Articles in the Mathematics category

1. How Are Numbers Built?

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

2. Doron’s Mathematical Amnesia

   Poor Doron has suffered a strange cognitive deficit. His language and speech skills have survived intact, but he has developed ‘selective mathematical amnesia’. He has forgotten much of high school mathematics—which for a person with a Master’s degree in engineering—is a rather tragic state of affairs. In fact, his knowledge of mathematics now resembles Emmental cheese—full of holes.

3. 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.

4. 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.

5. 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 \(2\pi\) radians for the angle of a full circle. \(\pi\) is forbidding, because it is not the convenient fractional fiction \(\frac{22}{7}\), 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.

6. Solving a Mathematics Olympiad problem

   During a casual tour of the Web, my attention was drawn to a problem that was stated so simply that it beckoned an attempt at a solution. It was purported to be from a Mathematical Olympiad, which raised its attractiveness index, as such problems are known to strenuously exercise the grey cells, while still retaining the charm of a sport. Only later did I find out that the problem I had written down had omitted an important constraint that made the problem all the more memorable. This is an account of my escapade into the land of mathematics in search of solution.

7. 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.