Abstracts to the papers that appeared in Journal of Recreational Mathematics 36(1)
A Numerological Mini Tour of Manhattan
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
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
Queens College CUNY
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
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
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.
Mark J. Lockwood
Dale K. Hathaway
Olivet Nazarene University
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©
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.
James M. Henle
Emma L. Schlatter
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
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.