The mathematician Leonhard Euler was born in this month 309 years ago. As he contributed in important ways to our understanding of some aspects of music, I thought I would use music to help understand some aspects of mathematics. The constant e, named after Euler, is one of the most important numbers in mathematics. One way of approximating e can be demonstrated using musical intervals:
At the least, this approach offers one answer to the question of when an approximation is good enough: it's good enough when you can't hear the difference between it and a better approximation.