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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 1426 molder 03-Oct-17 20:54
Re: David Kenworthy Cracking the Megalithic Code 1043 DavidK 22-Dec-17 23:40
Re: David Kenworthy Cracking the Megalithic Code 974 magisterchessmutt 25-Dec-17 16:52
Re: David Kenworthy Cracking the Megalithic Code 673 magisterchessmutt 25-Dec-17 17:20
Re: David Kenworthy Cracking the Megalithic Code 704 DavidK 27-Dec-17 16:42
Re: David Kenworthy Cracking the Megalithic Code 681 magisterchessmutt 28-Dec-17 02:37
Re: David Kenworthy Cracking the Megalithic Code 711 magisterchessmutt 28-Dec-17 05:35
Re: David Kenworthy Cracking the Megalithic Code 748 DavidK 28-Dec-17 14:21
Re: David Kenworthy Cracking the Megalithic Code 611 DavidK 19-Jan-18 13:05
Re: David Kenworthy Cracking the Megalithic Code 642 molder 19-Jan-18 22:57
Re: David Kenworthy Cracking the Megalithic Code 583 DavidK 21-Jan-18 22:27
Re: David Kenworthy Cracking the Megalithic Code 655 molder 22-Jan-18 00:13
Re: David Kenworthy Cracking the Megalithic Code 580 DavidK 22-Jan-18 09:55
Re: David Kenworthy Cracking the Megalithic Code 501 cloister 22-Jan-18 11:01
Re: David Kenworthy Cracking the Megalithic Code 504 DavidK 22-Jan-18 12:30
Re: David Kenworthy Cracking the Megalithic Code 486 cloister 22-Jan-18 12:40
Re: David Kenworthy Cracking the Megalithic Code 528 DavidK 22-Jan-18 13:15
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Re: David Kenworthy Cracking the Megalithic Code 525 cloister 22-Jan-18 16:34
Re: David Kenworthy Cracking the Megalithic Code 514 DavidK 17-Mar-18 17:24
Re: David Kenworthy Cracking the Megalithic Code 580 DavidK 17-Mar-18 17:30
Re: David Kenworthy Cracking the Megalithic Code 788 DavidK 03-Jan-18 23:58
Re: David Kenworthy Cracking the Megalithic Code 640 DavidK 05-Jan-18 18:27
Re: David Kenworthy Cracking the Megalithic Code 672 DavidK 05-Jan-18 20:55
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Re: Michell's Canon of Ancient Measure 544 molder 06-Jan-18 01:18
Re: Michell's Canon of Ancient Measure 624 DavidK 06-Jan-18 09:51
Re: Michell's Canon of Ancient Measure 843 magisterchessmutt 06-Jan-18 11:56
Re: Michell's Canon of Ancient Measure 624 DavidK 07-Jan-18 11:14
Re: Michell's Canon of Ancient Measure 662 DavidK 10-Jan-18 14:23
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Re: David Kenworthy Cracking the Megalithic Code 529 DavidK 19-Jan-18 12:47
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Re: Extracts from another website 525 DavidK 22-Jan-18 20:31
Re: Duplication of the cube 529 molder 22-Jan-18 23:24
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Re: Extracts from another website 643 DavidK 23-Jan-18 10:41
Re: Extracts from another website 524 molder 23-Jan-18 12:10
Re: Extracts from another website 576 cloister 23-Jan-18 14:05
Re: Extracts from another website 584 molder 23-Jan-18 21:52
Re: Extracts from another website 558 DavidK 24-Jan-18 09:59
Re: Extracts from another website 486 molder 24-Jan-18 11:39
Re: Extracts from another website 538 rodz111 24-Jan-18 18:59
Re: Extracts from another website 507 DavidK 24-Jan-18 21:12
Re: David Kenworthy Cracking the Megalithic Code 554 DavidK 24-Jan-18 12:03
Re: David Kenworthy Cracking the Megalithic Code 510 DavidK 25-Jan-18 07:06
Re: David Kenworthy Cracking the Megalithic Code 492 molder 25-Jan-18 12:19
Re: David Kenworthy Cracking the Megalithic Code 505 molder 25-Jan-18 12:36
Re: David Kenworthy Cracking the Megalithic Code 547 DavidK 25-Jan-18 13:50
Re: David Kenworthy Cracking the Megalithic Code 485 DavidK 25-Jan-18 13:43
Re: David Kenworthy Cracking the Megalithic Code 550 DavidK 25-Jan-18 09:41
Re: David Kenworthy Cracking the Megalithic Code 496 DavidK 27-Jan-18 12:17
Re: David Kenworthy Cracking the Megalithic Code 651 rodz111 28-Jan-18 09:54
Re: David Kenworthy Cracking the Megalithic Code 500 DavidK 28-Jan-18 20:49
Re: The Saros 611 molder 28-Jan-18 23:13
Re: The Saros 553 DavidK 29-Jan-18 12:25
Re: David Kenworthy Cracking the Megalithic Code 552 rodz111 29-Jan-18 16:38
Re: David Kenworthy Cracking the Megalithic Code 534 DavidK 29-Jan-18 17:07
Re: David Kenworthy Cracking the Megalithic Code 540 rodz111 29-Jan-18 18:04
Re: David Kenworthy Cracking the Megalithic Code 513 molder 30-Jan-18 06:05
Re: David Kenworthy Cracking the Megalithic Code 534 rodz111 31-Jan-18 21:24
Re: David Kenworthy Cracking the Megalithic Code 510 molder 29-Jan-18 22:32
Re: David Kenworthy Cracking the Megalithic Code 516 DavidK 30-Jan-18 10:06
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Re: David Kenworthy Cracking the Megalithic Code 653 rodz111 30-Jan-18 18:11
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Re: The Megalithic and Saxon Yard Relationship 454 DavidK 31-Jan-18 21:12
Re: The Megalithic and Saxon Yard Relationship 473 cloister 31-Jan-18 21:28
Re: The Megalithic and Saxon Yard Relationship 501 DavidK 01-Feb-18 08:49
Re: The Megalithic and Saxon Yard Relationship 534 cloister 01-Feb-18 09:39
Re: The Megalithic and Saxon Yard Relationship 637 DavidK 01-Feb-18 10:05
Re: The Megalithic and Saxon Yard Relationship 496 cloister 01-Feb-18 12:01
Re: The Megalithic and Saxon Yard Relationship 496 DavidK 01-Feb-18 14:44
Re: The Megalithic and Saxon Yard Relationship 521 cloister 01-Feb-18 20:23
Re: David Kenworthy Cracking the Megalithic Code 584 DavidK 29-Jan-18 19:39
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Re: The New SH GP calculator 585 molder 03-Feb-18 04:16
Re: The New SH GP calculator 567 DavidK 03-Feb-18 23:28
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Re: putting 90720 back into the GP 635 rodz111 04-Feb-18 13:30
Re: putting 90720 back into the GP 539 DavidK 06-Feb-18 15:41
Re: putting 90720 back into the GP 712 rodz111 06-Feb-18 18:13
Re: putting 90720 back into the GP 709 DavidK 06-Feb-18 22:24
Re: David Kenworthy Cracking the Megalithic Code 497 DavidK 06-Feb-18 15:56
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Re: why 2.7207 feet per Hugh Franklin? 641 DavidK 07-Feb-18 15:29
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Re: David Kenworthy Cracking the Megalithic Code 585 DavidK 12-Oct-18 21:21
Re: David Kenworthy Cracking the Megalithic Code 378 DavidK 16-Mar-19 23:50
Re: David Kenworthy Cracking the Megalithic Code 346 rodz111 17-Mar-19 14:54
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Re: Giza Great Pyramid design Proposal the royal cubit 20.625 imperial inches 415 DavidK 04-Apr-19 13:17
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Re: Giza Great Pyramid design Proposal the royal cubit 20.736 imperial inches 160 DavidK 22-Dec-19 18:09
Re: Giza Great Pyramid design Proposal the royal cubit 20.736 imperial inches 141 molder 23-Dec-19 10:47
Re: Giza Great Pyramid design Proposal the royal cubit 20.736 imperial inches 133 DavidK 23-Dec-19 11:42
Re: Giza Great Pyramid design Proposal the royal cubit 20.736 imperial inches 188 magisterchessmutt 23-Dec-19 12:48
Re: David Kenworthy Cracking the Megalithic Code 313 DavidK 25-Apr-19 21:52
Re: David Kenworthy Cracking the Megalithic Code 323 DavidK 21-May-19 23:59
Re: David Kenworthy Cracking the Megalithic Code 200 magisterchessmutt 22-Dec-19 22:24
Re: David Kenworthy Cracking the Megalithic Code 188 molder 23-Dec-19 10:38
Re: David Kenworthy Cracking the Megalithic Code 177 magisterchessmutt 23-Dec-19 12:25
Re: David Kenworthy Cracking the Megalithic Code 137 DavidK 13-Jan-20 15:51
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