Similarly, for the Euler-Mascheroni constant gamma, 0.577215665…, we see that Sqrt(3)/3 is 0.577350269… and the error is |gamma – 1/Sqrt(3)| / gamma = 0.000233196, or about 0.02% or thereabouts. Taunus Trumbo: And so what? These are transcendental numbers being approximated by rational numbers or algebraic irrationals (surds). Faustus Mortal: They establish a numerical criterion. For anything in the physical universe, a good approximation must have an error less than these. Taunus Trumbo: And this proves? Faustus Mortal: The error in A+1/A+B and e^(pi^2/2) is 0.000000146 or 0.00001%. Even the absolute error is small, 0.000020. Taunus Trumbo: This is a remarkable coincidence, but little more. Faustus Mortal: No. It is exact and the connecting number comes from f(x) = Exp(-x^2/2) where x is the imaginary number i*pi. Written out in expanded form we get f(i pi) = e^(-(i pi)^2/2). This is a compacta of symbols: e, i, pi, 2 and operations ^ / and so on. Remember its cousin e^(i*pi). "Carolyn said, "Weddings are emotional times. Weddings and holidays are the worse for loneliness. Maybe I would have felt differently, if I had felt that I had missed something before I got married; but I didn't. Maybe Mary and Dorothy felt they have." I don't know what it was. I guess I don't understand women. I'm not much lady's man. I know I'm really going to miss you when I go to school; and not just us making love." Me too, but we aren't going there. You would hate the New York social scene and I want to be a part of it."I nodded. I kissed her and we made love; nice and slow with a lot of feeling.As we cuddled, Carolyn said, "I think women know what they are doing. I don't think men fool them. You are a very handsome young man. You were handsome before you shaped up your body; now you are really something. You won't have any problems attracting women. You will learn to read their signals."If you had said you would go with me, I would have been very happy to take you to Alabama.
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