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e. The complex expansion
Part 1 – The story of e Part 1: What is the Euler Series? When mathematicians talk about the “Euler Series,” they are referring to a beautiful infinite sum that allows us to calculate the exact value of $e$ without guessing. Originally, $e$ was defined by a limit $$ \lim_{n \to \infty} (1 + 1/n)^n $$ which is incredibly slow and tedious to calculate manually. Leonhard Euler solved this by…
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The Story of e.
The story of Euler’s Number. A passionate engineer discussing it to a colleague over coffee. In 1683, a Swiss mathematician named Jacob Bernoulli was trying to solve a problem that had absolutely nothing to do with the secrets of the universe. He was just thinking about money. Specifically, he was dreaming up a hypothetical, completely unrealistic bank account that paid 100% interest every…
So, the proof for how e (2.718…) is irrational is a long proof by contradiction that ends with ‘if e is rational, then there must be an integer between 0 and 1’. Makes sense. However, when they made that proof, they forgot to account for theta prime.
