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For many of us, our forays into math began without calculators.

Anyway, I woke up during the night with a teaser floating around my head and I remembered most of it this morning and tried to play with it. I got so far and then got stuck.

"The Potter’s Wheel.

In the annals of history, before the wheel came the potter’s wheel, and depending on what one was constructed from meant how to transport it from here to there. Certainly having it on its edge became the norm, rolling it along, and when some smart bugger decided that moving two of them along could be better done if an axle linked them, he did so…and wallah! Something really amazing eventuated after that when someone put a box on the axle and created a cart.

I’m going to say that his two potter’s wheels were perfectly round and one was twice as large as the other, so that one could be considered as 1 unit and the other 2 units in radius. They both had a little nick in their edges. The axle linking them was perfectly straight and the wheels were solid in their position and perfectly upright. One day, they were rolled out after several days of rain and a couple of days of good sunshine, and the wheels went upon drying mud.

It was noticed that at a certain spot, both wheels and their nicks were in perfect alignment, and further along the small wheel showed its nick in the mud while twice as far along the large wheel showed its nick in the mud. Being curious, the potter got his ruler out of his bag, the one used to measure the radii of the wheels from, and found that there was a perfect association between both wheels and their circumferences…so much so that he decided he would investigate such a thing, and set about delineating his measure down to the smallest even parts that could fit upon the ruler.

In estimating the circumferences of the wheels, he found that they were between 3 1/8 and 3 1/7 larger than their radii. Ah, but he could better delineate his measure and did so, and did so again and again until he had a fine measure upon his ruler that offered up a hair’s breadth as a distance between one line and another on his ruler. He had very good eyesight.

Upon measuring again, he found that he had a better estimation of the circumference from the larger wheel against the smaller wheel, twice as good actually, and decided he would create two more potter’s wheels to see if he could better define this wonder of math that was appearing before him…he made one a half-unit radius, and the other 5 units radius, and created a small wallow and wheeled his potters wheels through it so that their edges were straight up and they had nicks and all four lines could be measured against a ruler that could tell one hair’s breadth from another. And he found that there was a simple formula that expressed what he was seeing. The measure of the wheel’s edge in relation to its half-width upon a face was: 2 x r x (628/200 + 1/628)…and he was satisfied that that was the best he was going to do under the circumstances.

Why 628?

In playing with the numbers the potter was using and seeing how the larger wheel related to the smaller wheel, he found that there was a nice surprize in such a number. 628 = 500 + 128

By adjusting the multiplication of such a number to go inward and outward according to the size of the wheel and determining the relationship between scale, he could have twice the figure showing an association to radius and circumference as he could with half the figure, and he also found something quite unique with this 500 + 128 identity. He tried something…

250 + 64; 125 + 32; 62 ½ + 16; 31 ¼ + 8; 15 5/8 + 4; 6 13/16 + 2; 3 13/32 + 1; 1 45/64 + ½.

He went the other way: 1000 + 256; 2000 + 512; 4000 + 1024; 8000 + 2048; 16,000 + 4096; 32,000 + 8192; 64,000 + 16,384; 128,000 + 32,768.

He pondered the ramifications…having the original 500 + 128 went 8 steps in either direction where 256 and 64 showed to be instrumental numbers. On the way down, 64 on one side became 64ths on the other; on the way up, 256 on one side became 256 x 500 and 128 on both sides. He pondered the ramifications of the 628 and the 64 first, and found 9 13/16 as the ratio between them, which was quite odd considering the 3 and 13/32 association to 1. He pondered that the ratio between greater and lesser numbers like 500 to 128 was strange. He had pondered what he saw with this piece of pi and observed 3.1415925…1 / .1415925 = 7.0625…1/.0625 = 16 therefore 0.1415925 = a seventh and a sixteenth of 1. Now he saw this same sixteenth in conjunction with nine tenths plus 3 of 500 to 128.

There was a difference between 500/128 and 64/16 of a tenth and 2/3s of 1."

...I got stuck because my head got fried in trying to express such things as 'a seventh of 1 plus a sixteenth of 1' relating to what 0.1415925 is. If I can grasp that, I'll be bale to fix up where the 500 and 128 were heading to.

If anyone and everyone can see us, what kind of character are we playing in our own story?

Subject Views Written By Posted
Pi or no Pi ?????????????? 3194 Sirfiroth 06-Feb-18 03:26
Re: Pi or no Pi ?????????????? 548 drew 06-Feb-18 04:18
Re: Pi or no Pi ?????????????? 510 Sirfiroth 06-Feb-18 17:37
Re: Pi or no Pi ?????????????? 414 drew 06-Feb-18 23:32
Re: Pi or no Pi ???????????????? 474 Dr. Troglodyte 07-Feb-18 14:44
Re: Pi or no Pi ?????????????? 398 molder 08-Feb-18 05:09
Re: Pi or no Pi ?????????????? 398 Sirfiroth 08-Feb-18 06:43
Re: Pi or no Pi ?????????????? 399 DavidK 08-Feb-18 10:48
Re: Pi or no Pi ?????????????? 398 molder 08-Feb-18 11:56
linking egyptian Pi to imperial Pi 336 DavidK 08-Feb-18 15:10
Re: Pi or no Pi ?????????????? 338 DavidK 08-Feb-18 13:58
cubit of 20.25? 305 DavidK 08-Feb-18 14:12
where does Fibonacci Pi come from? 338 DavidK 08-Feb-18 14:49
Re: cubit of 20.25? 396 Sirfiroth 08-Feb-18 15:08
Re: cubit of 20.25? 354 DavidK 08-Feb-18 15:15
Re: cubit of 20.25? 354 molder 09-Feb-18 03:58
Mod Note > Off-Topic Posts 374 Dr. Troglodyte 09-Feb-18 16:38
Re: cubit of 20.25? 517 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 386 drew 09-Feb-18 00:33
Re: Oh...what a shame... 387 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 407 drew 09-Feb-18 06:02
Re: Oh...what a shame... 410 Sirfiroth 09-Feb-18 13:28
Re: Oh...what a shame... 395 DavidK 22-Jun-18 05:58
Re: Oh...what a shame... 332 drew 22-Jun-18 09:54
Re: Oh...what a shame... 411 Sirfiroth 22-Jun-18 13:32
Re: Oh...what a shame... 488 drew 22-Jun-18 22:27
Re: Oh...what a shame... 360 Sirfiroth 23-Jun-18 01:48
Re: well put 332 drew 23-Jun-18 08:08
To put it bluntly! 373 Sirfiroth 23-Jun-18 12:40
Re: well put 352 Manu 23-Jun-18 18:33
Re: extensions of numbers 306 drew 24-Jun-18 00:40
Re: extensions of numbers 362 Sirfiroth 24-Jun-18 04:50
Re: extensions of numbers 318 drew 24-Jun-18 08:36
Re: extensions of numbers 309 Sirfiroth 24-Jun-18 12:22
Re: extensions of numbers 312 drew 24-Jun-18 20:53
Re: extensions of numbers 312 Sirfiroth 25-Jun-18 16:06
Re: extensions of numbers 289 DavidK 25-Jun-18 16:13
Re: extensions of numbers 296 Sirfiroth 25-Jun-18 16:46
the primitive calculator 293 drew 25-Jun-18 23:23
Re: the primitive calculator 349 Sirfiroth 26-Jun-18 02:24
Re: the primitive calculator 280 drew 26-Jun-18 07:06
Mod Note > Duplicate Post Removed 346 Dr. Troglodyte 26-Jun-18 12:45
Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 348 rodz111 26-Jun-18 13:55
Re: Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 248 drew 27-Jun-18 05:18
Re: the primitive calculator 322 Sirfiroth 26-Jun-18 17:00
Re: the primitive calculator 313 drew 27-Jun-18 00:01
Re: the primitive calculator 309 Sirfiroth 27-Jun-18 00:18
Re: the primitive calculator 283 drew 27-Jun-18 01:56
Re: well put 271 cloister 24-Jun-18 09:43
Re: well put 312 Manu 24-Jun-18 12:59
Re: well put 297 cloister 24-Jun-18 18:14
Re: well put 356 cloister 29-Jun-18 08:48
Re: well put 286 drew 27-Jun-18 05:11
Re: Oh...what a shame... 352 Sirfiroth 22-Jun-18 12:21
Re: Oh...what a shame... 381 molder 23-Jun-18 00:24
Re: Oh...what a shame... 362 DavidK 23-Jun-18 21:06
Re: Oh...what a shame... 320 DavidK 24-Jun-18 07:41
Understanding the differences! 319 Sirfiroth 24-Jun-18 12:50
No pie for jacob 358 DavidK 24-Jun-18 08:54
Re: No pie for jacob 297 Sirfiroth 25-Jun-18 16:44
Re: No pie for jacob 323 DavidK 25-Jun-18 20:21
Re: No pie for jacob 327 Sirfiroth 25-Jun-18 23:19
Re: 5 values for pi in GP here are 3 284 molder 26-Jun-18 00:51
Re: what value for pi? 287 drew 26-Jun-18 14:11
Re: what value for pi? 331 molder 26-Jun-18 21:30
Re: what value for pi? 285 drew 26-Jun-18 23:42
Re: 5 values for pi in GP here are 3 274 Sirfiroth 26-Jun-18 14:55
Re: 5 values for pi in GP here are 3 328 molder 26-Jun-18 21:18
Re: No pie for jacob 325 DavidK 26-Jun-18 10:34
Re: No pie for jacob 284 Sirfiroth 26-Jun-18 15:02
Re: No pie for jacob 284 DavidK 26-Jun-18 16:46
Re: No pie for jacob 292 Sirfiroth 26-Jun-18 17:12
Re: No pie for jacob 319 DavidK 26-Jun-18 18:58
Re: No pie for jacob 331 Sirfiroth 26-Jun-18 22:59
Re: No pie for jacob 280 DUNE 26-Jun-18 19:52
Re: No pie for jacob 284 DavidK 26-Jun-18 21:18
Re: No pie for jacob 284 Sirfiroth 26-Jun-18 23:10
Hard evidence for base 100 using egyptian maths 296 DavidK 27-Jun-18 05:37
Re: Hard evidence for base 100 using egyptian maths 322 drew 27-Jun-18 06:16
Re: Hard evidence for base 100 using egyptian maths 295 DavidK 27-Jun-18 10:25
Re: Hard evidence for base 100 using egyptian maths 309 drew 27-Jun-18 21:18
Re: Pi or no Pi ?????????????? 351 rodz111 25-Jun-18 17:48
Re: Pi or no Pi ?????????????? 326 Sirfiroth 25-Jun-18 19:54
Re: Pi or no Pi ?????????????? 295 rodz111 26-Jun-18 03:13
Re: Pi or no Pi ?????????????? 317 molder 26-Jun-18 03:19
Re: Pi or no Pi ?????????????? 313 rodz111 26-Jun-18 03:30
Re: Pi or no Pi ?????????????? 308 molder 26-Jun-18 21:52
Re: Pi or no Pi ?????????????? 360 rodz111 28-Jun-18 07:44
Re: Pi or no Pi ?????????????? 305 drew 28-Jun-18 09:56
Re: Pi or no Pi ?????????????? 336 rodz111 28-Jun-18 11:09
Re: Pi or no Pi ?????????????? 323 drew 28-Jun-18 17:13
Re: Pi or no Pi ?????????????? 339 DavidK 28-Jun-18 20:00
Tripping over museum rods 336 drew 28-Jun-18 23:52
Museum rods 302 drew 29-Jun-18 00:20
Re: Pi or no Pi ?????????????? 326 rodz111 29-Jun-18 00:37
You're as much as a complainer as anyone but you're not... 317 drew 29-Jun-18 01:24
Re: Pi or no Pi ?????????????? 387 rodz111 30-Jun-18 01:21
You down and dirty so-n-so 321 drew 27-Jun-18 05:29
Re: You down and dirty so-n-so 269 Sirfiroth 27-Jun-18 08:17
Re: You down and dirty so-n-so 263 drew 27-Jun-18 09:49
Re: You down and dirty so-n-so 400 Sirfiroth 27-Jun-18 17:12
The math or the pyramid? 337 drew 27-Jun-18 20:46
Re: You down and dirty so-n-so 256 DavidK 17-Jul-18 23:04
Re: You down and dirty so-n-so 280 Sirfiroth 17-Jul-18 23:16
Re: You down and dirty so-n-so 273 DavidK 17-Jul-18 23:20
Re: Pi or no Pi ?????????????? 381 spaceyhippie 19-Jul-18 10:32
Re: Pi or no Pi ?????????????? 296 molder 19-Jul-18 11:21
Re: Pi or no Pi ?????????????? 343 Sirfiroth 19-Jul-18 12:05
Re: Pi or no Pi ?????????????? 466 spaceyhippie 19-Jul-18 23:57
Re: Pi or no Pi ?????????????? 324 DavidK 20-Jul-18 08:20
Re: Pi or no Pi ?????????????? 376 spaceyhippie 20-Jul-18 21:58
Re: Pi or no Pi ?????????????? 258 DavidK 22-Jul-18 09:41
Re: Pi or no Pi ?????????????? 362 spaceyhippie 23-Jul-18 02:15
Re: Pi or no Pi ?????????????? 296 DavidK 23-Jul-18 08:09
Re: Pi or no Pi ?????????????? 317 Sirfiroth 23-Jul-18 13:49
Re: Pi or no Pi ?????????????? 291 DavidK 23-Jul-18 22:23
Re: Pi or no Pi ?????????????? 440 Sirfiroth 23-Jul-18 23:52
Re: Pi or no Pi ?????????????? 309 DavidK 24-Jul-18 09:11
Re: Pi or no Pi ?????????????? 257 Sirfiroth 24-Jul-18 13:11
Re: Pi or no Pi ?????????????? 248 DavidK 27-Jul-18 06:13
Re: Pi or no Pi ?????????????? 286 Sirfiroth 27-Jul-18 15:45
Re: Pi or no Pi ?????????????? 348 spaceyhippie 24-Jul-18 02:44
Re: Pi or no Pi ?????????????? 354 DavidK 24-Jul-18 17:10
Re: Pi or no Pi ?????????????? 408 spaceyhippie 27-Jul-18 00:51
Re: Pi or no Pi ?????????????? 318 spaceyhippie 27-Jul-18 14:36
Re: Pi or no Pi ?????????????? 439 spaceyhippie 29-Jul-18 11:01
Re: Pi or no Pi ?????????????? 317 DavidK 06-Aug-18 19:15
Re: Pi or no Pi ?????????????? 293 DavidK 07-Aug-18 05:16
Re: Pi or no Pi ?????????????? 297 spaceyhippie 08-Aug-18 09:20
Re: Pi or no Pi ?????????????? 302 DavidK 08-Aug-18 09:39
Re: Pi or no Pi ?????????????? 333 spaceyhippie 09-Aug-18 02:32
Re: Pi or no Pi ?????????????? 360 DavidK 09-Aug-18 08:00
ROTFLMAO! 254 Sirfiroth 09-Aug-18 13:22
Re: ROTFLMAO! 259 DavidK 09-Aug-18 14:12
Re: ROTFLMAO! 306 Sirfiroth 09-Aug-18 14:28
Re: ROTFLMAO! 247 DavidK 09-Aug-18 14:49
Re: ROTFLMAO! 253 Sirfiroth 09-Aug-18 15:03
Re: ROTFLMAO! 268 DavidK 09-Aug-18 21:39
Re: ROTFLMAO! 292 Sirfiroth 10-Aug-18 02:06
Re: Pi or no Pi ?????????????? 308 spaceyhippie 09-Aug-18 20:40
Re: Pi or no Pi ?????????????? 362 DavidK 10-Aug-18 07:59
Re: Pi or no Pi ?????????????? 370 Steve Clayton 12-Aug-18 18:16
Re: Pi or no Pi ?????????????? 153 DavidK 27-Dec-19 23:13
Re: Pi or no Pi ?????????????? 140 Sirfiroth 28-Dec-19 03:46
Pi. All Pi. All The Time. 154 thinkitover 28-Dec-19 04:59
Re: Pi. All Pi. All The Time. 128 molder 28-Dec-19 10:35
Re: Pi or no Pi ?????????????? 127 DavidK 28-Dec-19 10:20
Re: Pi or no Pi ?????????????? 137 Sirfiroth 28-Dec-19 15:13
Re: Pi or no Pi ?????????????? 150 Thanos5150 28-Dec-19 16:30
Re: Pi or no Pi ?????????????? 145 thinkitover 28-Dec-19 21:49
Re: Pi or no Pi ?????????????? 143 Thanos5150 29-Dec-19 04:35
Re: Pi or no Pi ?????????????? 134 Sirfiroth 29-Dec-19 02:17
Re: Pi or no Pi ?????????????? 137 molder 29-Dec-19 04:14
Re: Pi or no Pi ?????????????? 131 Sirfiroth 29-Dec-19 12:51
Re: Pi or no Pi ?????????????? 129 molder 29-Dec-19 22:31
Re: Pi or no Pi ?????????????? 122 Sirfiroth 30-Dec-19 14:11
Re: Pi or no Pi ?????????????? 170 magisterchessmutt 30-Dec-19 15:16
Re: Pi or no Pi ?????????????? 128 Sirfiroth 31-Dec-19 03:33
Re: Pi or no Pi ?????????????? 174 magisterchessmutt 31-Dec-19 04:33
Re: Pi or no Pi ?????????????? 146 Sirfiroth 31-Dec-19 15:04
Re: Pi or no Pi ?????????????? 155 spaceyhippie 31-Dec-19 23:37
Re: Pi or no Pi ?????????????? 147 Thanos5150 29-Dec-19 04:29
Re: Pi or no Pi ?????????????? 134 DavidK 29-Dec-19 09:32
Re: Pi or no Pi ?????????????? 136 Sirfiroth 29-Dec-19 14:09
Re: Pi or no Pi ?????????????? 137 spaceyhippie 01-Jan-20 23:18
Re: Pi or no Pi ?????????????? 151 Sirfiroth 02-Jan-20 01:33
Pi vs Pudding 141 thinkitover 02-Jan-20 21:45
Re: Pi vs Pudding 133 spaceyhippie 03-Jan-20 00:06
Re: Pi vs Pudding 149 seasmith 03-Jan-20 00:24
Re: Pi vs Pudding 132 spaceyhippie 07-Jan-20 23:06
Re: Pi vs Pudding 176 seasmith 08-Jan-20 02:54
Re: Pi vs Pudding 140 Sirfiroth 03-Jan-20 03:36
Re: Pi vs Pudding 140 molder 03-Jan-20 06:56
Re: Pi vs Pudding 141 Sirfiroth 03-Jan-20 18:25
Re: Pi vs Pudding 135 spaceyhippie 04-Jan-20 00:02
LOL, now that was hilarious ! 133 Sirfiroth 04-Jan-20 05:51
Re: LOL, now that was hilarious ! 175 hendrik dirker 04-Jan-20 09:32
Re: LOL, now that was hilarious ! 124 spaceyhippie 04-Jan-20 23:37
Re: LOL, now that was hilarious ! 132 spaceyhippie 04-Jan-20 23:39
Re: Pi vs Pudding 152 molder 04-Jan-20 11:03
Re: Pi vs Pudding 142 Sirfiroth 05-Jan-20 20:11
Re: Pi vs Pudding 133 molder 06-Jan-20 02:55
Re: Pi vs Pudding 165 magisterchessmutt 06-Jan-20 02:58
Re: Pi vs Pudding 126 molder 06-Jan-20 05:26
Re: Pi vs Pudding 131 spaceyhippie 07-Jan-20 01:32
Re: Pi vs Pudding 120 DavidK 07-Jan-20 02:02
Re: Pi vs Pudding 135 thinkitover 06-Jan-20 06:13
Re: Pi vs Pudding 149 Sirfiroth 07-Jan-20 02:18
Re: Pi vs Pudding 118 DavidK 07-Jan-20 14:25
Re: Pi vs Pudding 131 Sirfiroth 07-Jan-20 15:16
Re: Pi vs Pudding 129 DavidK 07-Jan-20 19:03
Re: Pi vs Pudding 124 Sirfiroth 07-Jan-20 20:08
Re: Pi vs Pudding 123 DavidK 07-Jan-20 20:11
Re: Pi or no Pi ?????????????? 152 DavidK 28-Dec-19 11:21
Re: Pi or no Pi ?????????????? 146 engbren 28-Dec-19 12:34
Re: Pi or no Pi ?????????????? 147 Sirfiroth 28-Dec-19 15:55
Re: Pi or no Pi ?????????????? 135 engbren 29-Dec-19 01:14
Re: Pi or no Pi ?????????????? 134 Sirfiroth 30-Dec-19 16:52
Re: Pi or no Pi ?????????????? 136 engbren 30-Dec-19 22:23
Re: Pi or no Pi ?????????????? 193 magisterchessmutt 30-Dec-19 23:24
Re: Pi or no Pi ?????????????? 159 engbren 31-Dec-19 11:31
Re: Pi or no Pi ?????????????? 141 spaceyhippie 04-Jan-20 00:42

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