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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
Pi or no Pi ?????????????? 3212 Sirfiroth 06-Feb-18 03:26
Re: Pi or no Pi ?????????????? 559 drew 06-Feb-18 04:18
Re: Pi or no Pi ?????????????? 521 Sirfiroth 06-Feb-18 17:37
Re: Pi or no Pi ?????????????? 424 drew 06-Feb-18 23:32
Re: Pi or no Pi ???????????????? 483 Dr. Troglodyte 07-Feb-18 14:44
Re: Pi or no Pi ?????????????? 410 molder 08-Feb-18 05:09
Re: Pi or no Pi ?????????????? 408 Sirfiroth 08-Feb-18 06:43
Re: Pi or no Pi ?????????????? 411 DavidK 08-Feb-18 10:48
Re: Pi or no Pi ?????????????? 409 molder 08-Feb-18 11:56
linking egyptian Pi to imperial Pi 346 DavidK 08-Feb-18 15:10
Re: Pi or no Pi ?????????????? 347 DavidK 08-Feb-18 13:58
cubit of 20.25? 315 DavidK 08-Feb-18 14:12
where does Fibonacci Pi come from? 351 DavidK 08-Feb-18 14:49
Re: cubit of 20.25? 405 Sirfiroth 08-Feb-18 15:08
Re: cubit of 20.25? 368 DavidK 08-Feb-18 15:15
Re: cubit of 20.25? 366 molder 09-Feb-18 03:58
Mod Note > Off-Topic Posts 384 Dr. Troglodyte 09-Feb-18 16:38
Re: cubit of 20.25? 529 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 399 drew 09-Feb-18 00:33
Re: Oh...what a shame... 396 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 417 drew 09-Feb-18 06:02
Re: Oh...what a shame... 446 Sirfiroth 09-Feb-18 13:28
Re: Oh...what a shame... 404 DavidK 22-Jun-18 05:58
Re: Oh...what a shame... 340 drew 22-Jun-18 09:54
Re: Oh...what a shame... 421 Sirfiroth 22-Jun-18 13:32
Re: Oh...what a shame... 497 drew 22-Jun-18 22:27
Re: Oh...what a shame... 369 Sirfiroth 23-Jun-18 01:48
Re: well put 341 drew 23-Jun-18 08:08
To put it bluntly! 383 Sirfiroth 23-Jun-18 12:40
Re: well put 362 Manu 23-Jun-18 18:33
Re: extensions of numbers 315 drew 24-Jun-18 00:40
Re: extensions of numbers 375 Sirfiroth 24-Jun-18 04:50
Re: extensions of numbers 328 drew 24-Jun-18 08:36
Re: extensions of numbers 318 Sirfiroth 24-Jun-18 12:22
Re: extensions of numbers 323 drew 24-Jun-18 20:53
Re: extensions of numbers 321 Sirfiroth 25-Jun-18 16:06
Re: extensions of numbers 298 DavidK 25-Jun-18 16:13
Re: extensions of numbers 305 Sirfiroth 25-Jun-18 16:46
the primitive calculator 304 drew 25-Jun-18 23:23
Re: the primitive calculator 359 Sirfiroth 26-Jun-18 02:24
Re: the primitive calculator 290 drew 26-Jun-18 07:06
Mod Note > Duplicate Post Removed 388 Dr. Troglodyte 26-Jun-18 12:45
Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 357 rodz111 26-Jun-18 13:55
Re: Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 259 drew 27-Jun-18 05:18
Re: the primitive calculator 333 Sirfiroth 26-Jun-18 17:00
Re: the primitive calculator 324 drew 27-Jun-18 00:01
Re: the primitive calculator 322 Sirfiroth 27-Jun-18 00:18
Re: the primitive calculator 293 drew 27-Jun-18 01:56
Re: well put 279 cloister 24-Jun-18 09:43
Re: well put 322 Manu 24-Jun-18 12:59
Re: well put 310 cloister 24-Jun-18 18:14
Re: well put 367 cloister 29-Jun-18 08:48
Re: well put 299 drew 27-Jun-18 05:11
Re: Oh...what a shame... 361 Sirfiroth 22-Jun-18 12:21
Re: Oh...what a shame... 391 molder 23-Jun-18 00:24
Re: Oh...what a shame... 370 DavidK 23-Jun-18 21:06
Re: Oh...what a shame... 331 DavidK 24-Jun-18 07:41
Understanding the differences! 329 Sirfiroth 24-Jun-18 12:50
No pie for jacob 369 DavidK 24-Jun-18 08:54
Re: No pie for jacob 306 Sirfiroth 25-Jun-18 16:44
Re: No pie for jacob 331 DavidK 25-Jun-18 20:21
Re: No pie for jacob 335 Sirfiroth 25-Jun-18 23:19
Re: 5 values for pi in GP here are 3 294 molder 26-Jun-18 00:51
Re: what value for pi? 297 drew 26-Jun-18 14:11
Re: what value for pi? 343 molder 26-Jun-18 21:30
Re: what value for pi? 299 drew 26-Jun-18 23:42
Re: 5 values for pi in GP here are 3 284 Sirfiroth 26-Jun-18 14:55
Re: 5 values for pi in GP here are 3 338 molder 26-Jun-18 21:18
Re: No pie for jacob 335 DavidK 26-Jun-18 10:34
Re: No pie for jacob 295 Sirfiroth 26-Jun-18 15:02
Re: No pie for jacob 293 DavidK 26-Jun-18 16:46
Re: No pie for jacob 302 Sirfiroth 26-Jun-18 17:12
Re: No pie for jacob 329 DavidK 26-Jun-18 18:58
Re: No pie for jacob 339 Sirfiroth 26-Jun-18 22:59
Re: No pie for jacob 288 DUNE 26-Jun-18 19:52
Re: No pie for jacob 294 DavidK 26-Jun-18 21:18
Re: No pie for jacob 296 Sirfiroth 26-Jun-18 23:10
Hard evidence for base 100 using egyptian maths 305 DavidK 27-Jun-18 05:37
Re: Hard evidence for base 100 using egyptian maths 333 drew 27-Jun-18 06:16
Re: Hard evidence for base 100 using egyptian maths 305 DavidK 27-Jun-18 10:25
Re: Hard evidence for base 100 using egyptian maths 317 drew 27-Jun-18 21:18
Re: Pi or no Pi ?????????????? 363 rodz111 25-Jun-18 17:48
Re: Pi or no Pi ?????????????? 337 Sirfiroth 25-Jun-18 19:54
Re: Pi or no Pi ?????????????? 306 rodz111 26-Jun-18 03:13
Re: Pi or no Pi ?????????????? 326 molder 26-Jun-18 03:19
Re: Pi or no Pi ?????????????? 324 rodz111 26-Jun-18 03:30
Re: Pi or no Pi ?????????????? 319 molder 26-Jun-18 21:52
Re: Pi or no Pi ?????????????? 368 rodz111 28-Jun-18 07:44
Re: Pi or no Pi ?????????????? 315 drew 28-Jun-18 09:56
Re: Pi or no Pi ?????????????? 345 rodz111 28-Jun-18 11:09
Re: Pi or no Pi ?????????????? 335 drew 28-Jun-18 17:13
Re: Pi or no Pi ?????????????? 350 DavidK 28-Jun-18 20:00
Tripping over museum rods 344 drew 28-Jun-18 23:52
Museum rods 311 drew 29-Jun-18 00:20
Re: Pi or no Pi ?????????????? 335 rodz111 29-Jun-18 00:37
You're as much as a complainer as anyone but you're not... 326 drew 29-Jun-18 01:24
Re: Pi or no Pi ?????????????? 398 rodz111 30-Jun-18 01:21
You down and dirty so-n-so 331 drew 27-Jun-18 05:29
Re: You down and dirty so-n-so 277 Sirfiroth 27-Jun-18 08:17
Re: You down and dirty so-n-so 273 drew 27-Jun-18 09:49
Re: You down and dirty so-n-so 411 Sirfiroth 27-Jun-18 17:12
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Re: You down and dirty so-n-so 266 DavidK 17-Jul-18 23:04
Re: You down and dirty so-n-so 289 Sirfiroth 17-Jul-18 23:16
Re: You down and dirty so-n-so 282 DavidK 17-Jul-18 23:20
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Re: Pi or no Pi ?????????????? 309 molder 19-Jul-18 11:21
Re: Pi or no Pi ?????????????? 353 Sirfiroth 19-Jul-18 12:05
Re: Pi or no Pi ?????????????? 478 spaceyhippie 19-Jul-18 23:57
Re: Pi or no Pi ?????????????? 332 DavidK 20-Jul-18 08:20
Re: Pi or no Pi ?????????????? 387 spaceyhippie 20-Jul-18 21:58
Re: Pi or no Pi ?????????????? 268 DavidK 22-Jul-18 09:41
Re: Pi or no Pi ?????????????? 373 spaceyhippie 23-Jul-18 02:15
Re: Pi or no Pi ?????????????? 306 DavidK 23-Jul-18 08:09
Re: Pi or no Pi ?????????????? 328 Sirfiroth 23-Jul-18 13:49
Re: Pi or no Pi ?????????????? 302 DavidK 23-Jul-18 22:23
Re: Pi or no Pi ?????????????? 534 Sirfiroth 23-Jul-18 23:52
Re: Pi or no Pi ?????????????? 320 DavidK 24-Jul-18 09:11
Re: Pi or no Pi ?????????????? 267 Sirfiroth 24-Jul-18 13:11
Re: Pi or no Pi ?????????????? 257 DavidK 27-Jul-18 06:13
Re: Pi or no Pi ?????????????? 294 Sirfiroth 27-Jul-18 15:45
Re: Pi or no Pi ?????????????? 356 spaceyhippie 24-Jul-18 02:44
Re: Pi or no Pi ?????????????? 366 DavidK 24-Jul-18 17:10
Re: Pi or no Pi ?????????????? 416 spaceyhippie 27-Jul-18 00:51
Re: Pi or no Pi ?????????????? 327 spaceyhippie 27-Jul-18 14:36
Re: Pi or no Pi ?????????????? 447 spaceyhippie 29-Jul-18 11:01
Re: Pi or no Pi ?????????????? 329 DavidK 06-Aug-18 19:15
Re: Pi or no Pi ?????????????? 302 DavidK 07-Aug-18 05:16
Re: Pi or no Pi ?????????????? 306 spaceyhippie 08-Aug-18 09:20
Re: Pi or no Pi ?????????????? 314 DavidK 08-Aug-18 09:39
Re: Pi or no Pi ?????????????? 342 spaceyhippie 09-Aug-18 02:32
Re: Pi or no Pi ?????????????? 370 DavidK 09-Aug-18 08:00
ROTFLMAO! 262 Sirfiroth 09-Aug-18 13:22
Re: ROTFLMAO! 270 DavidK 09-Aug-18 14:12
Re: ROTFLMAO! 355 Sirfiroth 09-Aug-18 14:28
Re: ROTFLMAO! 254 DavidK 09-Aug-18 14:49
Re: ROTFLMAO! 263 Sirfiroth 09-Aug-18 15:03
Re: ROTFLMAO! 277 DavidK 09-Aug-18 21:39
Re: ROTFLMAO! 301 Sirfiroth 10-Aug-18 02:06
Re: Pi or no Pi ?????????????? 314 spaceyhippie 09-Aug-18 20:40
Re: Pi or no Pi ?????????????? 371 DavidK 10-Aug-18 07:59
Re: Pi or no Pi ?????????????? 376 Steve Clayton 12-Aug-18 18:16
Re: Pi or no Pi ?????????????? 160 DavidK 27-Dec-19 23:13
Re: Pi or no Pi ?????????????? 147 Sirfiroth 28-Dec-19 03:46
Pi. All Pi. All The Time. 163 thinkitover 28-Dec-19 04:59
Re: Pi. All Pi. All The Time. 135 molder 28-Dec-19 10:35
Re: Pi or no Pi ?????????????? 134 DavidK 28-Dec-19 10:20
Re: Pi or no Pi ?????????????? 144 Sirfiroth 28-Dec-19 15:13
Re: Pi or no Pi ?????????????? 161 Thanos5150 28-Dec-19 16:30
Re: Pi or no Pi ?????????????? 151 thinkitover 28-Dec-19 21:49
Re: Pi or no Pi ?????????????? 149 Thanos5150 29-Dec-19 04:35
Re: Pi or no Pi ?????????????? 141 Sirfiroth 29-Dec-19 02:17
Re: Pi or no Pi ?????????????? 144 molder 29-Dec-19 04:14
Re: Pi or no Pi ?????????????? 138 Sirfiroth 29-Dec-19 12:51
Re: Pi or no Pi ?????????????? 137 molder 29-Dec-19 22:31
Re: Pi or no Pi ?????????????? 130 Sirfiroth 30-Dec-19 14:11
Re: Pi or no Pi ?????????????? 177 magisterchessmutt 30-Dec-19 15:16
Re: Pi or no Pi ?????????????? 136 Sirfiroth 31-Dec-19 03:33
Re: Pi or no Pi ?????????????? 180 magisterchessmutt 31-Dec-19 04:33
Re: Pi or no Pi ?????????????? 154 Sirfiroth 31-Dec-19 15:04
Re: Pi or no Pi ?????????????? 162 spaceyhippie 31-Dec-19 23:37
Re: Pi or no Pi ?????????????? 155 Thanos5150 29-Dec-19 04:29
Re: Pi or no Pi ?????????????? 142 DavidK 29-Dec-19 09:32
Re: Pi or no Pi ?????????????? 146 Sirfiroth 29-Dec-19 14:09
Re: Pi or no Pi ?????????????? 145 spaceyhippie 01-Jan-20 23:18
Re: Pi or no Pi ?????????????? 160 Sirfiroth 02-Jan-20 01:33
Pi vs Pudding 149 thinkitover 02-Jan-20 21:45
Re: Pi vs Pudding 141 spaceyhippie 03-Jan-20 00:06
Re: Pi vs Pudding 157 seasmith 03-Jan-20 00:24
Re: Pi vs Pudding 141 spaceyhippie 07-Jan-20 23:06
Re: Pi vs Pudding 183 seasmith 08-Jan-20 02:54
Re: Pi vs Pudding 149 Sirfiroth 03-Jan-20 03:36
Re: Pi vs Pudding 147 molder 03-Jan-20 06:56
Re: Pi vs Pudding 149 Sirfiroth 03-Jan-20 18:25
Re: Pi vs Pudding 144 spaceyhippie 04-Jan-20 00:02
LOL, now that was hilarious ! 143 Sirfiroth 04-Jan-20 05:51
Re: LOL, now that was hilarious ! 186 hendrik dirker 04-Jan-20 09:32
Re: LOL, now that was hilarious ! 132 spaceyhippie 04-Jan-20 23:37
Re: LOL, now that was hilarious ! 141 spaceyhippie 04-Jan-20 23:39
Re: Pi vs Pudding 160 molder 04-Jan-20 11:03
Re: Pi vs Pudding 149 Sirfiroth 05-Jan-20 20:11
Re: Pi vs Pudding 141 molder 06-Jan-20 02:55
Re: Pi vs Pudding 171 magisterchessmutt 06-Jan-20 02:58
Re: Pi vs Pudding 137 molder 06-Jan-20 05:26
Re: Pi vs Pudding 138 spaceyhippie 07-Jan-20 01:32
Re: Pi vs Pudding 128 DavidK 07-Jan-20 02:02
Re: Pi vs Pudding 142 thinkitover 06-Jan-20 06:13
Re: Pi vs Pudding 156 Sirfiroth 07-Jan-20 02:18
Re: Pi vs Pudding 126 DavidK 07-Jan-20 14:25
Re: Pi vs Pudding 138 Sirfiroth 07-Jan-20 15:16
Re: Pi vs Pudding 137 DavidK 07-Jan-20 19:03
Re: Pi vs Pudding 131 Sirfiroth 07-Jan-20 20:08
Re: Pi vs Pudding 131 DavidK 07-Jan-20 20:11
Re: Pi or no Pi ?????????????? 158 DavidK 28-Dec-19 11:21
Re: Pi or no Pi ?????????????? 153 engbren 28-Dec-19 12:34
Re: Pi or no Pi ?????????????? 153 Sirfiroth 28-Dec-19 15:55
Re: Pi or no Pi ?????????????? 141 engbren 29-Dec-19 01:14
Re: Pi or no Pi ?????????????? 140 Sirfiroth 30-Dec-19 16:52
Re: Pi or no Pi ?????????????? 143 engbren 30-Dec-19 22:23
Re: Pi or no Pi ?????????????? 200 magisterchessmutt 30-Dec-19 23:24
Re: Pi or no Pi ?????????????? 167 engbren 31-Dec-19 11:31
Re: Pi or no Pi ?????????????? 148 spaceyhippie 04-Jan-20 00:42


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