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moe darklight
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Square Root Of 2 (from Hardy "Course Of Pure Mathematics")
I was surprised to find it in my local bookstore amidst math "cheat" books in the one-shelf math section (and the fact that it was the last copy left... ??).
Is he asking to simply carry out the calculation? Or is he asking to answer why this method works, because I have no clue for the latter... how did he get that formula?
Also, I've noticed that if the formula is carried out on m=[tex]\sqrt{2}[/tex], n=1; then the formula does not apply. Is this due to the irrationality of the number? (as in: the approximation would never actually reach [tex]\sqrt{2}[/tex], so it is always applicable)
I was surprised to find it in my local bookstore amidst math "cheat" books in the one-shelf math section (and the fact that it was the last copy left... ??).
Section 5, Example 3:
Show that if m/n is a close approximation to [tex]\sqrt{2}[/tex], then (m+2n)/(m+n) is a better one, and that errors in both cases are in opposite directions.
Is he asking to simply carry out the calculation? Or is he asking to answer why this method works, because I have no clue for the latter... how did he get that formula?
Also, I've noticed that if the formula is carried out on m=[tex]\sqrt{2}[/tex], n=1; then the formula does not apply. Is this due to the irrationality of the number? (as in: the approximation would never actually reach [tex]\sqrt{2}[/tex], so it is always applicable)
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