What is your name?. . . Bob. Fine. O.K. So it’s two hundred and fifty- seven dollars plus twenty-nine dollars for Federal Express?”
“Do you want my MasterCard? Look, it’s really imperative that I get my unit tomorrow. A.K., please, I really need my unit bad.” David hung up the telephone and sighed. “This is what has happened to a pure mathematician.” In the junk yard, his nest, his paper-lined oubliette, Gregory kicked off hi gentleman’s slippers, lay down on the bed, and predicted the future. He said “The gigaflop supercomputers of today are almost useless. What is needed is a teraflop machine. That’s a machine that can run at a trillion flops, a trillion floating-point operations per second, or roughly a thousand times as fast as Cray Y-MP8. One such design for teraflop machine, by Monty Denneau at I.B.M.
The square root of two is an irrational number. There is simply no way to represent any irrational number as the ratio of two whole numbers; it can’t be done. Hippasus of Metapontum supposedly made this discovery in the fifth century B.C., while travelling in a boat with some mathematicians who were followers of Pythagoras.
You can take the Leibniz series out a long distance—you can even dramatically speed up its movement toward pi by adding a few corrections to it—but no matter how far you take the Leibniz series, and no matter how many corrections you hammer into it, when you stop the operation and sum the terms, you will get anumber that is somewhere around pi but is not pi, and you will be damned if you can put your hands on pi.
In 1873, Georg Cantor, a Russian-born mathematician who was one of the towering intellectual figures of the nineteenth century, proved that the set of transcendental numbers is infinitely more extensive than the set of algebraic numbers. That is, finite algebra can’t find or describe most numbers. To put it another way, most numbers are infinitely long and non-repeating in any rational form of representation. In this respect, most numbers are like pi.
“Pi is a damned good fake of a random number,” Gregory said. “I just wish it were not as good a fake. It would make our lives a lot easier.”
Their methods were used for
At one point, it felt like the Chudnovsky brothers could find the last digit of Pi before I could reach the end of this article!
Is this the inspiration for the Darren Aronovsky film?
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