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Drew,

The Eye of Horace is representative of all Ancient Egyptian Binary methods of additive multiplication and division.
Ancient Egyptians use of unit fractions and the Eye of Horace, producing is an infinite series.
Multiply the Perimeter of G1 of 1760 cubits times the Eye of Horace, 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 extending the series + 1/128 = 127/128 ect. Creating an infinite series never reaching one.
i.e.
1 –-1760 Base perimeter of G1.
1/2 –- 880
1/4 ---440
1/8 ---220
1/16---110
1/32 ---55
1/64 ---27 1/2
Adding the results fractional calcualtions totals 1732 1/2 cubits, this whole process is equal to our 1760 x (63/64) = 1732 1/2

Evidently I did not provide enough information since you seem not to understand when I said "The 'ro' is a Middle Kingdom creation that only distracts from what the missing 1/64 actually does!"

Here is some additional information for you to help:

[planetmath.org]
Quote

Prior to 2050 BCE Old Kingdom Egyptian scribes rounded off rational numbers to six-terms binary representations for 1,000 years. The binary notation was stated in 1/2n units with a 1/64 unit thrown away. The [planetmath.org] Horus-Eye recorded rational numbers in the cursive pattern:

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + (1/64).

Note that a potential 7th term (1/64) was rounded-off and thrown way.
The new Middle Kingdom math system ”healed” rounded off binary series by several finite methods. Two weights and measures finite systems can be reported by:

1. 1 hekat (a volume unit) used a unity (64/64)such that (32 + 16 + 8 + 4 + 2 + 1/64)hekat+ 5 ro

and (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)hekat + 5 ro

meant (64/64)/n = Q/64 + (5R/n)ro

Note that the hekat unity was generally divided by rational number n. To divide by 3 scribal long-hand would have written out

(64/64)/3 = 21/64 hekat + 5/192 = (16 + 4 + 1)/64 hekat + 5/3 ro =

(1/4 + 1/16 + 1/64)hekat + ( 1 + 2/3)ro

2. (100-hekat)/70 = (6400/64)/70 = 91/64 hekat + 30/4480 = (64 + 16 + 8+ 2 + 1)/64 hekat + 150/70 ro = (1 + 1/4 + 1/8 + 1/32 + 1/64)hekat + (2 + 1/7)ro

meant (6400/64)/n = Q/64 + (5R/n)ro was applied for almost any hekat division problem.

The hieratic word ro meant 1/320 of a hekat in a grain weights and measures system. Note that 5 ro meant 5/320 = 1/64.

Generally, scribal shorthand recorded duplation aspects of mental calculations and fully recorded two-part hekat quotients and ro remainders.

At other times 2/64 was scaled to 10/320 such that (8 + 2)/320 = 1/40 + 2 ro
Bold emphasis in above quote mine.

I did not say the Ancient Egyptians were not cognizant of rational values for phi, sqrt 2, sqrt 3, sqrt 5, in rational form, or their importance in calculations and constructions. The reality is there are fractional equivalents within 4 to 5 decimal places of accuracy for all our values listed above easily substituted for our current values. To the Ancient Egyptians our values simply did not exist.

You do know phi was first noted in rational form by Fibonacci in “Liber Abaci” in the 1299. originally expressed by a continued fractional series 1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34, 34/55, 55/89, 144/233 etc. The current incarnation of phi (1.618033989) is a modern irrational average based on the sqrt 5. That being said, the fact is the rise run of G1’s 5 1/2 seked 14/11 is within 0.000707623 of the current value for the sqrt phi 1.27201965. So it is very unlikely the Ancient Egyptians employed phi as we know and use it.

Sqrt 2: 1 + 1/9 times the rise run 1 + 1/4 * 1/44 of the 5 1/2 seked. Giving the value of 140/99 or a decimal value of 1.4141414… a difference of 0.000072148 from the sqrt 2, which is accurate enough for most calculations. i.e.140/99 = 1.414141414…minus the sqrt2 = 1.41213562 = 0.000072148

Several years ago Rob Miller found the Sqrt 3: in the form of 97/56 1 + 1/2 + 1/7 + 1/14 + 1/56 = 1 + 41/56, decimal value of 1.732142857…a difference of 0.00009205 compared to sqrt 3, again accurate enough for most calculations.
i.e. (97/56 = 1.732142857…) minus the (sqrt 3 = 1.732050808) = 0.00009205

As an example of what I told DavidK, understanding the difference between our current system and theirs will provide answers for many of the lingering questions accumulated over the years.
One interesting thing about 1 + 1/2 + 1/7 + 1/14 + 1/56 and just for fun because we know the Ancient Egyptians did not use angles as we do, but is: tan 97/56 = 60º 0’ 4.75” cotan 56/97 = 29º 59’ 55.25” compared to our measure for the latitude of G1 29ª 58’ 45.12“N having a difference of 0º 1’ 10.13” from our current noted location for G1.

Use or ignore the above information, It really doesn't matter to me it is your hypothesis.

Regards,
Jacob

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Subject Views Written By Posted
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Re: Pi or no Pi ?????????????? 531 Sirfiroth 06-Feb-18 17:37
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Re: Pi or no Pi ?????????????? 421 DavidK 08-Feb-18 10:48
Re: Pi or no Pi ?????????????? 421 molder 08-Feb-18 11:56
linking egyptian Pi to imperial Pi 356 DavidK 08-Feb-18 15:10
Re: Pi or no Pi ?????????????? 358 DavidK 08-Feb-18 13:58
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where does Fibonacci Pi come from? 361 DavidK 08-Feb-18 14:49
Re: cubit of 20.25? 415 Sirfiroth 08-Feb-18 15:08
Re: cubit of 20.25? 379 DavidK 08-Feb-18 15:15
Re: cubit of 20.25? 377 molder 09-Feb-18 03:58
Mod Note > Off-Topic Posts 394 Dr. Troglodyte 09-Feb-18 16:38
Re: cubit of 20.25? 580 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 408 drew 09-Feb-18 00:33
Re: Oh...what a shame... 407 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 426 drew 09-Feb-18 06:02
Re: Oh...what a shame... 510 Sirfiroth 09-Feb-18 13:28
Re: Oh...what a shame... 414 DavidK 22-Jun-18 05:58
Re: Oh...what a shame... 350 drew 22-Jun-18 09:54
Re: Oh...what a shame... 431 Sirfiroth 22-Jun-18 13:32
Re: Oh...what a shame... 507 drew 22-Jun-18 22:27
Re: Oh...what a shame... 380 Sirfiroth 23-Jun-18 01:48
Re: well put 350 drew 23-Jun-18 08:08
To put it bluntly! 392 Sirfiroth 23-Jun-18 12:40
Re: well put 372 Manu 23-Jun-18 18:33
Re: extensions of numbers 325 drew 24-Jun-18 00:40
Re: extensions of numbers 386 Sirfiroth 24-Jun-18 04:50
Re: extensions of numbers 337 drew 24-Jun-18 08:36
Re: extensions of numbers 327 Sirfiroth 24-Jun-18 12:22
Re: extensions of numbers 332 drew 24-Jun-18 20:53
Re: extensions of numbers 332 Sirfiroth 25-Jun-18 16:06
Re: extensions of numbers 308 DavidK 25-Jun-18 16:13
Re: extensions of numbers 316 Sirfiroth 25-Jun-18 16:46
the primitive calculator 313 drew 25-Jun-18 23:23
Re: the primitive calculator 368 Sirfiroth 26-Jun-18 02:24
Re: the primitive calculator 300 drew 26-Jun-18 07:06
Mod Note > Duplicate Post Removed 443 Dr. Troglodyte 26-Jun-18 12:45
Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 368 rodz111 26-Jun-18 13:55
Re: Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 270 drew 27-Jun-18 05:18
Re: the primitive calculator 355 Sirfiroth 26-Jun-18 17:00
Re: the primitive calculator 334 drew 27-Jun-18 00:01
Re: the primitive calculator 332 Sirfiroth 27-Jun-18 00:18
Re: the primitive calculator 304 drew 27-Jun-18 01:56
Re: well put 291 cloister 24-Jun-18 09:43
Re: well put 332 Manu 24-Jun-18 12:59
Re: well put 320 cloister 24-Jun-18 18:14
Re: well put 410 cloister 29-Jun-18 08:48
Re: well put 308 drew 27-Jun-18 05:11
Re: Oh...what a shame... 372 Sirfiroth 22-Jun-18 12:21
Re: Oh...what a shame... 401 molder 23-Jun-18 00:24
Re: Oh...what a shame... 382 DavidK 23-Jun-18 21:06
Re: Oh...what a shame... 342 DavidK 24-Jun-18 07:41
Understanding the differences! 385 Sirfiroth 24-Jun-18 12:50
No pie for jacob 380 DavidK 24-Jun-18 08:54
Re: No pie for jacob 317 Sirfiroth 25-Jun-18 16:44
Re: No pie for jacob 341 DavidK 25-Jun-18 20:21
Re: No pie for jacob 351 Sirfiroth 25-Jun-18 23:19
Re: 5 values for pi in GP here are 3 303 molder 26-Jun-18 00:51
Re: what value for pi? 306 drew 26-Jun-18 14:11
Re: what value for pi? 355 molder 26-Jun-18 21:30
Re: what value for pi? 308 drew 26-Jun-18 23:42
Re: 5 values for pi in GP here are 3 294 Sirfiroth 26-Jun-18 14:55
Re: 5 values for pi in GP here are 3 349 molder 26-Jun-18 21:18
Re: No pie for jacob 344 DavidK 26-Jun-18 10:34
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Re: No pie for jacob 348 Sirfiroth 26-Jun-18 22:59
Re: No pie for jacob 297 DUNE 26-Jun-18 19:52
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Re: Hard evidence for base 100 using egyptian maths 370 drew 27-Jun-18 06:16
Re: Hard evidence for base 100 using egyptian maths 314 DavidK 27-Jun-18 10:25
Re: Hard evidence for base 100 using egyptian maths 330 drew 27-Jun-18 21:18
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Re: Pi or no Pi ?????????????? 346 Sirfiroth 25-Jun-18 19:54
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Re: Pi or no Pi ?????????????? 337 molder 26-Jun-18 03:19
Re: Pi or no Pi ?????????????? 333 rodz111 26-Jun-18 03:30
Re: Pi or no Pi ?????????????? 329 molder 26-Jun-18 21:52
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Re: Pi or no Pi ?????????????? 366 spaceyhippie 24-Jul-18 02:44
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Re: Pi or no Pi ?????????????? 313 DavidK 07-Aug-18 05:16
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Re: Pi or no Pi ?????????????? 380 DavidK 09-Aug-18 08:00
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Re: ROTFLMAO! 415 Sirfiroth 09-Aug-18 14:28
Re: ROTFLMAO! 265 DavidK 09-Aug-18 14:49
Re: ROTFLMAO! 273 Sirfiroth 09-Aug-18 15:03
Re: ROTFLMAO! 287 DavidK 09-Aug-18 21:39
Re: ROTFLMAO! 311 Sirfiroth 10-Aug-18 02:06
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Re: Pi or no Pi ?????????????? 160 thinkitover 28-Dec-19 21:49
Re: Pi or no Pi ?????????????? 157 Thanos5150 29-Dec-19 04:35
Re: Pi or no Pi ?????????????? 150 Sirfiroth 29-Dec-19 02:17
Re: Pi or no Pi ?????????????? 153 molder 29-Dec-19 04:14
Re: Pi or no Pi ?????????????? 146 Sirfiroth 29-Dec-19 12:51
Re: Pi or no Pi ?????????????? 146 molder 29-Dec-19 22:31
Re: Pi or no Pi ?????????????? 138 Sirfiroth 30-Dec-19 14:11
Re: Pi or no Pi ?????????????? 185 magisterchessmutt 30-Dec-19 15:16
Re: Pi or no Pi ?????????????? 145 Sirfiroth 31-Dec-19 03:33
Re: Pi or no Pi ?????????????? 190 magisterchessmutt 31-Dec-19 04:33
Re: Pi or no Pi ?????????????? 162 Sirfiroth 31-Dec-19 15:04
Re: Pi or no Pi ?????????????? 171 spaceyhippie 31-Dec-19 23:37
Re: Pi or no Pi ?????????????? 164 Thanos5150 29-Dec-19 04:29
Re: Pi or no Pi ?????????????? 150 DavidK 29-Dec-19 09:32
Re: Pi or no Pi ?????????????? 157 Sirfiroth 29-Dec-19 14:09
Re: Pi or no Pi ?????????????? 155 spaceyhippie 01-Jan-20 23:18
Re: Pi or no Pi ?????????????? 169 Sirfiroth 02-Jan-20 01:33
Pi vs Pudding 158 thinkitover 02-Jan-20 21:45
Re: Pi vs Pudding 150 spaceyhippie 03-Jan-20 00:06
Re: Pi vs Pudding 168 seasmith 03-Jan-20 00:24
Re: Pi vs Pudding 150 spaceyhippie 07-Jan-20 23:06
Re: Pi vs Pudding 193 seasmith 08-Jan-20 02:54
Re: Pi vs Pudding 157 Sirfiroth 03-Jan-20 03:36
Re: Pi vs Pudding 158 molder 03-Jan-20 06:56
Re: Pi vs Pudding 159 Sirfiroth 03-Jan-20 18:25
Re: Pi vs Pudding 154 spaceyhippie 04-Jan-20 00:02
LOL, now that was hilarious ! 153 Sirfiroth 04-Jan-20 05:51
Re: LOL, now that was hilarious ! 198 hendrik dirker 04-Jan-20 09:32
Re: LOL, now that was hilarious ! 142 spaceyhippie 04-Jan-20 23:37
Re: LOL, now that was hilarious ! 152 spaceyhippie 04-Jan-20 23:39
Re: Pi vs Pudding 170 molder 04-Jan-20 11:03
Re: Pi vs Pudding 160 Sirfiroth 05-Jan-20 20:11
Re: Pi vs Pudding 151 molder 06-Jan-20 02:55
Re: Pi vs Pudding 179 magisterchessmutt 06-Jan-20 02:58
Re: Pi vs Pudding 145 molder 06-Jan-20 05:26
Re: Pi vs Pudding 148 spaceyhippie 07-Jan-20 01:32
Re: Pi vs Pudding 136 DavidK 07-Jan-20 02:02
Re: Pi vs Pudding 151 thinkitover 06-Jan-20 06:13
Re: Pi vs Pudding 165 Sirfiroth 07-Jan-20 02:18
Re: Pi vs Pudding 135 DavidK 07-Jan-20 14:25
Re: Pi vs Pudding 147 Sirfiroth 07-Jan-20 15:16
Re: Pi vs Pudding 146 DavidK 07-Jan-20 19:03
Re: Pi vs Pudding 141 Sirfiroth 07-Jan-20 20:08
Re: Pi vs Pudding 139 DavidK 07-Jan-20 20:11
Re: Pi or no Pi ?????????????? 167 DavidK 28-Dec-19 11:21
Re: Pi or no Pi ?????????????? 161 engbren 28-Dec-19 12:34
Re: Pi or no Pi ?????????????? 162 Sirfiroth 28-Dec-19 15:55
Re: Pi or no Pi ?????????????? 150 engbren 29-Dec-19 01:14
Re: Pi or no Pi ?????????????? 150 Sirfiroth 30-Dec-19 16:52
Re: Pi or no Pi ?????????????? 151 engbren 30-Dec-19 22:23
Re: Pi or no Pi ?????????????? 209 magisterchessmutt 30-Dec-19 23:24
Re: Pi or no Pi ?????????????? 176 engbren 31-Dec-19 11:31
Re: Pi or no Pi ?????????????? 158 spaceyhippie 04-Jan-20 00:42


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