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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 638 molder 03-Oct-17 20:54
Re: David Kenworthy Cracking the Megalithic Code 438 DavidK 22-Dec-17 23:40
Re: David Kenworthy Cracking the Megalithic Code 276 magisterchessmutt 25-Dec-17 16:52
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Re: David Kenworthy Cracking the Megalithic Code 227 DavidK 27-Dec-17 16:42
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Re: David Kenworthy Cracking the Megalithic Code 227 magisterchessmutt 28-Dec-17 05:35
Re: David Kenworthy Cracking the Megalithic Code 260 DavidK 28-Dec-17 14:21
Re: David Kenworthy Cracking the Megalithic Code 146 DavidK 19-Jan-18 13:05
Re: David Kenworthy Cracking the Megalithic Code 161 molder 19-Jan-18 22:57
Re: David Kenworthy Cracking the Megalithic Code 150 DavidK 21-Jan-18 22:27
Re: David Kenworthy Cracking the Megalithic Code 138 molder 22-Jan-18 00:13
Re: David Kenworthy Cracking the Megalithic Code 144 DavidK 22-Jan-18 09:55
Re: David Kenworthy Cracking the Megalithic Code 118 cloister 22-Jan-18 11:01
Re: David Kenworthy Cracking the Megalithic Code 108 DavidK 22-Jan-18 12:30
Re: David Kenworthy Cracking the Megalithic Code 98 cloister 22-Jan-18 12:40
Re: David Kenworthy Cracking the Megalithic Code 112 DavidK 22-Jan-18 13:15
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Re: David Kenworthy Cracking the Megalithic Code 107 cloister 22-Jan-18 16:34
Re: David Kenworthy Cracking the Megalithic Code 83 DavidK 17-Mar-18 17:24
Re: David Kenworthy Cracking the Megalithic Code 118 DavidK 17-Mar-18 17:30
Re: David Kenworthy Cracking the Megalithic Code 267 DavidK 03-Jan-18 23:58
Re: David Kenworthy Cracking the Megalithic Code 164 DavidK 05-Jan-18 18:27
Re: David Kenworthy Cracking the Megalithic Code 175 DavidK 05-Jan-18 20:55
Re: Michell's Canon of Ancient Measure 133 DavidK 05-Jan-18 23:48
Re: Michell's Canon of Ancient Measure 139 molder 06-Jan-18 01:18
Re: Michell's Canon of Ancient Measure 199 DavidK 06-Jan-18 09:51
Re: Michell's Canon of Ancient Measure 185 magisterchessmutt 06-Jan-18 11:56
Re: Michell's Canon of Ancient Measure 171 DavidK 07-Jan-18 11:14
Re: Michell's Canon of Ancient Measure 186 DavidK 10-Jan-18 14:23
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Re: David Kenworthy Cracking the Megalithic Code 120 DavidK 19-Jan-18 12:47
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Re: Extracts from another website 114 DavidK 22-Jan-18 20:31
Re: Duplication of the cube 113 molder 22-Jan-18 23:24
Re: Extracts from another website 139 Dr. Troglodyte 22-Jan-18 23:25
Re: Extracts from another website 157 DavidK 23-Jan-18 10:41
Re: Extracts from another website 117 molder 23-Jan-18 12:10
Re: Extracts from another website 151 cloister 23-Jan-18 14:05
Re: Extracts from another website 118 molder 23-Jan-18 21:52
Re: Extracts from another website 136 DavidK 24-Jan-18 09:59
Re: Extracts from another website 75 molder 24-Jan-18 11:39
Re: Extracts from another website 116 rodz111 24-Jan-18 18:59
Re: Extracts from another website 120 DavidK 24-Jan-18 21:12
Re: David Kenworthy Cracking the Megalithic Code 147 DavidK 24-Jan-18 12:03
Re: David Kenworthy Cracking the Megalithic Code 97 DavidK 25-Jan-18 07:06
Re: David Kenworthy Cracking the Megalithic Code 96 molder 25-Jan-18 12:19
Re: David Kenworthy Cracking the Megalithic Code 101 molder 25-Jan-18 12:36
Re: David Kenworthy Cracking the Megalithic Code 144 DavidK 25-Jan-18 13:50
Re: David Kenworthy Cracking the Megalithic Code 105 DavidK 25-Jan-18 13:43
Re: David Kenworthy Cracking the Megalithic Code 137 DavidK 25-Jan-18 09:41
Re: David Kenworthy Cracking the Megalithic Code 96 DavidK 27-Jan-18 12:17
Re: David Kenworthy Cracking the Megalithic Code 153 rodz111 28-Jan-18 09:54
Re: David Kenworthy Cracking the Megalithic Code 102 DavidK 28-Jan-18 20:49
Re: The Saros 153 molder 28-Jan-18 23:13
Re: The Saros 125 DavidK 29-Jan-18 12:25
Re: David Kenworthy Cracking the Megalithic Code 106 rodz111 29-Jan-18 16:38
Re: David Kenworthy Cracking the Megalithic Code 125 DavidK 29-Jan-18 17:07
Re: David Kenworthy Cracking the Megalithic Code 116 rodz111 29-Jan-18 18:04
Re: David Kenworthy Cracking the Megalithic Code 119 molder 30-Jan-18 06:05
Re: David Kenworthy Cracking the Megalithic Code 106 rodz111 31-Jan-18 21:24
Re: David Kenworthy Cracking the Megalithic Code 103 molder 29-Jan-18 22:32
Re: David Kenworthy Cracking the Megalithic Code 105 DavidK 30-Jan-18 10:06
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Re: David Kenworthy Cracking the Megalithic Code 162 rodz111 30-Jan-18 18:11
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Re: The Megalithic and Saxon Yard Relationship 72 DavidK 31-Jan-18 21:12
Re: The Megalithic and Saxon Yard Relationship 95 cloister 31-Jan-18 21:28
Re: The Megalithic and Saxon Yard Relationship 103 DavidK 01-Feb-18 08:49
Re: The Megalithic and Saxon Yard Relationship 111 cloister 01-Feb-18 09:39
Re: The Megalithic and Saxon Yard Relationship 143 DavidK 01-Feb-18 10:05
Re: The Megalithic and Saxon Yard Relationship 95 cloister 01-Feb-18 12:01
Re: The Megalithic and Saxon Yard Relationship 108 DavidK 01-Feb-18 14:44
Re: The Megalithic and Saxon Yard Relationship 104 cloister 01-Feb-18 20:23
Re: David Kenworthy Cracking the Megalithic Code 137 DavidK 29-Jan-18 19:39
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Re: The New SH GP calculator 158 molder 03-Feb-18 04:16
Re: The New SH GP calculator 157 DavidK 03-Feb-18 23:28
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Re: putting 90720 back into the GP 172 rodz111 04-Feb-18 13:30
Re: putting 90720 back into the GP 102 DavidK 06-Feb-18 15:41
Re: putting 90720 back into the GP 198 rodz111 06-Feb-18 18:13
Re: putting 90720 back into the GP 130 DavidK 06-Feb-18 22:24
Re: David Kenworthy Cracking the Megalithic Code 88 DavidK 06-Feb-18 15:56
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