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Was this really about to happen? Had all those hot nights talking about this very scenario come down to this simple yes or no from me? Almost as if someone had taken over my body, I heard myself say, "I think it's time we got out of here and took Frank home with us."Tina smiled, almost unnoticeably to anyone but me. It was a naughty smile I had often seen while watching a porno with her or reading a really good "naughty wife" story in Penthouse Letters.Frank was back from the rest room, and I was already hailing our waitress. Soon we were in the parking lot, and I was giving Frank directions. He was having trouble remembering all the turns it would take to get to our house. Tina suggested that she ride with him. I agreed, then jumped in the car and hurried home. (The last I saw of Tina and Frank, they got caught at a traffic light.) At home, I raced all around, readying the bedroom for the adventure to come.Some 15 minutes later they finally arrived. As they walked in, Tina announced. It is very close and a repeating decimal fraction: 3.142857 142857 142857 …. Now look at |pi – 22/7| / pi. What we have is an error of 0.000402499 or, about 0.04% Very close. 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.
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