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You may recognize Galileo's Law of Odd Numbers, distance versus time during fall. Suppose an expansion of squares following this sequence (ie of surface 1, 4, 9...etc), each with its inscribed circle. For each circle, compare its surface area to that of the preceding square. For example the inscribed circle of 52 =25 has a surface area of ~197/11. That circle is greater than the preceding square, 42 = 16.
197/11 > 16, right?

Do this comparison for the entire sequence from 1-19, i.e. 12 to 102. What do you observe? There is no need to use a calculator btw and you don't even need to have memorized the squares. You simply add successive odd numbers starting with "1". You compute each circle as 11/14 of its corresponding square. 11/14 is the Great Pyramid's seqed.

Something odd happens at "17", ie the inscribed circle of a square of surface 81, doesn't it? A cross-over.

The surface area of a square with a base of 8 (64) virtually eclipses the odd number expansion's next square's inscribed circle's surface area, 635/8.

Which means that at 64/81 you get the best possible approximation to a circle's surface using this method. And this method is very well within the knowledge base described in the Rhind Papyrus. That's where 8/9 comes from: It's a short-cut! Drew was correct. The Rhind Papyrus is based on some information missing in it and no leap is required to draw that conclusion. In fact, the alternative, that 8/9 just came out of thin air, is much less plausible. The Law of Odd numbers is nothing more than successively adding two strips of cubits (similar to "Cubit Strips"; see Rhind 49) summing to the next higher odd number in the sequence to two sides of a square to obtain the next square in the expansion.

Yes, you guessed it: Galileo wasn't the first...

Edited 3 time(s). Last edit at 24-Jun-18 13:16 by Manu.

Subject Views Written By Posted
Pi or no Pi ?????????????? 3085 Sirfiroth 06-Feb-18 03:26
Re: Pi or no Pi ?????????????? 493 drew 06-Feb-18 04:18
Re: Pi or no Pi ?????????????? 455 Sirfiroth 06-Feb-18 17:37
Re: Pi or no Pi ?????????????? 360 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? 444 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 330 drew 09-Feb-18 00:33
Re: Oh...what a shame... 331 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 354 drew 09-Feb-18 06:02
Re: Oh...what a shame... 343 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 256 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 253 Manu 24-Jun-18 12:59
Re: well put 247 cloister 24-Jun-18 18:14
Re: well put 296 cloister 29-Jun-18 08:48
Re: well put 231 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? 233 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 261 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 242 DavidK 27-Jun-18 05:37
Re: Hard evidence for base 100 using egyptian maths 268 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
The math or the pyramid? 283 drew 27-Jun-18 20:46
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
Re: Pi or no Pi ?????????????? 317 spaceyhippie 19-Jul-18 10:32
Re: Pi or no Pi ?????????????? 245 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 ?????????????? 232 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 ?????????????? 374 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 ?????????????? 315 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 ?????????????? 92 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 ?????????????? 114 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 105 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 112 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 ?????????????? 91 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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