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

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 2

^{k}(k ³ 0). Interesting questions have been resolved through the surprising involvement of Fermat numbers.
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