Every now and then I get impressed by mathematicians in books I read yet I have to face the reality and understand that I have no idea what they’re really saying. I’ve heard of this concepts, Euler’s Formula, a few times and they all romanticize it up the wazoo, I do have a book on mathematics and though I know all about the lead up, who Euler was, and the influence of the formula, I still have no idea how it exactly works. Would appreciate some hand holding.
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Euler was a very prolific mathematician who has a lot of things named after him so which “Euler’s formula” are you asking about?
Can you be more specific? Roughly half of all mathematics is named after Euler. Which kind of explains why he’s held in such high regard
The reason it’s romanticized in mathematics is because it’s a simple formula that contains all of the most useful numbers in mathematics: e, pi, 1 and 0.
The simple explanation of how the formula works is that ϴ tells the formula the angle to move around the unit circle. Setting ϴ equal to pi gives the result of moving half way around the circle, or -1.
Therefore e^i*pi +1 = 0 , giving rise to the famous formula
The proof of the formula is probably too complicated for eli5
Euler’s number is about exponential growth.
Pi is about circles.
The square root of negative one is the answer to the question “if you are at 0, one is to your right, and negative one is to your left, what number do you reach if you go up?”
Euler’s formula says that all of these numbers that seem to be involved in completely different areas of mathematics and aren’t remotely related, are in fact intimately related.
e^(i*pi) +1 = 0.
The why?
I cannot explain that better than wikipedia. https://en.wikipedia.org/wiki/Euler%27s_formula
The history section explains how they figured it out. If you do not understand calculus, the simple version is that e^(ix) = cos(x) + i*sin(x) and when you put pi in for x the right side is just -1.