## Monday, March 28, 2016

### Abstracts to the papers that appeared in "Journal of Recreational Mathematics 36(4)"

Abstracts to the papers that appeared in Journal of Recreational Mathematics 36(4)

Weighted Magic Squares

Hossein Behforooz
Utica College

Abstract
In this article, for the first time in the history of Magic Squares, you will be introduced to the weighted magic squares, obtained by changing the numbers to weights in the cells of the magic squares and we will discuss the centers of mass (fulcrums or pivot points) of these kinds of weighted magic squares.

Behforooz Magic Squares Derived From Magic-Latin-Sudoku Squares

Hossein Behforooz
Utica College

Abstract
The main motivation of this article goes back to August, 2003 when I was in Boulder, Colorado to present a talk at the Recreational Mathematics Session of the MAA Mathfest meeting. During one evening I attended a magic show on Boulder’s Main Street and in one part, the magician entertained the audience with a table of numbers. I tried to learn the secret of that table and after the the show I asked the magician to teach me the secret of that table and of course he didn’t tell me. I left the show with a 4 x 4 table written on my palm and tons of thoughts in my mind to discover the secret of that table ASAP. I could not sleep that night at all.
I will present the same show with my own homemade magic squares and I am sure that you will enjoy the show. By using 4 x 4 Magic-Latin-Sudoku (MLS) squares I will produce a set of 4 x 4 Behforooz Magic Squares. These squares have incredible and amazing properties. The squares can be used to construct different types of fourth order magic squares for any given integer as a pre-assigned magic sum. Very similar to the claim that Archimedes made centures ago, “Give me a place to stand and I will move the Earth!” Here, I am asking you to give me yoiur wish number S and I will present to you many 4 x 4 magic squares with magic sum equal to S. Furthermore, we can easily create curious mirror magic squares, permutation-free magic squares and upside down magic squares from these MLS squares.

Many Proofs That the Primes are Infinite

J. Marshall Ash
T. Kyle Petersen
DePaul University

Abstract
Many mathematicians know of more than one type of proof that there are infinitely many primes. In this article we present several different families of proofs, in which each family contains infinitely many distinct variations on the core proof idea.

Remarks on Integer Palindromes

Philip Kidder
Harris Wong
SUNY Fredonia

Abstract
In this short note, we present several remarks about palindromes. Among them are: generation of the nth palindrome and operations on palindromes that lead to interesting tresults.

Quantifying the Effect of Steroid Use on Major League Baseball Batters

Jeremy Roth
Macalester College

Abstract
In 2005, Major League Baseball (MLB) began releasing the names of players who tested positive for performance-enhancing drugs (PEDs). Through 2009, over 250 players have been suspended for a positive PED test. Moreover, the Mitchell Report yielded the names of 89 alleged PED users. This documentation enables quantification of the impact of steroids on player performance. We gathered the home-run-to-fly-ball ratio (HR/F) of all MLB batters with at least 100 plate appearances in a season between 2004 and 2009.
Batters were deemed to be steroid users if they were names as such in the Mitchell Report or suspended by MLB. Human growth hormone (HGH) was tracked separately. Using linear mixed effects, we modeled HR/F by steroid and HGH usage, a quadratic in age, position and park factor. Steroid use had a statistically, and practically, significant positive impact on HR/F.
When all control variables were included, steroid use was associated with an increase of 3.419% (p = 0.0001) in HR/F, equivalent to 35% of the mean HR/F of 9.79%. HGH use was not related to HR/F. This finding is consistent with past literature indicating that, unlike anabolic steroids, HGH does not help a player increase his strength.

A Pell and Pell-Lucas Hybridity

Thomas Koshy
Framingham State University

Abstract
This article presents an interesting pattern involving Pell and Pell-Lucas numbers and emplys determinants to establish the identity behind it. It illustrates the power of matrices and determinants in extracting properties of integer sequences.

Do Baseball’s Northernmost Teams Play Hot in Cold Weather?”

Paul M. Sommers
Middlebury College

Abstract
Three of the four northernmost teams in Major League Baseball ─ the Seattle Mariners, the Milwaukee Brewers and the Toronto Blue Jays, but not the Minnesota Twins ─ play at home in stadiums with a retractable roof.  The author runs a series of two-sample t-tests that compare the average start-time temperature for road wins against the average start-time temperature for road losses (month by month) for each of these four teams during the 2010 season.  The results show that for only the Blue Jays were the start-time temperatures in the months of April and September/October, on average, lower for road wins than for road losses.

Lennon?  McCartney?  Who was the Principal Author in ‘Lennon and McCartney’?”

Sydney L. Fuqua, Lauren C. Redfield, Schooner J. Sonntag, and Paul M. Sommers
Middlebury College

Abstract
The authors use a series of chi-square tests on the relative frequency of vowels and consonants in the lyrics of Paul McCartney and John Lennon songs on the Rubber Soul album, released by The Beatles in December 1965.  The two lyricists are divided into six different groups [alone, with contributions to the lyrics from the other, or with Richard Starkey (a.k.a. Ringo Starr)].  The results suggest that the lyrics in the songs ascribed to John Lennon as the principal lyricist or John (as the main composer) with contributions from either Paul or Ringo most closely resemble those “Lennon and McCartney” songs jointly credited to both John and Paul as equals.

Are Yankees vs. Red Sox Games Too Slow?
Paul M. Sommers
Middlebury College

Abstract
The author examines the average length of baseball games played during the 2010 regular season involving the Boston Red Sox and the New York Yankees against each other and with each of their American League (AL) opponents as well as their National League (NL) opponents in interleague games.  The results show that Red Sox games with the Yankees lasted longer (and in all but two of thirteen comparisons significantly longer) than their matchups with any other AL opponent (or with NL opponents in interleague games).