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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 ?????????????? 3086 Sirfiroth 06-Feb-18 03:26
Re: Pi or no Pi ?????????????? 493 drew 06-Feb-18 04:18
Re: Pi or no Pi ?????????????? 456 Sirfiroth 06-Feb-18 17:37
Re: Pi or no Pi ?????????????? 361 drew 06-Feb-18 23:32
Re: Pi or no Pi ???????????????? 419 Dr. Troglodyte 07-Feb-18 14:44
Re: Pi or no Pi ?????????????? 337 molder 08-Feb-18 05:09
Re: Pi or no Pi ?????????????? 346 Sirfiroth 08-Feb-18 06:43
Re: Pi or no Pi ?????????????? 340 DavidK 08-Feb-18 10:48
Re: Pi or no Pi ?????????????? 335 molder 08-Feb-18 11:56
linking egyptian Pi to imperial Pi 284 DavidK 08-Feb-18 15:10
Re: Pi or no Pi ?????????????? 287 DavidK 08-Feb-18 13:58
cubit of 20.25? 249 DavidK 08-Feb-18 14:12
where does Fibonacci Pi come from? 274 DavidK 08-Feb-18 14:49
Re: cubit of 20.25? 340 Sirfiroth 08-Feb-18 15:08
Re: cubit of 20.25? 298 DavidK 08-Feb-18 15:15
Re: cubit of 20.25? 296 molder 09-Feb-18 03:58
Mod Note > Off-Topic Posts 318 Dr. Troglodyte 09-Feb-18 16:38
Re: cubit of 20.25? 445 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 331 drew 09-Feb-18 00:33
Re: Oh...what a shame... 331 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 355 drew 09-Feb-18 06:02
Re: Oh...what a shame... 344 Sirfiroth 09-Feb-18 13:28
Re: Oh...what a shame... 334 DavidK 22-Jun-18 05:58
Re: Oh...what a shame... 278 drew 22-Jun-18 09:54
Re: Oh...what a shame... 340 Sirfiroth 22-Jun-18 13:32
Re: Oh...what a shame... 315 drew 22-Jun-18 22:27
Re: Oh...what a shame... 302 Sirfiroth 23-Jun-18 01:48
Re: well put 277 drew 23-Jun-18 08:08
To put it bluntly! 314 Sirfiroth 23-Jun-18 12:40
Re: well put 299 Manu 23-Jun-18 18:33
Re: extensions of numbers 250 drew 24-Jun-18 00:40
Re: extensions of numbers 306 Sirfiroth 24-Jun-18 04:50
Re: extensions of numbers 254 drew 24-Jun-18 08:36
Re: extensions of numbers 249 Sirfiroth 24-Jun-18 12:22
Re: extensions of numbers 257 drew 24-Jun-18 20:53
Re: extensions of numbers 257 Sirfiroth 25-Jun-18 16:06
Re: extensions of numbers 238 DavidK 25-Jun-18 16:13
Re: extensions of numbers 243 Sirfiroth 25-Jun-18 16:46
the primitive calculator 242 drew 25-Jun-18 23:23
Re: the primitive calculator 291 Sirfiroth 26-Jun-18 02:24
Re: the primitive calculator 224 drew 26-Jun-18 07:06
Mod Note > Duplicate Post Removed 255 Dr. Troglodyte 26-Jun-18 12:45
Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 273 rodz111 26-Jun-18 13:55
Re: Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 203 drew 27-Jun-18 05:18
Re: the primitive calculator 262 Sirfiroth 26-Jun-18 17:00
Re: the primitive calculator 260 drew 27-Jun-18 00:01
Re: the primitive calculator 246 Sirfiroth 27-Jun-18 00:18
Re: the primitive calculator 225 drew 27-Jun-18 01:56
Re: well put 223 cloister 24-Jun-18 09:43
Re: well put 254 Manu 24-Jun-18 12:59
Re: well put 248 cloister 24-Jun-18 18:14
Re: well put 297 cloister 29-Jun-18 08:48
Re: well put 232 drew 27-Jun-18 05:11
Re: Oh...what a shame... 300 Sirfiroth 22-Jun-18 12:21
Re: Oh...what a shame... 321 molder 23-Jun-18 00:24
Re: Oh...what a shame... 306 DavidK 23-Jun-18 21:06
Re: Oh...what a shame... 259 DavidK 24-Jun-18 07:41
Understanding the differences! 256 Sirfiroth 24-Jun-18 12:50
No pie for jacob 303 DavidK 24-Jun-18 08:54
Re: No pie for jacob 249 Sirfiroth 25-Jun-18 16:44
Re: No pie for jacob 270 DavidK 25-Jun-18 20:21
Re: No pie for jacob 252 Sirfiroth 25-Jun-18 23:19
Re: 5 values for pi in GP here are 3 236 molder 26-Jun-18 00:51
Re: what value for pi? 234 drew 26-Jun-18 14:11
Re: what value for pi? 272 molder 26-Jun-18 21:30
Re: what value for pi? 225 drew 26-Jun-18 23:42
Re: 5 values for pi in GP here are 3 225 Sirfiroth 26-Jun-18 14:55
Re: 5 values for pi in GP here are 3 272 molder 26-Jun-18 21:18
Re: No pie for jacob 262 DavidK 26-Jun-18 10:34
Re: No pie for jacob 228 Sirfiroth 26-Jun-18 15:02
Re: No pie for jacob 226 DavidK 26-Jun-18 16:46
Re: No pie for jacob 233 Sirfiroth 26-Jun-18 17:12
Re: No pie for jacob 249 DavidK 26-Jun-18 18:58
Re: No pie for jacob 271 Sirfiroth 26-Jun-18 22:59
Re: No pie for jacob 227 DUNE 26-Jun-18 19:52
Re: No pie for jacob 219 DavidK 26-Jun-18 21:18
Re: No pie for jacob 233 Sirfiroth 26-Jun-18 23:10
Hard evidence for base 100 using egyptian maths 243 DavidK 27-Jun-18 05:37
Re: Hard evidence for base 100 using egyptian maths 269 drew 27-Jun-18 06:16
Re: Hard evidence for base 100 using egyptian maths 246 DavidK 27-Jun-18 10:25
Re: Hard evidence for base 100 using egyptian maths 250 drew 27-Jun-18 21:18
Re: Pi or no Pi ?????????????? 277 rodz111 25-Jun-18 17:48
Re: Pi or no Pi ?????????????? 275 Sirfiroth 25-Jun-18 19:54
Re: Pi or no Pi ?????????????? 232 rodz111 26-Jun-18 03:13
Re: Pi or no Pi ?????????????? 266 molder 26-Jun-18 03:19
Re: Pi or no Pi ?????????????? 254 rodz111 26-Jun-18 03:30
Re: Pi or no Pi ?????????????? 249 molder 26-Jun-18 21:52
Re: Pi or no Pi ?????????????? 309 rodz111 28-Jun-18 07:44
Re: Pi or no Pi ?????????????? 246 drew 28-Jun-18 09:56
Re: Pi or no Pi ?????????????? 279 rodz111 28-Jun-18 11:09
Re: Pi or no Pi ?????????????? 262 drew 28-Jun-18 17:13
Re: Pi or no Pi ?????????????? 278 DavidK 28-Jun-18 20:00
Tripping over museum rods 269 drew 28-Jun-18 23:52
Museum rods 246 drew 29-Jun-18 00:20
Re: Pi or no Pi ?????????????? 267 rodz111 29-Jun-18 00:37
You're as much as a complainer as anyone but you're not... 255 drew 29-Jun-18 01:24
Re: Pi or no Pi ?????????????? 322 rodz111 30-Jun-18 01:21
You down and dirty so-n-so 266 drew 27-Jun-18 05:29
Re: You down and dirty so-n-so 210 Sirfiroth 27-Jun-18 08:17
Re: You down and dirty so-n-so 214 drew 27-Jun-18 09:49
Re: You down and dirty so-n-so 331 Sirfiroth 27-Jun-18 17:12
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Re: You down and dirty so-n-so 201 DavidK 17-Jul-18 23:04
Re: You down and dirty so-n-so 229 Sirfiroth 17-Jul-18 23:16
Re: You down and dirty so-n-so 223 DavidK 17-Jul-18 23:20
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Re: Pi or no Pi ?????????????? 246 molder 19-Jul-18 11:21
Re: Pi or no Pi ?????????????? 291 Sirfiroth 19-Jul-18 12:05
Re: Pi or no Pi ?????????????? 399 spaceyhippie 19-Jul-18 23:57
Re: Pi or no Pi ?????????????? 253 DavidK 20-Jul-18 08:20
Re: Pi or no Pi ?????????????? 317 spaceyhippie 20-Jul-18 21:58
Re: Pi or no Pi ?????????????? 210 DavidK 22-Jul-18 09:41
Re: Pi or no Pi ?????????????? 304 spaceyhippie 23-Jul-18 02:15
Re: Pi or no Pi ?????????????? 246 DavidK 23-Jul-18 08:09
Re: Pi or no Pi ?????????????? 260 Sirfiroth 23-Jul-18 13:49
Re: Pi or no Pi ?????????????? 238 DavidK 23-Jul-18 22:23
Re: Pi or no Pi ?????????????? 261 Sirfiroth 23-Jul-18 23:52
Re: Pi or no Pi ?????????????? 250 DavidK 24-Jul-18 09:11
Re: Pi or no Pi ?????????????? 207 Sirfiroth 24-Jul-18 13:11
Re: Pi or no Pi ?????????????? 190 DavidK 27-Jul-18 06:13
Re: Pi or no Pi ?????????????? 233 Sirfiroth 27-Jul-18 15:45
Re: Pi or no Pi ?????????????? 298 spaceyhippie 24-Jul-18 02:44
Re: Pi or no Pi ?????????????? 291 DavidK 24-Jul-18 17:10
Re: Pi or no Pi ?????????????? 337 spaceyhippie 27-Jul-18 00:51
Re: Pi or no Pi ?????????????? 274 spaceyhippie 27-Jul-18 14:36
Re: Pi or no Pi ?????????????? 375 spaceyhippie 29-Jul-18 11:01
Re: Pi or no Pi ?????????????? 262 DavidK 06-Aug-18 19:15
Re: Pi or no Pi ?????????????? 241 DavidK 07-Aug-18 05:16
Re: Pi or no Pi ?????????????? 249 spaceyhippie 08-Aug-18 09:20
Re: Pi or no Pi ?????????????? 249 DavidK 08-Aug-18 09:39
Re: Pi or no Pi ?????????????? 289 spaceyhippie 09-Aug-18 02:32
Re: Pi or no Pi ?????????????? 304 DavidK 09-Aug-18 08:00
ROTFLMAO! 206 Sirfiroth 09-Aug-18 13:22
Re: ROTFLMAO! 206 DavidK 09-Aug-18 14:12
Re: ROTFLMAO! 228 Sirfiroth 09-Aug-18 14:28
Re: ROTFLMAO! 196 DavidK 09-Aug-18 14:49
Re: ROTFLMAO! 202 Sirfiroth 09-Aug-18 15:03
Re: ROTFLMAO! 221 DavidK 09-Aug-18 21:39
Re: ROTFLMAO! 238 Sirfiroth 10-Aug-18 02:06
Re: Pi or no Pi ?????????????? 249 spaceyhippie 09-Aug-18 20:40
Re: Pi or no Pi ?????????????? 310 DavidK 10-Aug-18 07:59
Re: Pi or no Pi ?????????????? 316 Steve Clayton 12-Aug-18 18:16
Re: Pi or no Pi ?????????????? 106 DavidK 27-Dec-19 23:13
Re: Pi or no Pi ?????????????? 98 Sirfiroth 28-Dec-19 03:46
Pi. All Pi. All The Time. 106 thinkitover 28-Dec-19 04:59
Re: Pi. All Pi. All The Time. 86 molder 28-Dec-19 10:35
Re: Pi or no Pi ?????????????? 83 DavidK 28-Dec-19 10:20
Re: Pi or no Pi ?????????????? 95 Sirfiroth 28-Dec-19 15:13
Re: Pi or no Pi ?????????????? 108 Thanos5150 28-Dec-19 16:30
Re: Pi or no Pi ?????????????? 96 thinkitover 28-Dec-19 21:49
Re: Pi or no Pi ?????????????? 93 Thanos5150 29-Dec-19 04:35
Re: Pi or no Pi ?????????????? 95 Sirfiroth 29-Dec-19 02:17
Re: Pi or no Pi ?????????????? 85 molder 29-Dec-19 04:14
Re: Pi or no Pi ?????????????? 94 Sirfiroth 29-Dec-19 12:51
Re: Pi or no Pi ?????????????? 79 molder 29-Dec-19 22:31
Re: Pi or no Pi ?????????????? 82 Sirfiroth 30-Dec-19 14:11
Re: Pi or no Pi ?????????????? 115 magisterchessmutt 30-Dec-19 15:16
Re: Pi or no Pi ?????????????? 82 Sirfiroth 31-Dec-19 03:33
Re: Pi or no Pi ?????????????? 116 magisterchessmutt 31-Dec-19 04:33
Re: Pi or no Pi ?????????????? 95 Sirfiroth 31-Dec-19 15:04
Re: Pi or no Pi ?????????????? 97 spaceyhippie 31-Dec-19 23:37
Re: Pi or no Pi ?????????????? 98 Thanos5150 29-Dec-19 04:29
Re: Pi or no Pi ?????????????? 91 DavidK 29-Dec-19 09:32
Re: Pi or no Pi ?????????????? 97 Sirfiroth 29-Dec-19 14:09
Re: Pi or no Pi ?????????????? 86 spaceyhippie 01-Jan-20 23:18
Re: Pi or no Pi ?????????????? 105 Sirfiroth 02-Jan-20 01:33
Pi vs Pudding 102 thinkitover 02-Jan-20 21:45
Re: Pi vs Pudding 83 spaceyhippie 03-Jan-20 00:06
Re: Pi vs Pudding 91 seasmith 03-Jan-20 00:24
Re: Pi vs Pudding 87 spaceyhippie 07-Jan-20 23:06
Re: Pi vs Pudding 124 seasmith 08-Jan-20 02:54
Re: Pi vs Pudding 92 Sirfiroth 03-Jan-20 03:36
Re: Pi vs Pudding 88 molder 03-Jan-20 06:56
Re: Pi vs Pudding 93 Sirfiroth 03-Jan-20 18:25
Re: Pi vs Pudding 85 spaceyhippie 04-Jan-20 00:02
LOL, now that was hilarious ! 86 Sirfiroth 04-Jan-20 05:51
Re: LOL, now that was hilarious ! 104 hendrik dirker 04-Jan-20 09:32
Re: LOL, now that was hilarious ! 77 spaceyhippie 04-Jan-20 23:37
Re: LOL, now that was hilarious ! 87 spaceyhippie 04-Jan-20 23:39
Re: Pi vs Pudding 106 molder 04-Jan-20 11:03
Re: Pi vs Pudding 94 Sirfiroth 05-Jan-20 20:11
Re: Pi vs Pudding 79 molder 06-Jan-20 02:55
Re: Pi vs Pudding 113 magisterchessmutt 06-Jan-20 02:58
Re: Pi vs Pudding 80 molder 06-Jan-20 05:26
Re: Pi vs Pudding 86 spaceyhippie 07-Jan-20 01:32
Re: Pi vs Pudding 76 DavidK 07-Jan-20 02:02
Re: Pi vs Pudding 94 thinkitover 06-Jan-20 06:13
Re: Pi vs Pudding 99 Sirfiroth 07-Jan-20 02:18
Re: Pi vs Pudding 74 DavidK 07-Jan-20 14:25
Re: Pi vs Pudding 84 Sirfiroth 07-Jan-20 15:16
Re: Pi vs Pudding 87 DavidK 07-Jan-20 19:03
Re: Pi vs Pudding 76 Sirfiroth 07-Jan-20 20:08
Re: Pi vs Pudding 79 DavidK 07-Jan-20 20:11
Re: Pi or no Pi ?????????????? 103 DavidK 28-Dec-19 11:21
Re: Pi or no Pi ?????????????? 100 engbren 28-Dec-19 12:34
Re: Pi or no Pi ?????????????? 105 Sirfiroth 28-Dec-19 15:55
Re: Pi or no Pi ?????????????? 91 engbren 29-Dec-19 01:14
Re: Pi or no Pi ?????????????? 91 Sirfiroth 30-Dec-19 16:52
Re: Pi or no Pi ?????????????? 92 engbren 30-Dec-19 22:23
Re: Pi or no Pi ?????????????? 140 magisterchessmutt 30-Dec-19 23:24
Re: Pi or no Pi ?????????????? 108 engbren 31-Dec-19 11:31
Re: Pi or no Pi ?????????????? 98 spaceyhippie 04-Jan-20 00:42


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