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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 ?????????????? 3249 Sirfiroth 06-Feb-18 03:26
Re: Pi or no Pi ?????????????? 581 drew 06-Feb-18 04:18
Re: Pi or no Pi ?????????????? 563 Sirfiroth 06-Feb-18 17:37
Re: Pi or no Pi ?????????????? 441 drew 06-Feb-18 23:32
Re: Pi or no Pi ???????????????? 500 Dr. Troglodyte 07-Feb-18 14:44
Re: Pi or no Pi ?????????????? 429 molder 08-Feb-18 05:09
Re: Pi or no Pi ?????????????? 427 Sirfiroth 08-Feb-18 06:43
Re: Pi or no Pi ?????????????? 428 DavidK 08-Feb-18 10:48
Re: Pi or no Pi ?????????????? 428 molder 08-Feb-18 11:56
linking egyptian Pi to imperial Pi 363 DavidK 08-Feb-18 15:10
Re: Pi or no Pi ?????????????? 366 DavidK 08-Feb-18 13:58
cubit of 20.25? 361 DavidK 08-Feb-18 14:12
where does Fibonacci Pi come from? 370 DavidK 08-Feb-18 14:49
Re: cubit of 20.25? 423 Sirfiroth 08-Feb-18 15:08
Re: cubit of 20.25? 387 DavidK 08-Feb-18 15:15
Re: cubit of 20.25? 384 molder 09-Feb-18 03:58
Mod Note > Off-Topic Posts 402 Dr. Troglodyte 09-Feb-18 16:38
Re: cubit of 20.25? 624 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 415 drew 09-Feb-18 00:33
Re: Oh...what a shame... 414 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 436 drew 09-Feb-18 06:02
Re: Oh...what a shame... 557 Sirfiroth 09-Feb-18 13:28
Re: Oh...what a shame... 422 DavidK 22-Jun-18 05:58
Re: Oh...what a shame... 360 drew 22-Jun-18 09:54
Re: Oh...what a shame... 468 Sirfiroth 22-Jun-18 13:32
Re: Oh...what a shame... 519 drew 22-Jun-18 22:27
Re: Oh...what a shame... 390 Sirfiroth 23-Jun-18 01:48
Re: well put 362 drew 23-Jun-18 08:08
To put it bluntly! 399 Sirfiroth 23-Jun-18 12:40
Re: well put 382 Manu 23-Jun-18 18:33
Re: extensions of numbers 340 drew 24-Jun-18 00:40
Re: extensions of numbers 392 Sirfiroth 24-Jun-18 04:50
Re: extensions of numbers 348 drew 24-Jun-18 08:36
Re: extensions of numbers 335 Sirfiroth 24-Jun-18 12:22
Re: extensions of numbers 344 drew 24-Jun-18 20:53
Re: extensions of numbers 344 Sirfiroth 25-Jun-18 16:06
Re: extensions of numbers 317 DavidK 25-Jun-18 16:13
Re: extensions of numbers 322 Sirfiroth 25-Jun-18 16:46
the primitive calculator 321 drew 25-Jun-18 23:23
Re: the primitive calculator 377 Sirfiroth 26-Jun-18 02:24
Re: the primitive calculator 308 drew 26-Jun-18 07:06
Mod Note > Duplicate Post Removed 485 Dr. Troglodyte 26-Jun-18 12:45
Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 378 rodz111 26-Jun-18 13:55
Re: Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 277 drew 27-Jun-18 05:18
Re: the primitive calculator 398 Sirfiroth 26-Jun-18 17:00
Re: the primitive calculator 341 drew 27-Jun-18 00:01
Re: the primitive calculator 362 Sirfiroth 27-Jun-18 00:18
Re: the primitive calculator 314 drew 27-Jun-18 01:56
Re: well put 298 cloister 24-Jun-18 09:43
Re: well put 341 Manu 24-Jun-18 12:59
Re: well put 331 cloister 24-Jun-18 18:14
Re: well put 462 cloister 29-Jun-18 08:48
Re: well put 316 drew 27-Jun-18 05:11
Re: Oh...what a shame... 382 Sirfiroth 22-Jun-18 12:21
Re: Oh...what a shame... 410 molder 23-Jun-18 00:24
Re: Oh...what a shame... 391 DavidK 23-Jun-18 21:06
Re: Oh...what a shame... 352 DavidK 24-Jun-18 07:41
Understanding the differences! 395 Sirfiroth 24-Jun-18 12:50
No pie for jacob 386 DavidK 24-Jun-18 08:54
Re: No pie for jacob 325 Sirfiroth 25-Jun-18 16:44
Re: No pie for jacob 348 DavidK 25-Jun-18 20:21
Re: No pie for jacob 359 Sirfiroth 25-Jun-18 23:19
Re: 5 values for pi in GP here are 3 311 molder 26-Jun-18 00:51
Re: what value for pi? 313 drew 26-Jun-18 14:11
Re: what value for pi? 363 molder 26-Jun-18 21:30
Re: what value for pi? 317 drew 26-Jun-18 23:42
Re: 5 values for pi in GP here are 3 301 Sirfiroth 26-Jun-18 14:55
Re: 5 values for pi in GP here are 3 358 molder 26-Jun-18 21:18
Re: No pie for jacob 356 DavidK 26-Jun-18 10:34
Re: No pie for jacob 310 Sirfiroth 26-Jun-18 15:02
Re: No pie for jacob 310 DavidK 26-Jun-18 16:46
Re: No pie for jacob 368 Sirfiroth 26-Jun-18 17:12
Re: No pie for jacob 347 DavidK 26-Jun-18 18:58
Re: No pie for jacob 357 Sirfiroth 26-Jun-18 22:59
Re: No pie for jacob 309 DUNE 26-Jun-18 19:52
Re: No pie for jacob 310 DavidK 26-Jun-18 21:18
Re: No pie for jacob 313 Sirfiroth 26-Jun-18 23:10
Hard evidence for base 100 using egyptian maths 324 DavidK 27-Jun-18 05:37
Re: Hard evidence for base 100 using egyptian maths 417 drew 27-Jun-18 06:16
Re: Hard evidence for base 100 using egyptian maths 323 DavidK 27-Jun-18 10:25
Re: Hard evidence for base 100 using egyptian maths 340 drew 27-Jun-18 21:18
Re: Pi or no Pi ?????????????? 384 rodz111 25-Jun-18 17:48
Re: Pi or no Pi ?????????????? 357 Sirfiroth 25-Jun-18 19:54
Re: Pi or no Pi ?????????????? 324 rodz111 26-Jun-18 03:13
Re: Pi or no Pi ?????????????? 342 molder 26-Jun-18 03:19
Re: Pi or no Pi ?????????????? 342 rodz111 26-Jun-18 03:30
Re: Pi or no Pi ?????????????? 338 molder 26-Jun-18 21:52
Re: Pi or no Pi ?????????????? 386 rodz111 28-Jun-18 07:44
Re: Pi or no Pi ?????????????? 336 drew 28-Jun-18 09:56
Re: Pi or no Pi ?????????????? 364 rodz111 28-Jun-18 11:09
Re: Pi or no Pi ?????????????? 442 drew 28-Jun-18 17:13
Re: Pi or no Pi ?????????????? 370 DavidK 28-Jun-18 20:00
Tripping over museum rods 362 drew 28-Jun-18 23:52
Museum rods 330 drew 29-Jun-18 00:20
Re: Pi or no Pi ?????????????? 357 rodz111 29-Jun-18 00:37
You're as much as a complainer as anyone but you're not... 346 drew 29-Jun-18 01:24
Re: Pi or no Pi ?????????????? 418 rodz111 30-Jun-18 01:21
You down and dirty so-n-so 348 drew 27-Jun-18 05:29
Re: You down and dirty so-n-so 294 Sirfiroth 27-Jun-18 08:17
Re: You down and dirty so-n-so 291 drew 27-Jun-18 09:49
Re: You down and dirty so-n-so 429 Sirfiroth 27-Jun-18 17:12
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Re: You down and dirty so-n-so 283 DavidK 17-Jul-18 23:04
Re: You down and dirty so-n-so 306 Sirfiroth 17-Jul-18 23:16
Re: You down and dirty so-n-so 301 DavidK 17-Jul-18 23:20
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Re: Pi or no Pi ?????????????? 327 molder 19-Jul-18 11:21
Re: Pi or no Pi ?????????????? 373 Sirfiroth 19-Jul-18 12:05
Re: Pi or no Pi ?????????????? 497 spaceyhippie 19-Jul-18 23:57
Re: Pi or no Pi ?????????????? 352 DavidK 20-Jul-18 08:20
Re: Pi or no Pi ?????????????? 405 spaceyhippie 20-Jul-18 21:58
Re: Pi or no Pi ?????????????? 286 DavidK 22-Jul-18 09:41
Re: Pi or no Pi ?????????????? 390 spaceyhippie 23-Jul-18 02:15
Re: Pi or no Pi ?????????????? 323 DavidK 23-Jul-18 08:09
Re: Pi or no Pi ?????????????? 345 Sirfiroth 23-Jul-18 13:49
Re: Pi or no Pi ?????????????? 319 DavidK 23-Jul-18 22:23
Re: Pi or no Pi ?????????????? 741 Sirfiroth 23-Jul-18 23:52
Re: Pi or no Pi ?????????????? 339 DavidK 24-Jul-18 09:11
Re: Pi or no Pi ?????????????? 298 Sirfiroth 24-Jul-18 13:11
Re: Pi or no Pi ?????????????? 274 DavidK 27-Jul-18 06:13
Re: Pi or no Pi ?????????????? 312 Sirfiroth 27-Jul-18 15:45
Re: Pi or no Pi ?????????????? 384 spaceyhippie 24-Jul-18 02:44
Re: Pi or no Pi ?????????????? 384 DavidK 24-Jul-18 17:10
Re: Pi or no Pi ?????????????? 432 spaceyhippie 27-Jul-18 00:51
Re: Pi or no Pi ?????????????? 345 spaceyhippie 27-Jul-18 14:36
Re: Pi or no Pi ?????????????? 463 spaceyhippie 29-Jul-18 11:01
Re: Pi or no Pi ?????????????? 351 DavidK 06-Aug-18 19:15
Re: Pi or no Pi ?????????????? 324 DavidK 07-Aug-18 05:16
Re: Pi or no Pi ?????????????? 323 spaceyhippie 08-Aug-18 09:20
Re: Pi or no Pi ?????????????? 331 DavidK 08-Aug-18 09:39
Re: Pi or no Pi ?????????????? 359 spaceyhippie 09-Aug-18 02:32
Re: Pi or no Pi ?????????????? 394 DavidK 09-Aug-18 08:00
ROTFLMAO! 280 Sirfiroth 09-Aug-18 13:22
Re: ROTFLMAO! 286 DavidK 09-Aug-18 14:12
Re: ROTFLMAO! 428 Sirfiroth 09-Aug-18 14:28
Re: ROTFLMAO! 272 DavidK 09-Aug-18 14:49
Re: ROTFLMAO! 279 Sirfiroth 09-Aug-18 15:03
Re: ROTFLMAO! 293 DavidK 09-Aug-18 21:39
Re: ROTFLMAO! 318 Sirfiroth 10-Aug-18 02:06
Re: Pi or no Pi ?????????????? 334 spaceyhippie 09-Aug-18 20:40
Re: Pi or no Pi ?????????????? 386 DavidK 10-Aug-18 07:59
Re: Pi or no Pi ?????????????? 393 Steve Clayton 12-Aug-18 18:16
Re: Pi or no Pi ?????????????? 181 DavidK 27-Dec-19 23:13
Re: Pi or no Pi ?????????????? 164 Sirfiroth 28-Dec-19 03:46
Pi. All Pi. All The Time. 178 thinkitover 28-Dec-19 04:59
Re: Pi. All Pi. All The Time. 151 molder 28-Dec-19 10:35
Re: Pi or no Pi ?????????????? 153 DavidK 28-Dec-19 10:20
Re: Pi or no Pi ?????????????? 163 Sirfiroth 28-Dec-19 15:13
Re: Pi or no Pi ?????????????? 178 Thanos5150 28-Dec-19 16:30
Re: Pi or no Pi ?????????????? 167 thinkitover 28-Dec-19 21:49
Re: Pi or no Pi ?????????????? 172 Thanos5150 29-Dec-19 04:35
Re: Pi or no Pi ?????????????? 158 Sirfiroth 29-Dec-19 02:17
Re: Pi or no Pi ?????????????? 160 molder 29-Dec-19 04:14
Re: Pi or no Pi ?????????????? 154 Sirfiroth 29-Dec-19 12:51
Re: Pi or no Pi ?????????????? 153 molder 29-Dec-19 22:31
Re: Pi or no Pi ?????????????? 145 Sirfiroth 30-Dec-19 14:11
Re: Pi or no Pi ?????????????? 193 magisterchessmutt 30-Dec-19 15:16
Re: Pi or no Pi ?????????????? 153 Sirfiroth 31-Dec-19 03:33
Re: Pi or no Pi ?????????????? 201 magisterchessmutt 31-Dec-19 04:33
Re: Pi or no Pi ?????????????? 172 Sirfiroth 31-Dec-19 15:04
Re: Pi or no Pi ?????????????? 179 spaceyhippie 31-Dec-19 23:37
Re: Pi or no Pi ?????????????? 172 Thanos5150 29-Dec-19 04:29
Re: Pi or no Pi ?????????????? 159 DavidK 29-Dec-19 09:32
Re: Pi or no Pi ?????????????? 165 Sirfiroth 29-Dec-19 14:09
Re: Pi or no Pi ?????????????? 161 spaceyhippie 01-Jan-20 23:18
Re: Pi or no Pi ?????????????? 176 Sirfiroth 02-Jan-20 01:33
Pi vs Pudding 173 thinkitover 02-Jan-20 21:45
Re: Pi vs Pudding 157 spaceyhippie 03-Jan-20 00:06
Re: Pi vs Pudding 175 seasmith 03-Jan-20 00:24
Re: Pi vs Pudding 158 spaceyhippie 07-Jan-20 23:06
Re: Pi vs Pudding 204 seasmith 08-Jan-20 02:54
Re: Pi vs Pudding 165 Sirfiroth 03-Jan-20 03:36
Re: Pi vs Pudding 167 molder 03-Jan-20 06:56
Re: Pi vs Pudding 166 Sirfiroth 03-Jan-20 18:25
Re: Pi vs Pudding 161 spaceyhippie 04-Jan-20 00:02
LOL, now that was hilarious ! 159 Sirfiroth 04-Jan-20 05:51
Re: LOL, now that was hilarious ! 214 hendrik dirker 04-Jan-20 09:32
Re: LOL, now that was hilarious ! 149 spaceyhippie 04-Jan-20 23:37
Re: LOL, now that was hilarious ! 160 spaceyhippie 04-Jan-20 23:39
Re: Pi vs Pudding 177 molder 04-Jan-20 11:03
Re: Pi vs Pudding 168 Sirfiroth 05-Jan-20 20:11
Re: Pi vs Pudding 157 molder 06-Jan-20 02:55
Re: Pi vs Pudding 187 magisterchessmutt 06-Jan-20 02:58
Re: Pi vs Pudding 154 molder 06-Jan-20 05:26
Re: Pi vs Pudding 156 spaceyhippie 07-Jan-20 01:32
Re: Pi vs Pudding 144 DavidK 07-Jan-20 02:02
Re: Pi vs Pudding 160 thinkitover 06-Jan-20 06:13
Re: Pi vs Pudding 172 Sirfiroth 07-Jan-20 02:18
Re: Pi vs Pudding 144 DavidK 07-Jan-20 14:25
Re: Pi vs Pudding 156 Sirfiroth 07-Jan-20 15:16
Re: Pi vs Pudding 154 DavidK 07-Jan-20 19:03
Re: Pi vs Pudding 147 Sirfiroth 07-Jan-20 20:08
Re: Pi vs Pudding 147 DavidK 07-Jan-20 20:11
Re: Pi or no Pi ?????????????? 173 DavidK 28-Dec-19 11:21
Re: Pi or no Pi ?????????????? 169 engbren 28-Dec-19 12:34
Re: Pi or no Pi ?????????????? 168 Sirfiroth 28-Dec-19 15:55
Re: Pi or no Pi ?????????????? 157 engbren 29-Dec-19 01:14
Re: Pi or no Pi ?????????????? 158 Sirfiroth 30-Dec-19 16:52
Re: Pi or no Pi ?????????????? 161 engbren 30-Dec-19 22:23
Re: Pi or no Pi ?????????????? 217 magisterchessmutt 30-Dec-19 23:24
Re: Pi or no Pi ?????????????? 183 engbren 31-Dec-19 11:31
Re: Pi or no Pi ?????????????? 164 spaceyhippie 04-Jan-20 00:42


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