Friday, February 19, 2016

List of abstracts of the papers that appeared in "Topics in Recreational Mathematics Volume 4," ISBN: 978-1514317518

List of abstracts of the papers that appeared in Topics in Recreational Mathematics Volume 4, ISBN: 978-1514317518

Are Canadian NHL Hall Of Famers Winter Babies?
Arthur E. Mittnacht
Paul M. Sommers
Department of Economics
Middlebury College
Middlebury, Vermont 05753
 Canadian journalist Malcolm Gladwell has suggested that hockey players (particularly Canadians) with birthdays early in the year have a greater chance of becoming elite players than those with birthdays late in the year.  This note examines all Canadian players (by position, by birthdate, and by province of birth) elected to the NHL Hall of Fame through the year 2008.  The first three months in the Gladwell division are January, February, and March; the first three months in the seasonal division are December, January, and February.  Chi-square goodness-of-fit tests show no empirical support for the Gladwell breakdown, but disproportionately many winter babies for the seasonal breakdown.

Concentric Magic Cubes Of Prime Numbers
Natalia Makarova
Saratov, Russia
  Like their two-dimensional counterparts, three-dimensional magic cubes can fascinate and surprise you with their existence. The level of difficulty and fascination is even higher when magic cubes are constructed inside magic cubes. When there are several layers, they remind you of the Russian Matryoshka dolls-within-dolls. Several examples of magic cubes constructed using formulas are given in this paper, including some constructed from prime numbers. 

Concatenation Problems
Henry Ibstedt
 This study has been inspired by questions asked by Charles Ashbacher in the Journal of Recreational Mathematics, vol. 29.2 concerning the Smarandache Deconstructive Sequence. This sequence is a special case of a more general concatenation and sequencing procedure which is the subject of this study. The properties of this kind of sequences are studied with particular emphasis on the divisibility of their terms by primes.

Zeroes In The Digits Of N Factorial
Michael P. Cohen
 We study the proportion of zero digits in the decimal (base 10) representation of N!, building on earlier work in the Journal of Recreational Mathematics by H. L. Nelson and Charles Ashbacher.  The trailing zeroes (zeroes to the right of the rightmost nonzero digit) and internal zeroes (zeroes to the left of the trailing zeroes) are considered separately.

The Magic Of Three
David L. Emory
 The meaning of period length is explained as a basis for understanding the significance of the number three.  When an odd number is multiplied by three, a larger odd number is created with the same period length.  This multiplication by three can take place again and again, but there is a limit.  Here, only period lengths of six are examined, but many possibilities are demonstrated in a table.

A Brief Biography Of Al-Kashi
Osama Ta’ani
Department of Mathematics
Plymouth State University
Charles Ashbacher
 The man known simply as al-Kashi was born in Persia, now the modern nation of Iran, in the later part of the fourteenth century. He rose from a state of severe poverty to become an accomplished mathematician and scientist, working in many areas.
 His textbook Key to Arithmetic (Miftah al-Hisab) and the abbreviated version Concise Exposition of the Key (Talkhis Al-Miftah) was used to teach mathematics for approximately two centuries in Persia and the Ottoman Empire. This paper is a brief description of his life along with some of his accomplishments.
 The source for the material in this paper is “An Analysis of the Contents and Pegagogy of Al-Kashi’s 1427 ‘Key to Arithmetic’ (Miftah Al-Hisab)” by Osama Hekmatt Ta’ani, his Doctor of Philosophy dissertation at New Mexico State University.
Triangulation Of A Triangle With Triangles Having Equal Inscribed Circles

Professor Ion Patrascu
Fraţii Buzeşti National College
Craiova, Romania

Professor Florentin Smarandache
 University of New Mexico
 Gallup, USA

In this article, we solve the following problem:
Any triangle can be divided by a cevian into two triangles that have congruent inscribed circles.

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