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.
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
Vittorio Addona
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.
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).
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