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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 724 molder 03-Oct-17 20:54
Re: David Kenworthy Cracking the Megalithic Code 499 DavidK 22-Dec-17 23:40
Re: David Kenworthy Cracking the Megalithic Code 324 magisterchessmutt 25-Dec-17 16:52
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Re: David Kenworthy Cracking the Megalithic Code 264 DavidK 27-Dec-17 16:42
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Re: David Kenworthy Cracking the Megalithic Code 272 magisterchessmutt 28-Dec-17 05:35
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Re: David Kenworthy Cracking the Megalithic Code 181 DavidK 19-Jan-18 13:05
Re: David Kenworthy Cracking the Megalithic Code 201 molder 19-Jan-18 22:57
Re: David Kenworthy Cracking the Megalithic Code 188 DavidK 21-Jan-18 22:27
Re: David Kenworthy Cracking the Megalithic Code 182 molder 22-Jan-18 00:13
Re: David Kenworthy Cracking the Megalithic Code 189 DavidK 22-Jan-18 09:55
Re: David Kenworthy Cracking the Megalithic Code 149 cloister 22-Jan-18 11:01
Re: David Kenworthy Cracking the Megalithic Code 141 DavidK 22-Jan-18 12:30
Re: David Kenworthy Cracking the Megalithic Code 129 cloister 22-Jan-18 12:40
Re: David Kenworthy Cracking the Megalithic Code 144 DavidK 22-Jan-18 13:15
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Re: David Kenworthy Cracking the Megalithic Code 140 cloister 22-Jan-18 16:34
Re: David Kenworthy Cracking the Megalithic Code 118 DavidK 17-Mar-18 17:24
Re: David Kenworthy Cracking the Megalithic Code 156 DavidK 17-Mar-18 17:30
Re: David Kenworthy Cracking the Megalithic Code 326 DavidK 03-Jan-18 23:58
Re: David Kenworthy Cracking the Megalithic Code 203 DavidK 05-Jan-18 18:27
Re: David Kenworthy Cracking the Megalithic Code 214 DavidK 05-Jan-18 20:55
Re: Michell's Canon of Ancient Measure 166 DavidK 05-Jan-18 23:48
Re: Michell's Canon of Ancient Measure 177 molder 06-Jan-18 01:18
Re: Michell's Canon of Ancient Measure 241 DavidK 06-Jan-18 09:51
Re: Michell's Canon of Ancient Measure 241 magisterchessmutt 06-Jan-18 11:56
Re: Michell's Canon of Ancient Measure 208 DavidK 07-Jan-18 11:14
Re: Michell's Canon of Ancient Measure 226 DavidK 10-Jan-18 14:23
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Re: David Kenworthy Cracking the Megalithic Code 149 DavidK 19-Jan-18 12:47
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Re: Extracts from another website 148 DavidK 22-Jan-18 20:31
Re: Duplication of the cube 149 molder 22-Jan-18 23:24
Re: Extracts from another website 175 Dr. Troglodyte 22-Jan-18 23:25
Re: Extracts from another website 192 DavidK 23-Jan-18 10:41
Re: Extracts from another website 149 molder 23-Jan-18 12:10
Re: Extracts from another website 192 cloister 23-Jan-18 14:05
Re: Extracts from another website 154 molder 23-Jan-18 21:52
Re: Extracts from another website 169 DavidK 24-Jan-18 09:59
Re: Extracts from another website 102 molder 24-Jan-18 11:39
Re: Extracts from another website 151 rodz111 24-Jan-18 18:59
Re: Extracts from another website 158 DavidK 24-Jan-18 21:12
Re: David Kenworthy Cracking the Megalithic Code 183 DavidK 24-Jan-18 12:03
Re: David Kenworthy Cracking the Megalithic Code 135 DavidK 25-Jan-18 07:06
Re: David Kenworthy Cracking the Megalithic Code 134 molder 25-Jan-18 12:19
Re: David Kenworthy Cracking the Megalithic Code 134 molder 25-Jan-18 12:36
Re: David Kenworthy Cracking the Megalithic Code 184 DavidK 25-Jan-18 13:50
Re: David Kenworthy Cracking the Megalithic Code 138 DavidK 25-Jan-18 13:43
Re: David Kenworthy Cracking the Megalithic Code 170 DavidK 25-Jan-18 09:41
Re: David Kenworthy Cracking the Megalithic Code 129 DavidK 27-Jan-18 12:17
Re: David Kenworthy Cracking the Megalithic Code 194 rodz111 28-Jan-18 09:54
Re: David Kenworthy Cracking the Megalithic Code 136 DavidK 28-Jan-18 20:49
Re: The Saros 194 molder 28-Jan-18 23:13
Re: The Saros 155 DavidK 29-Jan-18 12:25
Re: David Kenworthy Cracking the Megalithic Code 142 rodz111 29-Jan-18 16:38
Re: David Kenworthy Cracking the Megalithic Code 160 DavidK 29-Jan-18 17:07
Re: David Kenworthy Cracking the Megalithic Code 146 rodz111 29-Jan-18 18:04
Re: David Kenworthy Cracking the Megalithic Code 150 molder 30-Jan-18 06:05
Re: David Kenworthy Cracking the Megalithic Code 139 rodz111 31-Jan-18 21:24
Re: David Kenworthy Cracking the Megalithic Code 139 molder 29-Jan-18 22:32
Re: David Kenworthy Cracking the Megalithic Code 143 DavidK 30-Jan-18 10:06
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Re: David Kenworthy Cracking the Megalithic Code 210 rodz111 30-Jan-18 18:11
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Re: The Megalithic and Saxon Yard Relationship 103 DavidK 31-Jan-18 21:12
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Re: The Megalithic and Saxon Yard Relationship 136 DavidK 01-Feb-18 08:49
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Re: The Megalithic and Saxon Yard Relationship 128 cloister 01-Feb-18 12:01
Re: The Megalithic and Saxon Yard Relationship 139 DavidK 01-Feb-18 14:44
Re: The Megalithic and Saxon Yard Relationship 135 cloister 01-Feb-18 20:23
Re: David Kenworthy Cracking the Megalithic Code 172 DavidK 29-Jan-18 19:39
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Re: putting 90720 back into the GP 135 DavidK 06-Feb-18 15:41
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Re: putting 90720 back into the GP 162 DavidK 06-Feb-18 22:24
Re: David Kenworthy Cracking the Megalithic Code 119 DavidK 06-Feb-18 15:56
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Re: why 2.7207 feet per Hugh Franklin? 218 DavidK 07-Feb-18 15:29
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