How to compute Pi in Calculus Style
Last week we dipped our toes into the strange world of limits. We have seen in last post that many discret particles interacting with each other lead to a continuous phenomenon like diffusion! This week, we show how you can actually compute pi using calculus. Before doing so, we learn about one of the crown jewels of Calculus: Taylor series. It is the mathematical equivalent of taking apart a function’s DNA and rebuilding it out of simple pieces. This is a natural follow-up on the series of last week. First of all, we need to ask ourselves one big question. Today, we use calculus to find the value of pi. What is the Taylor series? In calculus, Taylor’s theorem gives an approximation of a $n$-times differentiable function around a given point $a$ by a polynomial of degree $n$. This is the n th order Taylor polynomial. For a smooth function, we can consider the polynomial for an arbitrary degree. In that case, the Taylor polynomial is the truncation at t...









Comments
Post a Comment