

Scott Cram Inner circle 2677 Posts 
Recently posted at Futility Closet:
Create two columns, one starting with the numbers 12 and 18 and the other with 5 and 5. Continue each column, deriving each new number by adding the two that precede it: 12...........5...........12 / 5 = 2.40000 18...........5...........18 / 5 = 3.60000 30...........10...........30 / 10 = 3.00000 48...........15...........48 / 15 = 3.20000 78...........25...........78 / 25 = 3.12000 126...........40...........126 / 40 = 3.15000 204...........65...........204 / 65 = 3.13846 330...........105...........330 / 105 = 3.1486 534...........170...........534 / 170 = 3.14118 864...........275...........864 / 275 = 3.14182 1398...........445...........1398 / 445 = 3.14157 In the Journal of Recreational Mathematics, James Davis writes, “Forming successive pairs with adjoining numbers from each column one finds the ratio of the two numbers in each pair converges to Pi!” How can this be? “The alert reader will suspect there is a trick in this method, as I did when Pi first presented it to me. The labor of several hours of computation coupled with trial and error produced half of the secret of the method. It is obviously based somehow on the fact that Phi (the golden mean, which equals (1 + (sqrt 5))/2, can be closely approximated by the nifty pseudo equation below:” 1.2 x Phi^2 = Pi “Can the reader decipher Pi’s technique for making herself with Phi?” 
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