Re:BetterExplained: Math Lessons That Explain Concepts
by ThrustVectoring on Tuesday December 22, 2015 @01:07PM
(#10779250)
Euler's Identity is often explained in terms of mysterious language as well. Like, e^i*pi = -1 makes a lot more sense when you consider the exponential function as "proportional growth", i as "sideways", and pi as "halfway around a circle" - all Euler's Identity does is rephrase "going halfway around a circle" in terms of continuous and proportional sideways growth.
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Re:BetterExplained: Math Lessons That Explain Concepts
by kalid on Tuesday December 22, 2015 @01:47PM
(#10779494)
Exactly! I hate the Taylor Series explanation of Euler's formula. "Oh, just take the most analytic definitions of e^x, sin(x), cos(x), mix-n-match, and it works!" All symbols, no intuition.
If we see each concept individually (continuous growth + rotation) we can deduce that we get something like "continuous rotation" or a circular orbit.
And if we use a complex number (a + bi, not purely imaginary i) we get a spiral pattern. Euler's Formula becomes "obvious" dare I say ("obvious after the greatest mathematician figured it out for us".)