Before the days of Calculus, one Pierre de Fermat wanted to find the area under the function f(x)=x^n. This problem we now call "integration" was then called "quadrature" or "squaring". Fermat was able to square every function f(x)=x^n for any rational n except for one case: n=-1 (that is, the hyperbola). It turns out that this unique nature of the hyperbola was tied to logarithms and Euler's number e. But why? Why does the area under the hyperbola have anything to do with logarithms or e?

Other resources
e: The Story of a Number by Eli Maor
https://www.amazon.com/Story-Number-P...

Images
https://upload.wikimedia.org/wikipedi...

Music
https://patriciataxxon.bandcamp.com/a...
Starboard by Patricia Taxxon