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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 number i*pi. Written out in expanded form we get f(i pi). I started recording just as Wendy came into the room and stripped down to her panties and bra. She was standing right in front of the window and I saw the three men rush over to see her. She went into the bathroom and closed the door. I could hear the shower start and realized they were missing the show with the door closed. I got up and walked into our bedroom, I stood in front of the window and looked out. I wondered if they all hid but I could not tell because it was too dark for me to see them. I then opened the bathroom door and asked, "Do you want to watch some TV before we go to bed?" She yelled back over the sound of the shower, "Yes, for a little while." I walked away leaving the bathroom door wide open. The guys outside now had a direct view of my wife inside the glass shower. I turned on our TV, which sat on a dresser in front of the bed and turned off the bedroom light. I returned to my office and on my computer I could see Wendy showering and the group of men outside.
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