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I pull Jake aside and ask him something he might be a littleuncomfortable with."Jake, I don't want to pressure you into anything," I begin, "but thereis one aspect of my life I would like to share with you if you arewilling. It is entirely up to you, but I'd like to set up a double datefor us with Zach and his son."Jake seems a little hesitant, but he eventually agrees to the idea. Icall my boyfriend Zach and explain the situation to him. Zach has an 18year old son, Ian, who is pretty good friends with Jake. I wait as Zachtalks to Ian, and soon it is all set up. We say goodbye to my friendsand head home to get ready for our date. I instruct the babysitter totake the kids out to dinner, and the two of us spend the evening gettingready. The guys will be taking us out someplace nice, so Jake puts on ablack dress that ends just above the knee.When Zach and Ian arrive, they hand us each a bouquet of flowers and takeour arms as they lead us to their car. Ian seems quite taken. 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) = e^(-(i pi)^2/2). This is a compacta of symbols: e, i, pi, 2 and operations ^ / and.
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