Estimation quiz!
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08-08-2020, 05:01 PM
Post: #57
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RE: Estimation quiz!
(08-08-2020 07:35 AM)EdS2 Wrote: Albert: Pythogrean triples a,b,c = 5,12,13 had ∠A ≈ 22.6° L = pi*R * sec(22.5°) ≈ 20000*13/12 = 20000+10000/6 ≈ 21667 km --- This is equivalent to assuming √2 = 238/13² ≈ 1.4083 sec(22.5°) = 2/√(2+√2) ≈ 2/√(2+238/13²) = 2*13/√576 = 13/12 A better estimate for √2 is 239/13² ≈ 1.4142 (this is actually √2 rational convergent, after 99/70) sec(22.5°) ≈ 2*13/√577 = 13/12 / √(1+1/576) ≈ 13/12 * √(1-1/576) ≈ 13/12 * (1-1/1152) ≈ 1.0824 |
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