Blogs

1. The Wonder That Is Pi

   This is a sequel to the blog “The Pi of Archimedes”. We look at π as a number rather than the ratio of two lengths, and try to unravel how and why it is ubiquitous in mathematics.

2. Same Action: Four Castes

   This blog was originally penned on 24 October 2008. It is one among many dozen blogs that have not been released publicly on the Web. I will be gradually refreshing and releasing all those unpublished blogs on this website. They are generally short and tightly focused pieces of writing, readable in a few minutes. Where possible, I have retained the original contextual immediacy and topical relevance. I have used the IAST transliteration scheme for the Sanskrit terms; consult the link for the correct pronunciation. The upshot of this blog is that caste is spiritual in nature, and that all individuals may exhibit all four castes at different times—according to attitude to action—regardless of birth or occupation.

3. The Pi of Archimedes

   This blog—and its companion, The Wonder That Is Pi—began life in 2004, as part of a series of lectures I delivered to some very bright first-year engineering students at an Australian university. The number π (pronounced ‘pie’) has been recognized from time immemorial because its physical significance can be grasped easily: it is the ratio of the circumference of a circle to its diameter. But who would have thought that such an innocent ratio would exercise such endless fascination because of the complexities it enfolds? Not surprisingly, some high school students I met recently wanted to know more about π and how it got its unusual value of ²²⁄₇. Accordingly, I have substantially recast and refreshed my original presentation to better accord with the form and substance of a blog. The online references have also been updated to keep up with a rapidly changing Web. My original intention was to write a single blog on π. But because I did not want it to become yet another overly long slog, I have decided to divide the material into two parts.

4. From Calculus to Analysis: Limits

   At high school you were taught how to integrate and differentiate. You were exposed to all sorts of tricks and special techniques—such as the chain rule for differentiation, and integration by parts for integration. If you revelled in mastering and applying such techniques, you might find that what succeeds high school calculus, is a horse of an entirely different colour, called analysis, at university.

5. How Are Numbers Built?

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

6. 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.

7. Using Typst for Letters

   So, I was eager with anticipation when I first stumbled upon mention of Typst [1,2] which exhorted “Compose papers/theses faster”. The Typst home page claims it is a “A new markup-based typesetting system that is powerful and easy to learn.” Piqued by these promising assertions, I decided to take the plunge with Typst for the specific but express purpose of writing letters. I have chronicled my experiences here.

8. Euler Two with Julia

   The Julia programming language is refreshingly adaptive in its syntax and allows the programmer to solve a problem in very many ways. In the case of Euler Project Problem 2, I got into trouble, mostly because I was running foul of doing things the “right way”. The language gently nudges one to think again before coding. It coaxes rather than coerces the programmer to adopt efficient and safe coding practices. The existence of a knowledgeable user-community who were ready to help, and who could illuminate the problem from different angles, made learning Julia enjoyable, educational, and enriching. It is a language that I will spend time learning properly, and use in the future.

9. The Most Scary Experience

   My redoubtable friend Solus “Sol” Simkin wandered into my office late one afternoon and asked me, “What is the most scary experience for a human being? I thought but for an instant as I replied, almost reflexively,”Death. What else? Or a close shave with death.”

10. A Foray into Rust: Euler One

    Rust is the emerging programming language. I decided to start learning Rust by solving Euler Project One. This is a chronicle of my first efforts, including false starts, errors, backtracks, etc.