3blue1brown
@3blue1brown·8.4M subscribers·240 videos
What is Euler's formula actually saying? | Ep. 4 Lockdown live math
Posted
April 28, 2020
Views
1,663,831
Likes
33,657
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Engagement
2.15%
April 28, 2020
1,663,831
33,657
2,135
2.15%
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51:16Now PlayingWhat does it mean to compute e^{pi i}?
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Beautiful pictorial summary by @ThuyNganVu:
Not on the "homework" to show that exp(x + y) = exp(x) * exp(y). This gets a little more intricate if you start asking seriously about whether the series really converge, what they converge to, and how exactly you define a product with infinitely many terms. For anyone curious about the technical details, what you would want to show is that the Cauchy Product of the series for exp(x) and exp(y) converges to the product of the values exp(x) and exp(y) for any particular x and y. That requires the Merten's Theorem.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
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