is solved in this paper.
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