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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 1159 molder 03-Oct-17 20:54
Re: David Kenworthy Cracking the Megalithic Code 876 DavidK 22-Dec-17 23:40
Re: David Kenworthy Cracking the Megalithic Code 671 magisterchessmutt 25-Dec-17 16:52
Re: David Kenworthy Cracking the Megalithic Code 532 magisterchessmutt 25-Dec-17 17:20
Re: David Kenworthy Cracking the Megalithic Code 567 DavidK 27-Dec-17 16:42
Re: David Kenworthy Cracking the Megalithic Code 514 magisterchessmutt 28-Dec-17 02:37
Re: David Kenworthy Cracking the Megalithic Code 549 magisterchessmutt 28-Dec-17 05:35
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Re: David Kenworthy Cracking the Megalithic Code 433 DavidK 19-Jan-18 13:05
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Re: David Kenworthy Cracking the Megalithic Code 441 DavidK 21-Jan-18 22:27
Re: David Kenworthy Cracking the Megalithic Code 447 molder 22-Jan-18 00:13
Re: David Kenworthy Cracking the Megalithic Code 445 DavidK 22-Jan-18 09:55
Re: David Kenworthy Cracking the Megalithic Code 385 cloister 22-Jan-18 11:01
Re: David Kenworthy Cracking the Megalithic Code 379 DavidK 22-Jan-18 12:30
Re: David Kenworthy Cracking the Megalithic Code 363 cloister 22-Jan-18 12:40
Re: David Kenworthy Cracking the Megalithic Code 387 DavidK 22-Jan-18 13:15
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Re: David Kenworthy Cracking the Megalithic Code 385 cloister 22-Jan-18 16:34
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Re: David Kenworthy Cracking the Megalithic Code 428 DavidK 17-Mar-18 17:30
Re: David Kenworthy Cracking the Megalithic Code 620 DavidK 03-Jan-18 23:58
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Re: Michell's Canon of Ancient Measure 407 molder 06-Jan-18 01:18
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Re: Michell's Canon of Ancient Measure 558 magisterchessmutt 06-Jan-18 11:56
Re: Michell's Canon of Ancient Measure 473 DavidK 07-Jan-18 11:14
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Re: David Kenworthy Cracking the Megalithic Code 380 DavidK 19-Jan-18 12:47
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Re: Extracts from another website 415 cloister 23-Jan-18 14:05
Re: Extracts from another website 432 molder 23-Jan-18 21:52
Re: Extracts from another website 423 DavidK 24-Jan-18 09:59
Re: Extracts from another website 327 molder 24-Jan-18 11:39
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Re: David Kenworthy Cracking the Megalithic Code 419 DavidK 24-Jan-18 12:03
Re: David Kenworthy Cracking the Megalithic Code 376 DavidK 25-Jan-18 07:06
Re: David Kenworthy Cracking the Megalithic Code 362 molder 25-Jan-18 12:19
Re: David Kenworthy Cracking the Megalithic Code 370 molder 25-Jan-18 12:36
Re: David Kenworthy Cracking the Megalithic Code 424 DavidK 25-Jan-18 13:50
Re: David Kenworthy Cracking the Megalithic Code 366 DavidK 25-Jan-18 13:43
Re: David Kenworthy Cracking the Megalithic Code 406 DavidK 25-Jan-18 09:41
Re: David Kenworthy Cracking the Megalithic Code 372 DavidK 27-Jan-18 12:17
Re: David Kenworthy Cracking the Megalithic Code 460 rodz111 28-Jan-18 09:54
Re: David Kenworthy Cracking the Megalithic Code 362 DavidK 28-Jan-18 20:49
Re: The Saros 457 molder 28-Jan-18 23:13
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Re: David Kenworthy Cracking the Megalithic Code 415 rodz111 29-Jan-18 16:38
Re: David Kenworthy Cracking the Megalithic Code 400 DavidK 29-Jan-18 17:07
Re: David Kenworthy Cracking the Megalithic Code 393 rodz111 29-Jan-18 18:04
Re: David Kenworthy Cracking the Megalithic Code 382 molder 30-Jan-18 06:05
Re: David Kenworthy Cracking the Megalithic Code 379 rodz111 31-Jan-18 21:24
Re: David Kenworthy Cracking the Megalithic Code 383 molder 29-Jan-18 22:32
Re: David Kenworthy Cracking the Megalithic Code 381 DavidK 30-Jan-18 10:06
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Re: David Kenworthy Cracking the Megalithic Code 492 rodz111 30-Jan-18 18:11
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Re: The Megalithic and Saxon Yard Relationship 389 cloister 01-Feb-18 20:23
Re: David Kenworthy Cracking the Megalithic Code 446 DavidK 29-Jan-18 19:39
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Re: Giza Great Pyramid design Proposal the royal cubit 20.736 imperial inches 50 DavidK 22-Dec-19 18:09
Re: Giza Great Pyramid design Proposal the royal cubit 20.736 imperial inches 35 molder 23-Dec-19 10:47
Re: Giza Great Pyramid design Proposal the royal cubit 20.736 imperial inches 34 DavidK 23-Dec-19 11:42
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Re: David Kenworthy Cracking the Megalithic Code 203 DavidK 21-May-19 23:59
Re: David Kenworthy Cracking the Megalithic Code 47 magisterchessmutt 22-Dec-19 22:24
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Re: David Kenworthy Cracking the Megalithic Code 26 DavidK 13-Jan-20 15:51
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