Is Pi more than just a ratio for circles? Is there a easy way to understand the universality of Pi?
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There was a very influential mathematician, named [Euler](https://en.wikipedia.org/wiki/Leonhard_Euler), that helped write down much of the fundamentals that we use in modern calculus. One of his contributions was using *i* for the imaginary numbers, and he was also the guy that started actually using pi (the letter) to represent pi (the number).
In his work, he used circles to simplify many of the complex parts of imaginary numbers. This allowed him to use functions that work with circles (sine, cosine, tangent) to relate the two different types of numbers, even if it required him to use pi all over the place. It’s how we know that 3 numbers that are either irrational or imaginary combine into -1: [e^(pi*i)+1=0](https://en.wikipedia.org/wiki/Euler%27s_identity). Because it was so effective, the formulas he came up with are still in use even when people aren’t using circles or imaginary numbers. You see this as pi being everywhere without a circle, but back in the day he needed the circle to come first.
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