Website review: Euler's Identity |Futility ...
jaumesol discovered this in Mathematics
•63 reviews since Jul 17, 2007
mathematics, eulers-identity, math
•futilitycloset.com/2007/07/15/eulers-identity...
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Reviews of this website
- gogodidi rated 8 weeks ago
- I'm not gonna bother checking if Tracer-Bullet's question was ever answered, I'll just do it here.
The solution to this "problem" is through eulers relation:
a*e^(i*b) = a( cos(b) + i * sin(b))
Where b is an angle in polar form
We know this as it can be observed on the argand diagram (still, you have to imagine what genius it took to see this relationship in the first place). The proof for this relationship was made some time in the 18th century, but we now have multiple proofs for it. (Wikipedia probably has one and if you're familier with calculus should be easy enough to comprehend)
e^(i*pi):
cos(pi) = -1
i * sin(pi) = i * 0 = 0
hence:
e^(i*pi) = -1 + 0*i = -1
This is taught (or if you weren't, good luck in college) in high school and is nothing new, but it is a sensational relationship.
If you're interested in the applications of this, you may want to look into fourier series, which can me simplified into exponential form using this relation. Fourier series have several applications, among others finding solutions to partial differential equations. That is but one of many applications of it, though.
Hope that answers your question Tracer. - I'm not gonna bother checking if Tracer-Bullet's question was ever answered, I'll just do it here.
avre rated 4 months ago- That's possible just in maths, to prove that something is true even if you don't know what it means and can't understand it either.
- JG-NUKE rated 5 months ago
- i should have studied
- 11saga11 rated 5 months ago
- Harvard mathematician Benjamin Peirce told a class, "It is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth."
- iggigic rated 5 months ago
- WOW..WOW..the square root of -1 is i the number used as a base for natural logarithems is e........and good old pi is related to circles. None of these 3 numbers seem related , but e to the pi times i power =-1
- Tracer-Bullet rated 5 months ago
- Is there more of an explanation? I'd like to see how we know it's true.
- stumbledvd rated 8 months ago
- I love math
- ngenie rated 8 months ago
- The miracles of math... take a bunch of seemingly unrelated numbers and combine them to make a wonderfully simple formula.
Though I'll have to agree with Vallam, XKCD said it better:
- The miracles of math... take a bunch of seemingly unrelated numbers and combine them to make a wonderfully simple formula.
