## Wednesday, February 24, 2016

### Abstracts of papers appearing in "Topics in Recreational Mathematics Volume 2," edited by Charles Ashbacher.

Abstracts of papers appearing in Topics in Recreational Mathematics Volume 2, edited by Charles Ashbacher. ISBN 978-1508617099

Here’s the Scoop: Ground Balls Win Lacrosse Games

Peter R. Smith, Russell K. Banker, Paul M. Sommers
Department of Economics
Middlebury College
Abstract
A key metric in lacrosse is the number of times a team scoops up a ground ball.  Box scores of every men’s lacrosse game for Division III colleges in the New England Small College Athletic Conference (NESCAC) between 2005 and 2009 were examined to gauge the importance of ground balls to winning.  A series of chi-square tests, one for each school in NESCAC, shows that ground balls were critical to success.   For each school, the authors also use regression analysis to show a strong direct relationship between the team’s margin of victory and the percentage of ground balls won.

An Example of a Smarandache Geometry

Professor Ion Patrascu
National College Fraţii Buzeşti
Craiova, Romania
Abstract
For centuries it was thought that the geometry codified by Euclid and based on the parallel postulate
Given any line l and a point p not on l, one and only one line can be drawn through p parallel to l.
was the only geometry that existed. This idea was overturned when two other geometries based on a different number of parallel lines being drawn through p were discovered. In a hyperbolic geometry it is possible to construct infinitely many lines parallel to l passing through p and in an elliptic geometry it is not possible to construct any lines through p parallel to l.
This paper gives an example of a geometry where more than one form of the parallel axiom is valid within the geometry.

Smarandache’s Concurrent Lines Theorem

Edited by Dr. M. Khoshnevisan

Neuro Intelligence Center, Australia

Abstract
In this paper we present the Smarandache’s Concurrent Lines Theorem in the geometry of the polygon. The theorem states that if a polygon having any number of sides greater than 3 is circumscribed around a circle then the set of lines connecting vertices of the polygon in combination with the set of lines connecting points of tangency to the circle has at least three of the lines are concurrent.

The Career Save Percentage Profile of NHL Goalies

Douglas A. Raeder, Paul M. Sommers
Middlebury College

Abstract
Physical abilities of professional athletes eventually depreciate with age.  The authors examine 75 goalies in the National Hockey League (NHL) who played at least five games in the 2008-09 season and how their save percentage varied from season to season throughout their career.  The authors’ regression model indicates that the save percentage profile of a representative NHL goalie reaches a peak around their sixth year in the NHL.

Some Unsolved Problems in Number Theory
Taken from Only Problems, Not Solutions!, by Florentin Smarandache, Chicago, 1991, 1993.

Alternating Iterations Of The Sum Of Divisors Function And The
Pseudo-Smarandache Function

Henry Ibstedt
Sweden

Abstract
This study is an extension of work done by Charles Ashbacher [3]. Iteration results have been re-defined in terms of invariants and loops. Further empirical studies and analysis of results have helped throw light on a few intriguing questions.

Alternating Iterations of the Euler f Function and the Pseudo-Smarandache Function
Henry Ibstedt
Sweden

Abstract
This study originates from questions posed on alternating iterations involving the Pseudo-Smarandache function Z(n) and the Euler function f(n). An important part of the study is a formal proof of the fact that Z(n) < n for all n ¹ 2k (k ³ 0). Interesting questions have been resolved through the surprising involvement of Fermat numbers.