Roar. Bears, Pi Day is coming, and I just happened to spend a day reading a book on simulations with Python for calculus and statistics topics, something that troubled a lot of bears before they became math heroes. A large portion of the chapter was coding an equation in Python and plugging in different numbers, which didn't appeal to me as much, until in one problem where this equation caught my eye:
The section was about estimating the time it takes for sunlight to reach the earth. The denominator was a term, something I recall from a book I read last year for Pi Day. I then asked AI what this was, and it turned out this was the polar equation of an ellipse, being the semi-major axis and being the eccentricity.
Drawn by this equation, I continued with the book. Then in the very last section, it discussed Euler's Method and Runge-Kutta methods for solving differential equations. Both were new to me, until I realised they weren't. Both methods estimate the solution with two things at a known point: the value and the derivative (i.e., how things are changing at that point), and it was something the book from last year did to solve the Kepler's Equation.
The book for last year's Pi Day was very difficult. It required tough maths from various subjects including aerodynamics, astrophysics, electromagnetism and of course calculus. While reading the Python simulation book this year, the scene of me sitting at a slightly lit desk, copying down equations and trying to figure out what they mean immediately came back to me. Unfortunately that year, before I could finish the book, a new project idea came up and I worked on that instead.
In retrospect, I often think, how capable could I have been if I had finished that book? Would I learn all the calculus I needed along the way to get to that level? Would I be able to do the kind of work the book described, which is "too scary", but also too cool, to some of you?
I currently read about reinforcement learning (RL) every Monday and Tuesday. The question this time is, if we could understand all 14 algorithms implemented in the Stable Baselines 3 library, and more to come in the future, how capable would we be? Will we be able to train a robot dog ourselves like in the many RL papers? Or will we be able to do something else cute and capable that will define ourselves?
So for this year's Pi Day, and the Pi Days from now on, I will not be making things using my existing knowledge like showing off, but reading new things and making things with those instead. I hope this gives you some inspiration for what you would do for this year's Pi Day celebration.