Abstracts to the papers that appeared in Journal of Recreational Mathematics 38(2)

Abstracts to the papers that appeared in Journal of Recreational Mathematics 38(2)

Restaurant Customer Satisfaction in Manhattan

Julianna G. Gardner, Peter J. DiPrinzio, and Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 The authors examine OpenTable^® restaurant ratings in November 2012 at 980 Manhattan restaurants by cuisine (America, European, Asian, and Latin American) and by price (low ─ $30 and under per person; middle ─ $31 to $49 per person; and high ─ $50 and over per person).  For each of the three different price categories, patrons rated all four types of cuisine about the same, with one exception: the lowest-priced European restaurants are rated higher than all comparably priced other restaurants.  The authors also find that for each of the four different cuisine types, spending more at a restaurant in Manhattan leads to greater customer satisfaction.

Which NHL Team Wins in Overtime?  These CHIS Know

Nicholas W. BonDurant, Alexandra L. DeMarco, Derek Pimentel, and Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 The authors use chi-square (χ²) tests to determine whether there is any relationship between National Hockey League teams that score the tying goal late in the third (and final) period of regulation and winning in overtime (OT).  All regular-season and playoff games are examined over eight seasons,    2005-06 through 2012-13.  When teams are tied after three periods in regular season (playoff) games, the authors show that the home team wins in OT about 54 (66) percent of the time no matter which team ─ the home team or the visiting team ─ scores in the last three minutes of regulation.

Evaluating Agreement and Disagreement between the U.S. and Middle East Countries in the UN General Assembly

Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 The author examines the voting records of the United States, Israel, Iran, Iraq, and Afghanistan for each of twenty sessions of the United Nations (UN) General Assembly from 1991 through 2010.  For each of 1435 UN General Assembly resolutions adopted by vote, the author uses alternative measures of agreement or disagreement between pairs of nations (the agreement rate in square contingency tables, Cohen’s kappa, and Spearman rank correlation) for each of four five-year periods.  While Israel’s alignment with the United States has been strong over the last fifteen years, disagreement between the U.S. and Iran became progressively more intense for each of the last three five-year periods.        

Generalized Palindromes with Leading Zeroes

John J. J. Matulis Jr.

john.matulis@villanova.edu

Abstract

  A palindrome is a character string that reads the same forwards and backwards. For example,  527725 and POTSTOP are palindromes. The generalized palindrome is a character string where a proper grouping of the characters can create a palindrome. For example, 73653657 is not a palindrome, but if it is grouped in the following way (7)(365)(365)(7) it is. This paper is an extension of that idea by allowing for leading zeroes. 

A Convergent Sequence of Circles

Henry Ibstedt
henry.ibstedt@gmail.com

Abstract

 The coordinates and radii of the infinite sequence of circles shown in the figure are all rational numbers.  An in depth study of the equation x = y + 4 + 4*sqrt(y - 8) reveals some interesting properties among which a sequence of 8 prime numbers occurring in a regular fashion.

Should Investors Fear Friday the 13^th?

Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 The author examines the daily performance of the Dow Jones Industrial Average (DOW) reported on the New York Stock Exchange on all Friday the 13^ths between 1950 and 2014, by decade and by month.  Apart from a significant upside on June Friday the 13^ths, there were no discernable differences by month.  And, while Friday the 13^ths in the 1970s were bad news for investors, there have been no differences between decades since then.  In both the 1950s and 1960s, the DOW on Friday the 13^ths outperformed the DOW the day before as well as the DOW the Monday that followed the 13^th.  No such pattern emerges after the 1960s.   

The Influence of Free Agency on NHL Player Performance

Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 The author examines the performance of all non-goalie free agents in the National Hockey League in the years 2012 and 2013 one season before and after free agency.  The free agents in each season are divided into two age groups: players younger than 30 years of age and players 30 years of age or older.  The free agents 30 years of age or older had uniformly lower (and in most cases significantly lower) average points per game in the year following free agency, although the lower performance appears to be no different if they re-signed with their previous team or signed with a new team.