Assignment 1 Takeaway

 Reflections and takeaway from Assignment 1:

Digging deeper into ancient methods of computing trigonometry is quite interesting. I am not sure if others have the same lingering questions when they have been exposed to topics as such trig functions and exponential function in high school, but I personally do and have no received a good answer up until I took complex analysis. The question is how would I explain sin(sqrt(pi))? Or 2^e. It seems like on the grade 12 level, in pre-Calculus and Calculus, we should just accept that exponential and trigonometric functions are nice and smooth and defined everywhere, but HOW? We can reason about rational exponents, but what about irrational? And the same goes for trig functions. (It's cool that complex analysis gives the answer as Taylor series, and I think we might be too comfortable consulting our calculators for answers. The question is then how do calculators calculate different functions with ease and speed? That's a whole different field)

I like the way the assignment has brought us to the ancient methods, where we get to see how these concepts were discovered and built upon by mathematicians later. It is not a process that happens in a day or a term, and giving that perspective I think helps with learning difficult concepts. The Babylonians started out with tables for right angle triangle, and tables for taking square roots, multiplication and division, and I think that is quite inspiring, from a teaching perspective. We can start with simpler problems, make tablets, find patterns, and use methods to approximate with reasonable accuracy, and I think too often we are simply being presented with the beautiful work of precision developed over the course of history without seeing all the effort and attempts it took to get to what we see today.