The Most Beautiful Formula
6/27/202617 min
Joseph Bennish discusses Euler’s formula, which involves pi, e, the imagery i, 0 and 1, a beautiful formula that unites disparate types of numbers. We can think of e raised to an exponent as compound interest or a function with a remarkable property. We can extend the properties we expect from exponentials to imaginary numbers, which gives us periodicity instead of the usual steadily rising exponential growth.
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First 90 secondsCarol Jacobi· Host0:00
[upbeat music] Welcome to The Art of Mathematics. I'm Carol Jacobi, and joining us today, once again, is Joseph Benisz, professor emeritus from California State University, Long Beach. And I'm interested in what he has to say about Euler's formula, which is E to the pi I plus one equals zero. Welcome, Joe. It's great to have you back.
Joseph Bennish· Guest0:29
It's good to be back, Carol. Thanks for the invitation.
Carol Jacobi· Host0:32
One thing that I wanted to talk to you about is Euler's identity, which is, has always fascinated me, and apparently many other mathematicians. What is it, and what's so special about it?
Joseph Bennish· Guest0:46
It's a curious thing, Carol. So many mathematicians regard it as the most beautiful formula in all of mathematics, but it would be hard to say why they feel that way. In fact, I think I share that opinion. Combines five numbers, E, pi, I, one, and zero, which could be considered, I think I consider them, the most important constants in all of mathematics. So here you have a very simple formula which combines five very important numbers, very important constants. I don't think it goes too far to say the five most important constants in mathematics.
Carol Jacobi· Host1:25
What's interesting about it is they're from all different fields of mathematics.