Wait! There's an improved version:    • Euler's formula with introductory gro...  
Also, for the calculus-savvy, you'll prefer this one:    • e^(iπ) in 3.14 minutes, using dynamic...  
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The enigmatic equation e^{pi i} = -1 is usually explained using Taylor's formula during a calculus class. This video offers a different perspective, which involves thinking about numbers as actions, and about e^x as something which turns one action into another.

For more information on viewing exponential functions in this new light, check out this article: http://goo.gl/LPyc4R

Music: "Wyoming 307" by Time For Three, http://www.tf3.com/