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IN MATLAB

The following method of computing \( \pi \) is due to Archimedes: 1. Let \( A=1 \) and \( N=6 \) 2. Repeat 10 times, say: Replace \( N \) by \( 2 N \) Replace \( A \) by \( \left.\left[2-\sqrt{(} 4-A^{2}\right)\right]^{1 / 2} \) Let \( L=N A / 2 \) Let \( U=L / \sqrt{1-A^{2} / 2} \) Let \( P=(U+L) / 2( \) estimate of \( \pi) \) Let \( E=(U-L) / 2 \) (estimate of error) Print \( N, P, E \)

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