Category Archives: Math

The Golden Cut!

Today, I read an (old, but) interesting book on “Fibonacci Numbers” (only about 70 pages). It was mathematically intense most of the time, proving theorems and other boring stuff. But, the results were nice & fun to read. A few of my old questions were answered today, and it’s surprising that they were connected by Fibonacci numbers.

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Statistics of my professor…

I guess I’ve already told you about my aerodynamics professor when I talked about my newly found way of memorizing. But, that’s history. It happened during the last semester, it makes use of low speed flow. This time, it’s high speed!

So, today we had our usual aerodynamics class. As usual, I was reading my “Classical Mechanics” book (Well, I don’t feel comfortable taking notes during classes of these kind). Soon, three of us got bored. Our professor is well-known for his amazing habit of copy-pasting stuff (equations & derivations go to the blackboard, paragraphs & history spills outta his mouth, often with the question, “Right?”) – from books like “Fundamentals of Aerodynamics” (by J.D. Anderson – last sem) and “Gas Dynamics” (by E. Radhakrishnan – going on now).

Within a few minutes since the start of his class, we started observing the same “thing”, inferred his activity, smiled at one another, and converged on the same idea…

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Understanding Gradient and Divergence

I should’ve written this a while ago, when I understood the inner workings of this stuff. But well, I believe that it’s never late to teach something. So, here goes…

I wasn’t aware of these stuff until lately…

I rote-learned vector calculus during my second semester, when I was doing nothing but complaining all the time about the crappy system we have in our college. (ehm, you can always skip my history)

I had to swallow things like curl, divergence, gradient, and theorems from Gauss and Stokes’, etc. and loss-lessly vomit in the exams. That time, I wasn’t even aware of the elegance of these operations, nor did I understood the working of vectors (things which defined symmetry, and gave an ingenious touch to the physical laws).

When I first learned Electromagnetism, I was unable to see the physical significance of Maxwell equations (I’m a geek who loves to gather knowledge, provided that I’m really able to comprehend its physical significance quite satisfactorily). Moreover, as a terrific lover of Physics, I’ve always learned things (whatever that is!) conceptually.

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An elegant analysis of a summation…

Today, I’ve prepared myself to expound a math problem. And yeah, this is the first time I’m introducing math into my blog. Before we get into that, you gotta believe me that I’m no “big guy” in math. I have some unsaturated background in math, which (as far as I know) is good enough to “understand” my amateur Physics (quite satisfactorily). If Physics is sorcery, then math is um, totally wicked. Both are fun and exceedingly enjoyable. Well usually, I don’t spend much of my brain-time dwelling inside math, but I do often go around and read posts written by others.

Every month, one or two posts loom into the crowd and attracts my mind in some way. Within hours, they become a vote-magnet. I’m way too sure that that’s due to the modesty of the answerer, especially the elegance of the solution he has brought upfront. So, I thought I could selectively bring those here, where I can write a bit more about it. No, I’m not just copy-pasting stuff. Like I said, I’ll blog about those, only if I feel like having some of my own enhancements to the existing solution.

So, math posts are gonna be a part of my future posts. Don’t worry, they won’t be complicated at all. They’d be very easy, just like the squeeze of a toothpaste. And mind you, there exist numerous solutions to a specific problem, because it’s math. It’s crazy. But like I said, these are somewhat attractive, in the sense that an elegant generalization comes out at last.

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