Close Enough?
Originally published at https://holdenweb.blogspot.com/2007/08/close-enough.html
I have long admired the formula often known as Euler's identity. It was probably known before Euler's time, but it is associated inextricably with his name because it is a special case of a more general formula, with π as the value of the bound variable. The identity asserts that
To me this is a thing of beauty and a joy forever, but I have long since given up trying to explain to other people why or how I perceive beauty in mathematics. Anyway I thought I would see how close my trusty laptop could get to emulating this mystic identity (it's amazing what I get up to when procrastinating), and naturally chose Python (though I believe the results would be just as disappointing in any other language). Here's what I got:
>>> math.e**(math.pi*-1j)
(-1-1.2246467991473532e-16j)
Definitely not quite the same mystical properties there, even though numerically quite close. No wonder I never liked applied mathematics!
