4 ms·
i wish someone had explained this to me about 15 years ago. i had sought, and settled on the unsatisfying explanation that it is a conventional notation with us
by vain 15y ago
i wish someone had explained this to me about 15 years ago. i had sought, and settled on the unsatisfying explanation that it is a conventional notation with useful ways to do coordinate geometry. non essential, but a way of doing it. though i have looked at euler's identity with awe, it's mostly been a mystical sort of awe.
I hate to admit it but i had started using a line of argument to certain theist friends, that if god helps you, as a concept, no need to be bothered, think no more of it than a concept such as the the mathematical concept of i, its a number that does not exist but has real consequences. now I feel stupid for doubting the existence of i.
I keep trying to relearn my fundamentals, and this article does that beautifully. i would otherwise have died a disbeliever.
- AndrewMoffat 15y ago> though i have looked at euler's identity with awe, it's mostly been a mystical sort of awe. betterexplained also has a fantastic visual explanation of euler's identity: http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ http://betterexplained.com/articles/intuitive-understanding-...
- kalid 15y agoThanks so much for helping share this! :) My goal is to get all these concepts out of awe (which I had too) into a real sense of "Ah, I get it!". It doesn't help anyone to memorize incantations. Two other insights I love: * e as continuous growth: http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/ http://betterexplained.com/articles/an-intuitive-guide-to-ex... * radians as the perspective of the mover: http://betterexplained.com/articles/intuitive-guide-to-angles-degrees-and-radians/ http://betterexplained.com/articles/intuitive-guide-to-angle... I realized that I didn't really get what e and radians were about -- I memorized them, but I wasn't comfortable. Once you have the right analogies, Euler's formula starts making sense (without resorting to "Oh, take the Taylor series expansion of each and see how they match up", which is essentially an incantation).
- AndrewMoffat 15y agoNo problem, I'm happy to share something that genuinely helped me. I love what you're doing, please keep doing it :)