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Hi David

That solution is refering to the ancient problem of squaring the circle and refers to a square with an area equal to that of the circle.

The solution given " If we take this solution as a general formula, then in modern notation we obtain the “formula” for the area A of a circle of diameter d as: A = d−d 9 2 = 64 81 d2. From this we deduce (since A = π d2/4) that the ancient Egyptians implicitly used the value π = 256/81 = (4/3)4 = 3.160493827..."

However there are 2 questions in this problem. 1. to find a square equal in area to that of the circle and 2. to find a square with perimeter equal to the circumference. Many think 1 square solves both questions however not so.

By the way it's not possible to do this with the exact value for pi and Rind 50 is using 3.1604.

I first published one solution on this in 1995.

For example your number 897.6 has a diameter of 284.00625 using the Egyptian value for pi.


If you wanted to 'square the circle' using the Egyptian value for pi 3.1604 then simply do this.

Take the number 897.6 make the diameter of a circle 284.00625 then divide it by construction into 9 even spaces / 9 = 31.55625 then measure to the 8th space.

31.55625 x 8 = 252.45 this then is the side of a square the area of which equals that of the circle using the Egyptian value for pi 3.1604 63731.00251 square feet

The diameter / 2 and squared and multiplied by 3.1604 or 284.00625 / 2 = 142.003125

142.003125 squared = 20,164.88751 x 3.160493827 = 63731.00251 same number arrived at by simply dividing by 9 and multiplying by 8 then squaring.

The next problem is to find a square equal in perimeter to that of the circles circumference.

Your number as diameter 284.00625

Begin where we left off and repeat process 252.45 / 9 = 28.05 x 8 = 224.4 this then is the side of a square the perimeter of which equals that of the circle. 224.4 x 4 = 897.6 or 284.00625 x 3.16049... = 897.6

The Egyptians were indeed squaring a circle and interesting how your number 897.6 worked out so neatly with diameter 284.00625. Hope I havnt made a mistake.

Jim

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Re: David Kenworthy Cracking the Megalithic Code 410 magisterchessmutt 25-Dec-17 16:52
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Re: David Kenworthy Cracking the Megalithic Code 351 magisterchessmutt 28-Dec-17 05:35
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Re: David Kenworthy Cracking the Megalithic Code 264 DavidK 21-Jan-18 22:27
Re: David Kenworthy Cracking the Megalithic Code 269 molder 22-Jan-18 00:13
Re: David Kenworthy Cracking the Megalithic Code 275 DavidK 22-Jan-18 09:55
Re: David Kenworthy Cracking the Megalithic Code 221 cloister 22-Jan-18 11:01
Re: David Kenworthy Cracking the Megalithic Code 208 DavidK 22-Jan-18 12:30
Re: David Kenworthy Cracking the Megalithic Code 195 cloister 22-Jan-18 12:40
Re: David Kenworthy Cracking the Megalithic Code 216 DavidK 22-Jan-18 13:15
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Re: David Kenworthy Cracking the Megalithic Code 212 cloister 22-Jan-18 16:34
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Re: David Kenworthy Cracking the Megalithic Code 239 DavidK 17-Mar-18 17:30
Re: David Kenworthy Cracking the Megalithic Code 423 DavidK 03-Jan-18 23:58
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Re: Michell's Canon of Ancient Measure 248 molder 06-Jan-18 01:18
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Re: Michell's Canon of Ancient Measure 285 DavidK 07-Jan-18 11:14
Re: Michell's Canon of Ancient Measure 302 DavidK 10-Jan-18 14:23
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Re: David Kenworthy Cracking the Megalithic Code 219 DavidK 19-Jan-18 12:47
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Re: Extracts from another website 272 DavidK 23-Jan-18 10:41
Re: Extracts from another website 220 molder 23-Jan-18 12:10
Re: Extracts from another website 264 cloister 23-Jan-18 14:05
Re: Extracts from another website 234 molder 23-Jan-18 21:52
Re: Extracts from another website 249 DavidK 24-Jan-18 09:59
Re: Extracts from another website 164 molder 24-Jan-18 11:39
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Re: Extracts from another website 227 DavidK 24-Jan-18 21:12
Re: David Kenworthy Cracking the Megalithic Code 262 DavidK 24-Jan-18 12:03
Re: David Kenworthy Cracking the Megalithic Code 204 DavidK 25-Jan-18 07:06
Re: David Kenworthy Cracking the Megalithic Code 200 molder 25-Jan-18 12:19
Re: David Kenworthy Cracking the Megalithic Code 202 molder 25-Jan-18 12:36
Re: David Kenworthy Cracking the Megalithic Code 262 DavidK 25-Jan-18 13:50
Re: David Kenworthy Cracking the Megalithic Code 204 DavidK 25-Jan-18 13:43
Re: David Kenworthy Cracking the Megalithic Code 237 DavidK 25-Jan-18 09:41
Re: David Kenworthy Cracking the Megalithic Code 198 DavidK 27-Jan-18 12:17
Re: David Kenworthy Cracking the Megalithic Code 273 rodz111 28-Jan-18 09:54
Re: David Kenworthy Cracking the Megalithic Code 200 DavidK 28-Jan-18 20:49
Re: The Saros 272 molder 28-Jan-18 23:13
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Re: David Kenworthy Cracking the Megalithic Code 223 rodz111 29-Jan-18 16:38
Re: David Kenworthy Cracking the Megalithic Code 232 DavidK 29-Jan-18 17:07
Re: David Kenworthy Cracking the Megalithic Code 222 rodz111 29-Jan-18 18:04
Re: David Kenworthy Cracking the Megalithic Code 221 molder 30-Jan-18 06:05
Re: David Kenworthy Cracking the Megalithic Code 212 rodz111 31-Jan-18 21:24
Re: David Kenworthy Cracking the Megalithic Code 210 molder 29-Jan-18 22:32
Re: David Kenworthy Cracking the Megalithic Code 215 DavidK 30-Jan-18 10:06
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Re: David Kenworthy Cracking the Megalithic Code 306 rodz111 30-Jan-18 18:11
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