Abstracts to the papers that appeared in "Journal of Recreational Mathematics 37(4)"

Abstracts to the papers that appeared in Journal of Recreational Mathematics 37(4)

Mathematics and Geography: The Changing Geographic Midpoint of Baseball’s All-Stars

Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 The author uses information on every major leaguer who has ever been selected  to baseball’s  All-Star game between 1933 and 2009 to find how the geographic midpoint of their birthplaces has changed over this 77-year period.   Players are divided by league (American and National) into pitchers and non-pitchers for each of the eight decades.  Simple bilinear regression of the latitude (or longitude of the geographic midpoint) and year shows that the influx of players from Latin America and more recently Asia has moved the geographic midpoint for all players from St. Louis, Missouri (in the 1930s) to Pittsboro, Mississippi (in the 2000s).  

Eat Fresh, Be Happy?

Daniel A. Crepps, Pathik R. Root, Benjamin K. Wessel, and Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 The authors endeavor to explain variation in an index of happiness (based on interviews conducted by World Values Survey) defined for each of 103 countries in 2008 using contemporaneous data on gross domestic product (GDP) per capita and the number of SUBWAY® restaurants per 100,000 population.  The regression equation using only GDP per capita indicates that the happiness index reaches a peak at a level comparable to Norway’s GDP per capita.  Adding the number of SUBWAY® restaurants per 100,000 population to GDP per capita helps explain 35 percent of the total variation in the happiness index across countries. 

Edge-Matching, Polyominoes and Jigsaw Puzzles – Can They Be Combined?

Zdravko Zivkovic

zdravci.zivkovic@vojvodina.gov.rs

Abstract

 For many years MacMahon’s 24 3-color squares had inspired generations of puzzle designers, especially those who find the edge-matching puzzles the most combinatorial and challenging. Many articles are written on that subject and a lot of books contain at least a paragraph about a solid color stylish solution that can be achieved with those magic squares. The first attempt to enhance the original set was a movement of the colors from the edges to the corners and the result was the corner-colored squares. Instead of matching color of the adjacent fields on the edges with the new squares, there was a need to match two colors simultaneously, which was even more challenging. Unfortunately, that change significantly decreases the number of possible combinations with the correct solution. The jig-saw puzzles that serious recreational mathematicians consider childish, because of one ready-made solution, without any combinatorial possibilities, have one great feature: the interlocking system that holds all solved pieces together. The purpose of this paper is to show (1) how the interlocking system can be applied to the edge-matching puzzles providing full combinatorics of all the pieces and (2) to show how the MacMahon’s original 24 square set and its variant of corner-colored square can be replaced with just one 24 3-color hybrid set which can solve each and any pattern of the ancestors and add the new features non-existent in the previous sets, thus significantly increasing the total number of correct combinations.

Sandwiches

Dave Miller and Steven Kahan

skalpha1@aol.com

 Abstract

 For a given positive integer k, suppose that there are exactly k integers strictly between x and x*x, where x > 1 is a real number. What can we predict about x in order for this condition to be satisfied?

A Few Beautiful Prime Number Sequences

Henry Ibstedt

hibstedt@gmail.com

Abstract

 In a recent study of p ± 2^k where p is a prime number and k is a natural number, I came across a few interesting sequences.

Home Prime Reversals

Jay L. Schiffman

Rowan University

schiffman@rowan.edu

Abstract

 During a paper presentation on the Home Prime Conjecture at the Advances in Recreational Mathematics Contributed Paper Session at MathFest 2011 in Lexington, KY, one of the editors of Journal of Recreational Mathematics asked if there was any known research on reversing the order of the factors at each steo of the repeated factoring and concatentation process. Since I was unaware of any such research, I undertook a journey through each of the odd composite integers less than one thousand. Utilizing the CAS package of Mathematica 8.0, I generate the results I have secured and facilitate the important infdings via the use of tables.