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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 770 molder 03-Oct-17 20:54
Re: David Kenworthy Cracking the Megalithic Code 535 DavidK 22-Dec-17 23:40
Re: David Kenworthy Cracking the Megalithic Code 366 magisterchessmutt 25-Dec-17 16:52
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Re: David Kenworthy Cracking the Megalithic Code 308 magisterchessmutt 28-Dec-17 05:35
Re: David Kenworthy Cracking the Megalithic Code 332 DavidK 28-Dec-17 14:21
Re: David Kenworthy Cracking the Megalithic Code 211 DavidK 19-Jan-18 13:05
Re: David Kenworthy Cracking the Megalithic Code 234 molder 19-Jan-18 22:57
Re: David Kenworthy Cracking the Megalithic Code 221 DavidK 21-Jan-18 22:27
Re: David Kenworthy Cracking the Megalithic Code 222 molder 22-Jan-18 00:13
Re: David Kenworthy Cracking the Megalithic Code 226 DavidK 22-Jan-18 09:55
Re: David Kenworthy Cracking the Megalithic Code 181 cloister 22-Jan-18 11:01
Re: David Kenworthy Cracking the Megalithic Code 167 DavidK 22-Jan-18 12:30
Re: David Kenworthy Cracking the Megalithic Code 154 cloister 22-Jan-18 12:40
Re: David Kenworthy Cracking the Megalithic Code 175 DavidK 22-Jan-18 13:15
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Re: David Kenworthy Cracking the Megalithic Code 175 cloister 22-Jan-18 16:34
Re: David Kenworthy Cracking the Megalithic Code 149 DavidK 17-Mar-18 17:24
Re: David Kenworthy Cracking the Megalithic Code 195 DavidK 17-Mar-18 17:30
Re: David Kenworthy Cracking the Megalithic Code 370 DavidK 03-Jan-18 23:58
Re: David Kenworthy Cracking the Megalithic Code 239 DavidK 05-Jan-18 18:27
Re: David Kenworthy Cracking the Megalithic Code 249 DavidK 05-Jan-18 20:55
Re: Michell's Canon of Ancient Measure 201 DavidK 05-Jan-18 23:48
Re: Michell's Canon of Ancient Measure 209 molder 06-Jan-18 01:18
Re: Michell's Canon of Ancient Measure 277 DavidK 06-Jan-18 09:51
Re: Michell's Canon of Ancient Measure 279 magisterchessmutt 06-Jan-18 11:56
Re: Michell's Canon of Ancient Measure 245 DavidK 07-Jan-18 11:14
Re: Michell's Canon of Ancient Measure 256 DavidK 10-Jan-18 14:23
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Re: David Kenworthy Cracking the Megalithic Code 177 DavidK 19-Jan-18 12:47
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Re: Extracts from another website 178 DavidK 22-Jan-18 20:31
Re: Duplication of the cube 176 molder 22-Jan-18 23:24
Re: Extracts from another website 214 Dr. Troglodyte 22-Jan-18 23:25
Re: Extracts from another website 226 DavidK 23-Jan-18 10:41
Re: Extracts from another website 180 molder 23-Jan-18 12:10
Re: Extracts from another website 222 cloister 23-Jan-18 14:05
Re: Extracts from another website 190 molder 23-Jan-18 21:52
Re: Extracts from another website 205 DavidK 24-Jan-18 09:59
Re: Extracts from another website 127 molder 24-Jan-18 11:39
Re: Extracts from another website 179 rodz111 24-Jan-18 18:59
Re: Extracts from another website 192 DavidK 24-Jan-18 21:12
Re: David Kenworthy Cracking the Megalithic Code 222 DavidK 24-Jan-18 12:03
Re: David Kenworthy Cracking the Megalithic Code 163 DavidK 25-Jan-18 07:06
Re: David Kenworthy Cracking the Megalithic Code 163 molder 25-Jan-18 12:19
Re: David Kenworthy Cracking the Megalithic Code 164 molder 25-Jan-18 12:36
Re: David Kenworthy Cracking the Megalithic Code 221 DavidK 25-Jan-18 13:50
Re: David Kenworthy Cracking the Megalithic Code 163 DavidK 25-Jan-18 13:43
Re: David Kenworthy Cracking the Megalithic Code 197 DavidK 25-Jan-18 09:41
Re: David Kenworthy Cracking the Megalithic Code 160 DavidK 27-Jan-18 12:17
Re: David Kenworthy Cracking the Megalithic Code 230 rodz111 28-Jan-18 09:54
Re: David Kenworthy Cracking the Megalithic Code 165 DavidK 28-Jan-18 20:49
Re: The Saros 225 molder 28-Jan-18 23:13
Re: The Saros 184 DavidK 29-Jan-18 12:25
Re: David Kenworthy Cracking the Megalithic Code 177 rodz111 29-Jan-18 16:38
Re: David Kenworthy Cracking the Megalithic Code 194 DavidK 29-Jan-18 17:07
Re: David Kenworthy Cracking the Megalithic Code 181 rodz111 29-Jan-18 18:04
Re: David Kenworthy Cracking the Megalithic Code 181 molder 30-Jan-18 06:05
Re: David Kenworthy Cracking the Megalithic Code 170 rodz111 31-Jan-18 21:24
Re: David Kenworthy Cracking the Megalithic Code 168 molder 29-Jan-18 22:32
Re: David Kenworthy Cracking the Megalithic Code 173 DavidK 30-Jan-18 10:06
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Re: David Kenworthy Cracking the Megalithic Code 257 rodz111 30-Jan-18 18:11
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Re: The Megalithic and Saxon Yard Relationship 132 DavidK 31-Jan-18 21:12
Re: The Megalithic and Saxon Yard Relationship 154 cloister 31-Jan-18 21:28
Re: The Megalithic and Saxon Yard Relationship 165 DavidK 01-Feb-18 08:49
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Re: The Megalithic and Saxon Yard Relationship 157 cloister 01-Feb-18 12:01
Re: The Megalithic and Saxon Yard Relationship 170 DavidK 01-Feb-18 14:44
Re: The Megalithic and Saxon Yard Relationship 163 cloister 01-Feb-18 20:23
Re: David Kenworthy Cracking the Megalithic Code 211 DavidK 29-Jan-18 19:39
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Re: The New SH GP calculator 234 DavidK 03-Feb-18 23:28
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Re: putting 90720 back into the GP 166 DavidK 06-Feb-18 15:41
Re: putting 90720 back into the GP 302 rodz111 06-Feb-18 18:13
Re: putting 90720 back into the GP 192 DavidK 06-Feb-18 22:24
Re: David Kenworthy Cracking the Megalithic Code 145 DavidK 06-Feb-18 15:56
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Re: why 2.7207 feet per Hugh Franklin? 250 DavidK 07-Feb-18 15:29
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