Egyptian Equivalent of PiDate: 05/15/2003 at 22:09:15 From: Willabee Subject: Pi The ancient Egyptians used the formula (d-d/9)^2 for the area of a circle with diameter d. What value for pi does the formula yield? Date: 05/16/2003 at 12:54:43 From: Doctor Dotty Subject: Re: Pi Hi Willabee, Thanks for the question, We currently use the formula: a = Pi * r^2 Where r is the radius, and a is the area of the circle. We are told the Ancient Egyptians used: a = (d - d/9)^2 Let's multiply out the brackets: a = (d - d/9)(d - d/9) a = (d)(d) - (d/9)(d) - (d/9)(d) + (d/9)(d/9) d^2 d^2 d^2 a = d^2 - --- - --- + --- 9 9 81 2d^2 d^2 a = d^2 - ---- + --- 9 81 Now let's look again at our present formula: a = Pi * r^2 It is in terms of the radius (r), and the Egyptian one is in terms of the diameter (d). We know that 2r = d (write back if you would like this explained), so we can rewrite the Egyptian equation as: 2(2r)^2 (2r)^2 a = (2r)^2 - ------- + ------ 9 81 8r^2 4r^2 a = 4r^2 - ---- + ---- 9 81 Common denominate: 4r^2 8r^2 4r^2 a = ---- - ---- + ---- 1 9 81 324r^2 72r^2 4r^2 a = ------ - ----- + ---- 81 81 81 Can you collect the terms, and find what the Egyptian equivalent of Pi is from here? Write back if I can be of any more help - on this or anything else. - Doctor Dotty, The Math Forum http://mathforum.org/dr.math/ |
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