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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 1268 molder 03-Oct-17 20:54
Re: David Kenworthy Cracking the Megalithic Code 935 DavidK 22-Dec-17 23:40
Re: David Kenworthy Cracking the Megalithic Code 743 magisterchessmutt 25-Dec-17 16:52
Re: David Kenworthy Cracking the Megalithic Code 587 magisterchessmutt 25-Dec-17 17:20
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Re: David Kenworthy Cracking the Megalithic Code 587 magisterchessmutt 28-Dec-17 02:37
Re: David Kenworthy Cracking the Megalithic Code 621 magisterchessmutt 28-Dec-17 05:35
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Re: David Kenworthy Cracking the Megalithic Code 492 DavidK 19-Jan-18 13:05
Re: David Kenworthy Cracking the Megalithic Code 550 molder 19-Jan-18 22:57
Re: David Kenworthy Cracking the Megalithic Code 485 DavidK 21-Jan-18 22:27
Re: David Kenworthy Cracking the Megalithic Code 511 molder 22-Jan-18 00:13
Re: David Kenworthy Cracking the Megalithic Code 499 DavidK 22-Jan-18 09:55
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Re: David Kenworthy Cracking the Megalithic Code 430 DavidK 22-Jan-18 12:30
Re: David Kenworthy Cracking the Megalithic Code 405 cloister 22-Jan-18 12:40
Re: David Kenworthy Cracking the Megalithic Code 428 DavidK 22-Jan-18 13:15
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Re: David Kenworthy Cracking the Megalithic Code 438 cloister 22-Jan-18 16:34
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Re: David Kenworthy Cracking the Megalithic Code 486 DavidK 17-Mar-18 17:30
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Re: Michell's Canon of Ancient Measure 610 magisterchessmutt 06-Jan-18 11:56
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Re: Extracts from another website 470 DavidK 24-Jan-18 09:59
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Re: David Kenworthy Cracking the Megalithic Code 466 DavidK 24-Jan-18 12:03
Re: David Kenworthy Cracking the Megalithic Code 423 DavidK 25-Jan-18 07:06
Re: David Kenworthy Cracking the Megalithic Code 408 molder 25-Jan-18 12:19
Re: David Kenworthy Cracking the Megalithic Code 417 molder 25-Jan-18 12:36
Re: David Kenworthy Cracking the Megalithic Code 468 DavidK 25-Jan-18 13:50
Re: David Kenworthy Cracking the Megalithic Code 410 DavidK 25-Jan-18 13:43
Re: David Kenworthy Cracking the Megalithic Code 459 DavidK 25-Jan-18 09:41
Re: David Kenworthy Cracking the Megalithic Code 416 DavidK 27-Jan-18 12:17
Re: David Kenworthy Cracking the Megalithic Code 542 rodz111 28-Jan-18 09:54
Re: David Kenworthy Cracking the Megalithic Code 410 DavidK 28-Jan-18 20:49
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Re: David Kenworthy Cracking the Megalithic Code 469 rodz111 29-Jan-18 16:38
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Re: David Kenworthy Cracking the Megalithic Code 439 rodz111 29-Jan-18 18:04
Re: David Kenworthy Cracking the Megalithic Code 430 molder 30-Jan-18 06:05
Re: David Kenworthy Cracking the Megalithic Code 438 rodz111 31-Jan-18 21:24
Re: David Kenworthy Cracking the Megalithic Code 426 molder 29-Jan-18 22:32
Re: David Kenworthy Cracking the Megalithic Code 434 DavidK 30-Jan-18 10:06
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Re: David Kenworthy Cracking the Megalithic Code 544 rodz111 30-Jan-18 18:11
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Re: David Kenworthy Cracking the Megalithic Code 247 DavidK 21-May-19 23:59
Re: David Kenworthy Cracking the Megalithic Code 100 magisterchessmutt 22-Dec-19 22:24
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