Mysteries :  The Official GrahamHancock.com forums
For serious discussion of the controversies, approaches and enigmas surrounding the origins and development of the human species and of human civilization. (NB: for more ‘out there’ posts we point you in the direction of the ‘Paranormal & Supernatural’ Message Board). 
Welcome! Log InRegister
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

Options: ReplyQuote


Subject Views Written By Posted
Pi or no Pi ?????????????? 3026 Sirfiroth 06-Feb-18 03:26
Re: Pi or no Pi ?????????????? 458 drew 06-Feb-18 04:18
Re: Pi or no Pi ?????????????? 430 Sirfiroth 06-Feb-18 17:37
Re: Pi or no Pi ?????????????? 337 drew 06-Feb-18 23:32
Re: Pi or no Pi ???????????????? 390 Dr. Troglodyte 07-Feb-18 14:44
Re: Pi or no Pi ?????????????? 310 molder 08-Feb-18 05:09
Re: Pi or no Pi ?????????????? 316 Sirfiroth 08-Feb-18 06:43
Re: Pi or no Pi ?????????????? 310 DavidK 08-Feb-18 10:48
Re: Pi or no Pi ?????????????? 306 molder 08-Feb-18 11:56
linking egyptian Pi to imperial Pi 253 DavidK 08-Feb-18 15:10
Re: Pi or no Pi ?????????????? 261 DavidK 08-Feb-18 13:58
cubit of 20.25? 224 DavidK 08-Feb-18 14:12
where does Fibonacci Pi come from? 250 DavidK 08-Feb-18 14:49
Re: cubit of 20.25? 310 Sirfiroth 08-Feb-18 15:08
Re: cubit of 20.25? 271 DavidK 08-Feb-18 15:15
Re: cubit of 20.25? 269 molder 09-Feb-18 03:58
Mod Note > Off-Topic Posts 285 Dr. Troglodyte 09-Feb-18 16:38
Re: cubit of 20.25? 399 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 304 drew 09-Feb-18 00:33
Re: Oh...what a shame... 302 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 327 drew 09-Feb-18 06:02
Re: Oh...what a shame... 317 Sirfiroth 09-Feb-18 13:28
Re: Oh...what a shame... 303 DavidK 22-Jun-18 05:58
Re: Oh...what a shame... 251 drew 22-Jun-18 09:54
Re: Oh...what a shame... 312 Sirfiroth 22-Jun-18 13:32
Re: Oh...what a shame... 285 drew 22-Jun-18 22:27
Re: Oh...what a shame... 275 Sirfiroth 23-Jun-18 01:48
Re: well put 252 drew 23-Jun-18 08:08
To put it bluntly! 290 Sirfiroth 23-Jun-18 12:40
Re: well put 274 Manu 23-Jun-18 18:33
Re: extensions of numbers 225 drew 24-Jun-18 00:40
Re: extensions of numbers 283 Sirfiroth 24-Jun-18 04:50
Re: extensions of numbers 216 drew 24-Jun-18 08:36
Re: extensions of numbers 221 Sirfiroth 24-Jun-18 12:22
Re: extensions of numbers 226 drew 24-Jun-18 20:53
Re: extensions of numbers 227 Sirfiroth 25-Jun-18 16:06
Re: extensions of numbers 209 DavidK 25-Jun-18 16:13
Re: extensions of numbers 210 Sirfiroth 25-Jun-18 16:46
the primitive calculator 216 drew 25-Jun-18 23:23
Re: the primitive calculator 257 Sirfiroth 26-Jun-18 02:24
Re: the primitive calculator 199 drew 26-Jun-18 07:06
Mod Note > Duplicate Post Removed 218 Dr. Troglodyte 26-Jun-18 12:45
Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 245 rodz111 26-Jun-18 13:55
Re: Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 180 drew 27-Jun-18 05:18
Re: the primitive calculator 229 Sirfiroth 26-Jun-18 17:00
Re: the primitive calculator 233 drew 27-Jun-18 00:01
Re: the primitive calculator 219 Sirfiroth 27-Jun-18 00:18
Re: the primitive calculator 201 drew 27-Jun-18 01:56
Re: well put 197 cloister 24-Jun-18 09:43
Re: well put 226 Manu 24-Jun-18 12:59
Re: well put 217 cloister 24-Jun-18 18:14
Re: well put 261 cloister 29-Jun-18 08:48
Re: well put 206 drew 27-Jun-18 05:11
Re: Oh...what a shame... 274 Sirfiroth 22-Jun-18 12:21
Re: Oh...what a shame... 291 molder 23-Jun-18 00:24
Re: Oh...what a shame... 278 DavidK 23-Jun-18 21:06
Re: Oh...what a shame... 228 DavidK 24-Jun-18 07:41
Understanding the differences! 222 Sirfiroth 24-Jun-18 12:50
No pie for jacob 275 DavidK 24-Jun-18 08:54
Re: No pie for jacob 224 Sirfiroth 25-Jun-18 16:44
Re: No pie for jacob 242 DavidK 25-Jun-18 20:21
Re: No pie for jacob 221 Sirfiroth 25-Jun-18 23:19
Re: 5 values for pi in GP here are 3 212 molder 26-Jun-18 00:51
Re: what value for pi? 208 drew 26-Jun-18 14:11
Re: what value for pi? 239 molder 26-Jun-18 21:30
Re: what value for pi? 197 drew 26-Jun-18 23:42
Re: 5 values for pi in GP here are 3 197 Sirfiroth 26-Jun-18 14:55
Re: 5 values for pi in GP here are 3 247 molder 26-Jun-18 21:18
Re: No pie for jacob 231 DavidK 26-Jun-18 10:34
Re: No pie for jacob 196 Sirfiroth 26-Jun-18 15:02
Re: No pie for jacob 195 DavidK 26-Jun-18 16:46
Re: No pie for jacob 208 Sirfiroth 26-Jun-18 17:12
Re: No pie for jacob 212 DavidK 26-Jun-18 18:58
Re: No pie for jacob 232 Sirfiroth 26-Jun-18 22:59
Re: No pie for jacob 201 DUNE 26-Jun-18 19:52
Re: No pie for jacob 192 DavidK 26-Jun-18 21:18
Re: No pie for jacob 209 Sirfiroth 26-Jun-18 23:10
Hard evidence for base 100 using egyptian maths 218 DavidK 27-Jun-18 05:37
Re: Hard evidence for base 100 using egyptian maths 242 drew 27-Jun-18 06:16
Re: Hard evidence for base 100 using egyptian maths 219 DavidK 27-Jun-18 10:25
Re: Hard evidence for base 100 using egyptian maths 225 drew 27-Jun-18 21:18
Re: Pi or no Pi ?????????????? 244 rodz111 25-Jun-18 17:48
Re: Pi or no Pi ?????????????? 250 Sirfiroth 25-Jun-18 19:54
Re: Pi or no Pi ?????????????? 205 rodz111 26-Jun-18 03:13
Re: Pi or no Pi ?????????????? 236 molder 26-Jun-18 03:19
Re: Pi or no Pi ?????????????? 228 rodz111 26-Jun-18 03:30
Re: Pi or no Pi ?????????????? 224 molder 26-Jun-18 21:52
Re: Pi or no Pi ?????????????? 268 rodz111 28-Jun-18 07:44
Re: Pi or no Pi ?????????????? 217 drew 28-Jun-18 09:56
Re: Pi or no Pi ?????????????? 251 rodz111 28-Jun-18 11:09
Re: Pi or no Pi ?????????????? 227 drew 28-Jun-18 17:13
Re: Pi or no Pi ?????????????? 253 DavidK 28-Jun-18 20:00
Tripping over museum rods 240 drew 28-Jun-18 23:52
Museum rods 217 drew 29-Jun-18 00:20
Re: Pi or no Pi ?????????????? 237 rodz111 29-Jun-18 00:37
You're as much as a complainer as anyone but you're not... 230 drew 29-Jun-18 01:24
Re: Pi or no Pi ?????????????? 293 rodz111 30-Jun-18 01:21
You down and dirty so-n-so 237 drew 27-Jun-18 05:29
Re: You down and dirty so-n-so 182 Sirfiroth 27-Jun-18 08:17
Re: You down and dirty so-n-so 192 drew 27-Jun-18 09:49
Re: You down and dirty so-n-so 297 Sirfiroth 27-Jun-18 17:12
The math or the pyramid? 251 drew 27-Jun-18 20:46
Re: You down and dirty so-n-so 173 DavidK 17-Jul-18 23:04
Re: You down and dirty so-n-so 197 Sirfiroth 17-Jul-18 23:16
Re: You down and dirty so-n-so 196 DavidK 17-Jul-18 23:20
Re: Pi or no Pi ?????????????? 287 spaceyhippie 19-Jul-18 10:32
Re: Pi or no Pi ?????????????? 221 molder 19-Jul-18 11:21
Re: Pi or no Pi ?????????????? 262 Sirfiroth 19-Jul-18 12:05
Re: Pi or no Pi ?????????????? 345 spaceyhippie 19-Jul-18 23:57
Re: Pi or no Pi ?????????????? 225 DavidK 20-Jul-18 08:20
Re: Pi or no Pi ?????????????? 287 spaceyhippie 20-Jul-18 21:58
Re: Pi or no Pi ?????????????? 180 DavidK 22-Jul-18 09:41
Re: Pi or no Pi ?????????????? 277 spaceyhippie 23-Jul-18 02:15
Re: Pi or no Pi ?????????????? 221 DavidK 23-Jul-18 08:09
Re: Pi or no Pi ?????????????? 235 Sirfiroth 23-Jul-18 13:49
Re: Pi or no Pi ?????????????? 208 DavidK 23-Jul-18 22:23
Re: Pi or no Pi ?????????????? 228 Sirfiroth 23-Jul-18 23:52
Re: Pi or no Pi ?????????????? 220 DavidK 24-Jul-18 09:11
Re: Pi or no Pi ?????????????? 179 Sirfiroth 24-Jul-18 13:11
Re: Pi or no Pi ?????????????? 162 DavidK 27-Jul-18 06:13
Re: Pi or no Pi ?????????????? 206 Sirfiroth 27-Jul-18 15:45
Re: Pi or no Pi ?????????????? 267 spaceyhippie 24-Jul-18 02:44
Re: Pi or no Pi ?????????????? 257 DavidK 24-Jul-18 17:10
Re: Pi or no Pi ?????????????? 304 spaceyhippie 27-Jul-18 00:51
Re: Pi or no Pi ?????????????? 248 spaceyhippie 27-Jul-18 14:36
Re: Pi or no Pi ?????????????? 345 spaceyhippie 29-Jul-18 11:01
Re: Pi or no Pi ?????????????? 233 DavidK 06-Aug-18 19:15
Re: Pi or no Pi ?????????????? 213 DavidK 07-Aug-18 05:16
Re: Pi or no Pi ?????????????? 224 spaceyhippie 08-Aug-18 09:20
Re: Pi or no Pi ?????????????? 221 DavidK 08-Aug-18 09:39
Re: Pi or no Pi ?????????????? 264 spaceyhippie 09-Aug-18 02:32
Re: Pi or no Pi ?????????????? 278 DavidK 09-Aug-18 08:00
ROTFLMAO! 182 Sirfiroth 09-Aug-18 13:22
Re: ROTFLMAO! 178 DavidK 09-Aug-18 14:12
Re: ROTFLMAO! 199 Sirfiroth 09-Aug-18 14:28
Re: ROTFLMAO! 172 DavidK 09-Aug-18 14:49
Re: ROTFLMAO! 178 Sirfiroth 09-Aug-18 15:03
Re: ROTFLMAO! 195 DavidK 09-Aug-18 21:39
Re: ROTFLMAO! 209 Sirfiroth 10-Aug-18 02:06
Re: Pi or no Pi ?????????????? 221 spaceyhippie 09-Aug-18 20:40
Re: Pi or no Pi ?????????????? 277 DavidK 10-Aug-18 07:59
Re: Pi or no Pi ?????????????? 287 Steve Clayton 12-Aug-18 18:16
Re: Pi or no Pi ?????????????? 86 DavidK 27-Dec-19 23:13
Re: Pi or no Pi ?????????????? 75 Sirfiroth 28-Dec-19 03:46
Pi. All Pi. All The Time. 82 thinkitover 28-Dec-19 04:59
Re: Pi. All Pi. All The Time. 62 molder 28-Dec-19 10:35
Re: Pi or no Pi ?????????????? 60 DavidK 28-Dec-19 10:20
Re: Pi or no Pi ?????????????? 73 Sirfiroth 28-Dec-19 15:13
Re: Pi or no Pi ?????????????? 84 Thanos5150 28-Dec-19 16:30
Re: Pi or no Pi ?????????????? 73 thinkitover 28-Dec-19 21:49
Re: Pi or no Pi ?????????????? 67 Thanos5150 29-Dec-19 04:35
Re: Pi or no Pi ?????????????? 73 Sirfiroth 29-Dec-19 02:17
Re: Pi or no Pi ?????????????? 63 molder 29-Dec-19 04:14
Re: Pi or no Pi ?????????????? 69 Sirfiroth 29-Dec-19 12:51
Re: Pi or no Pi ?????????????? 57 molder 29-Dec-19 22:31
Re: Pi or no Pi ?????????????? 60 Sirfiroth 30-Dec-19 14:11
Re: Pi or no Pi ?????????????? 76 magisterchessmutt 30-Dec-19 15:16
Re: Pi or no Pi ?????????????? 59 Sirfiroth 31-Dec-19 03:33
Re: Pi or no Pi ?????????????? 76 magisterchessmutt 31-Dec-19 04:33
Re: Pi or no Pi ?????????????? 71 Sirfiroth 31-Dec-19 15:04
Re: Pi or no Pi ?????????????? 72 spaceyhippie 31-Dec-19 23:37
Re: Pi or no Pi ?????????????? 73 Thanos5150 29-Dec-19 04:29
Re: Pi or no Pi ?????????????? 67 DavidK 29-Dec-19 09:32
Re: Pi or no Pi ?????????????? 73 Sirfiroth 29-Dec-19 14:09
Re: Pi or no Pi ?????????????? 60 spaceyhippie 01-Jan-20 23:18
Re: Pi or no Pi ?????????????? 82 Sirfiroth 02-Jan-20 01:33
Pi vs Pudding 79 thinkitover 02-Jan-20 21:45
Re: Pi vs Pudding 59 spaceyhippie 03-Jan-20 00:06
Re: Pi vs Pudding 66 seasmith 03-Jan-20 00:24
Re: Pi vs Pudding 62 spaceyhippie 07-Jan-20 23:06
Re: Pi vs Pudding 97 seasmith 08-Jan-20 02:54
Re: Pi vs Pudding 69 Sirfiroth 03-Jan-20 03:36
Re: Pi vs Pudding 62 molder 03-Jan-20 06:56
Re: Pi vs Pudding 70 Sirfiroth 03-Jan-20 18:25
Re: Pi vs Pudding 62 spaceyhippie 04-Jan-20 00:02
LOL, now that was hilarious ! 62 Sirfiroth 04-Jan-20 05:51
Re: LOL, now that was hilarious ! 81 hendrik dirker 04-Jan-20 09:32
Re: LOL, now that was hilarious ! 52 spaceyhippie 04-Jan-20 23:37
Re: LOL, now that was hilarious ! 61 spaceyhippie 04-Jan-20 23:39
Re: Pi vs Pudding 82 molder 04-Jan-20 11:03
Re: Pi vs Pudding 71 Sirfiroth 05-Jan-20 20:11
Re: Pi vs Pudding 54 molder 06-Jan-20 02:55
Re: Pi vs Pudding 69 magisterchessmutt 06-Jan-20 02:58
Re: Pi vs Pudding 54 molder 06-Jan-20 05:26
Re: Pi vs Pudding 58 spaceyhippie 07-Jan-20 01:32
Re: Pi vs Pudding 51 DavidK 07-Jan-20 02:02
Re: Pi vs Pudding 71 thinkitover 06-Jan-20 06:13
Re: Pi vs Pudding 76 Sirfiroth 07-Jan-20 02:18
Re: Pi vs Pudding 52 DavidK 07-Jan-20 14:25
Re: Pi vs Pudding 62 Sirfiroth 07-Jan-20 15:16
Re: Pi vs Pudding 65 DavidK 07-Jan-20 19:03
Re: Pi vs Pudding 53 Sirfiroth 07-Jan-20 20:08
Re: Pi vs Pudding 59 DavidK 07-Jan-20 20:11
Re: Pi or no Pi ?????????????? 81 DavidK 28-Dec-19 11:21
Re: Pi or no Pi ?????????????? 73 engbren 28-Dec-19 12:34
Re: Pi or no Pi ?????????????? 81 Sirfiroth 28-Dec-19 15:55
Re: Pi or no Pi ?????????????? 69 engbren 29-Dec-19 01:14
Re: Pi or no Pi ?????????????? 67 Sirfiroth 30-Dec-19 16:52
Re: Pi or no Pi ?????????????? 68 engbren 30-Dec-19 22:23
Re: Pi or no Pi ?????????????? 101 magisterchessmutt 30-Dec-19 23:24
Re: Pi or no Pi ?????????????? 83 engbren 31-Dec-19 11:31
Re: Pi or no Pi ?????????????? 72 spaceyhippie 04-Jan-20 00:42


Sorry, only registered users may post in this forum.