Could Archimedes have known this?
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From: Ludovicus on 10 May 2010 08:46 Could Archimedes have known this ? Limit of (Arc - cord) = (Tangent - arc) / 2 Because in that case he could have improved the calcul of Pi through: Limit of Arc = (2*cord + tangent) / 3. Using a polygon of 96 sides he obtained 3 + 10/71 with the cords, and 3 + 1/7 with the tangents. 3 + 10 / 71 < pi < 3 + 1 / 7. If he had taken C = (20 / 71 + 1 / 7) / 3 then: pi aprox. = 3 + C = 3.14151... Much better than the mean: 3.14185... This is a problem on History of Mathematics, not a question cast to tarnish Archimedes reputation. Ludovicus |