3 papers
math.GR2015
A paradoxical decomposition of the real line
Shelley Kandola, Sam Vandervelde
In this paper we demonstrate how to partition the real number line into four subsets which may be reassembled, via "piecewise rigid functions" that preserve Lebesgue measure, into…
math.NT2006
The Mahler Measure of Parametrizable Polynomials
Sam Vandervelde
Our aim is to explain instances in which the value of the logarithmic Mahler measure of a polynomial can be written in an unexpectedly neat manner. To this end we examine polynomia…
math.NT2006
A Clean Approach to Rational Cubic Residues
Sam Vandervelde
In 1958 E. Lehmer found an explicit description of those primes p for which a given prime q is a cubic residue. In this paper we demonstrate that a similar result may be obtained f…