6 Nov 2008

The Babylonian Method for Approximating the Square Root of 2

by Corry Shores
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For \sqrt{2}:

1) Make a guess; even a bad one: 4

2) ½ (4 + 2/4) = 2.25

3) ½(2.25 + 2/2.25) = 1.56

4) Repeat, thereby obtaining: 1.42 , 1.41

1.412 ≈ 2

(from Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002)

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