Articles tagged with “Mathematical Musings”

1. How Are Numbers Built?

   Decimals and continued fractions are two different ways to represent numbers succinctly, with complementary strengths.

2. Varieties of Multiplication

   I want to look at some of the varieties of multiplication that mathematicians have developed over time. It is a survey that will serve as a pinhole through which we can view how a single, simple mathematical idea has been expanded and elaborated into uses far beyond its historical moorings.

3. The Two Most Important Numbers: Zero and One

   The unique properties of the numbers zero and one make them mathematically interesting and indispensable. In this slow-paced stroll though the ideas streaming out of these two numbers, we uncover well-known as well as relatively obscure facts about them. It is hoped that in the process we may discover how they cement together disparate areas of Mathematics.

4. A tale of two measures: degrees and radians

   The transition from degrees to radians is often the most traumatic mathematical change that the student has to endure when moving from elementary to intermediate mathematics. The simplicity of 360° seems so much more welcoming than the equivalent of 2⁢𝜋 radians for the angle of a full circle. 𝜋 is forbidding, because it is not the convenient fractional fiction 227, but rather a number which is both transcendental and irrational and therefore, somewhat “untidy”. Surely this tradeoff between simplicity and complexity must have been worth it, or it would not have been so ordained. Here we attempt to fathom the method in the madness.

5. Eigenvalues and Eigenvectors—Why are they important?

   A university academic friend of mine recently remarked that it was not easy to motivate students to study eigenvalues and eigenvectors, let alone appreciate their importance: the subject itself was abstract, and the applications tended to be domain-specific and somewhat arcane.