Volume 57
, Issue 2

2021

Dear Reader, welcome to this issue of Parabola!

In this paper we look at musical scales, particularly equally tempered scales. Using continued fractions to approximate irrational numbers with optimal fractions, we develop an algorithm to classify musical scales with any number of notes to an octave based on their consonance.

In this note, we prove a useful general formula for limits involving two or more two square roots with quadratic radicands.

This article is an introduction to the topic of infinite products and a treatment of some of the very elegant results in this area of mathematics.

Let me introduce to you some necessary (but not sufficient) requirements for the existence of an odd perfect number.

The Nobel Prize-winning Black-Scholes model (BSM) for financial derivatives pricing is inextricably linked to the study of econophysics, where concepts from statistical physics are applied to economic systems.

In previous issues of Parabola, Randell Heyman showed that $c_n = (1 + \sqrt{2})^n + (1 - \sqrt{2})^n$ is an integer for each natural number $n$ and Xiaoyan Hu derived a recursion relation for this sequence. This article extends upon these results, by providing another method to arrive at the recursive relation.

What is the probability that the COVID-19 virus complete dissappears? An old and simple model is used to give an answer to this question.

Problems 1651–1660 are dedicated to the editor of Parabola, Thomas Britz, and his partner Ania, in celebration of the arrival of their twin sons Alexander and Benjamin.