0 like 0 dislike
0 like 0 dislike
Today I learned how to derive Euler's identity...

11 Answers

0 like 0 dislike
0 like 0 dislike
Congratulations! Today is also a great day for me, i've learned the generalized stokes' theorem proof. Understanding those cool theorems is what makes me love math
0 like 0 dislike
0 like 0 dislike
Congratulations! Have a happy seal. Imagine it pushed its way through the ice and now it enjoys the sun on its face, just like you pushed through difficulty and self-doubt to enjoy some of the secret beauty of our universe.
0 like 0 dislike
0 like 0 dislike
My favorite proofs of trancendental identies these days come down to the fact that solutions of linear differential equations with constant coefficients can be expressed in terms of a basis.

Since sine and cosine satisfy f’’=-f, then any solution of that differential equation can be written as f(t)=a cos(t)+ b sin(t). Since e^it is also a solution:

e^it = a cos(t)+b sin(t)

taking the derivative we also have

ie^it = -a sin(t)+b cos(t)

and setting t=0 in both equations says

a = 1, b = i

as required.
0 like 0 dislike
0 like 0 dislike
I heard someone stole Euler's identity and opened a bunch of credit cards.  Turns out his Social Security number is the third Mersenne composite.
0 like 0 dislike
0 like 0 dislike
Love that for you!
0 like 0 dislike
0 like 0 dislike
Really bad joke based on the title alone tho..


"Ya just go and as him, about his identity".
0 like 0 dislike
0 like 0 dislike
Yeah!  Just don't drink and derive.
by
0 like 0 dislike
0 like 0 dislike
What are your starting assumptions?
by
0 like 0 dislike
0 like 0 dislike
Oh man. I barely graduated high school, but always excelled at math. During Covid quarantine I started watching math tutorials on YouTube. I somehow intuitively gained an understanding of Euler's identity. I can't believe that amazing little expression holds so much information.
0 like 0 dislike
0 like 0 dislike
Don't tell anyone: it's Leonhard.

Related questions

0 like 0 dislike
0 like 0 dislike
2 answers
a_dalgleish asked Jun 21
Contributing to the right math area, If all areas are equally curious
a_dalgleish asked Jun 21
0 like 0 dislike
0 like 0 dislike
5 answers
BrianDenver7 asked Jun 21
Is there a nice way to recast riemannian geometry in terms of principal bundles?
BrianDenver7 asked Jun 21
0 like 0 dislike
0 like 0 dislike
4 answers
hat_films asked Jun 21
How many AMS 2020 subject classifications to list?
hat_films asked Jun 21
0 like 0 dislike
0 like 0 dislike
14 answers
hiribarren2 asked Jun 21
Topics appropriate to teach high school students
hiribarren2 asked Jun 21
0 like 0 dislike
0 like 0 dislike
2 answers
ConradDubai asked Jun 21
How to “topologize” the fundamental group: a primer
ConradDubai asked Jun 21

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!