A Curiosity

Thoughts on the power series for  , which I found curious. Last week someone asked me a question about the Maclaurin series for  .  Finding the Maclaurin series is straightforward:   Substituting for x gives   We can find the radius and interval of convergence by using the Ratio test: This indicates that Maclaurin series…

What’s the “Best” Error Bound?

A know a lot of people like mathematics because there is only one answer, everything is exact. Alas, that’s not really the case. Numbers written as non-terminating decimals are not “exact;” they must be rounded or truncated somewhere. Even things like  and 5/17 may look “exact,” but if you ever had to measure something to…

π from Collisions

  One of my sons sent me the link to the videos below. They show a very unusual way to find the digits of π. The problems and its two solutions show the connections and the interplay between mathematics and physics. The quality of the illustrations and the verbal explanations are excellent. Here are the…