The latter is cliched because it incorporates an additional fundamental constant, pi. Who would have thought that the ratio of the circumference of a circle to the diameter when multiplied by the imaginary number and then exponentiated by another constant e would produce such a simple equation which also includes the multiplication identity and the addition identity? Yes, pi is chosen but it certainly encompasses the trigonometry and geometry (rotations, sinx, cosx, etc.).
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I think the actually remarkable equation is
The cliched "e^(i pi) + 1 = 0" is a fairly mundane consequence of the fact that pi was chosen to make this equation hold.The latter is cliched because it incorporates an additional fundamental constant, pi. Who would have thought that the ratio of the circumference of a circle to the diameter when multiplied by the imaginary number and then exponentiated by another constant e would produce such a simple equation which also includes the multiplication identity and the addition identity? Yes, pi is chosen but it certainly encompasses the trigonometry and geometry (rotations, sinx, cosx, etc.).
My point is that it is only fundamental because it leads to this equation!