Professor Arnone Co-Authors Papers in Two Scientific Journals
Professor of Mathematics Stefano Arnone co-authored two papers that were recently published in two international peer-reviewed scientific journals.
A member of John Cabot University’s faculty since 2007, Professor Arnone is the Chair of the Mathematics, Natural Science & Computer Science Department. For a list of his previous publications, click here.
The first paper, titled “A modern Galileo tale,” was published in Physics Education, an international peer-reviewed journal for those involved in the teaching of physics in schools and colleges.
The year 2014 marked the four-hundred-and-fiftieth anniversary of Galileo’s birth, making it the perfect occasion to present and illustrate a GeoGebra applet which reproduces some of Galileo’s celebrated experiments on the uniformly accelerated motion, as reported on in ‘Discourses and Mathematical Demonstrations Relating to Two New Sciences’.
Our applet is inexpensive, makes up for the lack of a fully-fledged physics lab and can be used as an accompanying activity in an (open) online course. The version we present allows for an ’empirical’ test of three of the most relevant theorems in the third day of Galileo’s Discourses. By three different experimental setups, students can see a ball roll down a slope, take measures and perform data analysis, following Galileo’s footsteps.
The applet is made freely available on the internet, so it can be downloaded and modified to cater for different students’ needs.
The second paper, titled “On Numbers in Different Bases: Symmetries and a Conjecture,” appeared in Experimental Mathematics, an international peer-reviewed journal that publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses.
Any number may be written in many different ways, using different strings in different bases. In few, very special cases, a symmetry emerges which is usually hidden beneath the surface: 230164 and 164230 are both equal to 54284 in base ten. This article analyzes the solution set to the (constrained) Diophantine equation that implements such symmetry, culminating in a conjecture on the number of solutions of the equation.