Euler's Formula and Sine Wave
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- čas přidán 30. 08. 2019
- An animation explaining the geometric intuition behind the relation between Euler's Formula and Sine wave.
Acknowledgements:
-- Soundtrack:
Music from CZcams Audio Library
Music(Birds Of Flight) provided by : / animal liberation orch...
Animations:
--github.com/TheRookieNerd/Mani...
Thanks to:
github.com/3b1b/manim
Created by Grant Sanderson:
www.3blue1brown.com/
czcams.com/channels/YO_.html...
Wow.....an excellent use of manim. Keep going guyss.
Glad you liked it :)
Wonderful !
I think we can get different frequencies of the sinosoid depending on how fast we move the origin towards right (keeping the rate with which theta changes to be constant). The faster it moves the sine wave gets more stretched out or a lower frequency and vice versa.
Brilliant explanation...🔥🔥🔥
Loved it, man....!
Expert explanation 💓
beautiful
Very nice.
I didn't bel. in Your Irrelev. E Major Melody?!
This is very nice. :) The only thing is that I'm not a big fan of the flashing.
Sharing with my students.
Can someone help me make sure I understand correctly?
1. The sum of Z1 and Z2 give you a resultant vector Z3 (yellow line)
2. As theta decreases for Z1 and increases for Z2, the resultant vector will always remain parallel to the imaginary axis and over time draw out the plot for Sin(theta).
Also, if e^iθ = cos(θ) + isin(θ), I assume the cos(θ) represents the real axis and the isin(θ) represents the imaginary?
Yes you are right.
Infact, the initial card showing equation must contain "i" on the RHS.
In 0:16 you depict the complex plane where i (=sqrg(-1)) is depicted equal in length to the real unit 1. Can you elaborate on that? Is sqrt(-1)=1?
Since I've Iabelled the axis as imaginary, I have not added "i". So It's an imaginary unit.
@@TheRookieNerdsReally now? Is that the best answer you can think?