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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 necessity is the mother of invention, why is there a monster under my bed?

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Subject Views Written By Posted
Pi or no Pi ?????????????? 3067 Sirfiroth 06-Feb-18 03:26
Re: Pi or no Pi ?????????????? 480 drew 06-Feb-18 04:18
Re: Pi or no Pi ?????????????? 443 Sirfiroth 06-Feb-18 17:37
Re: Pi or no Pi ?????????????? 348 drew 06-Feb-18 23:32
Re: Pi or no Pi ???????????????? 405 Dr. Troglodyte 07-Feb-18 14:44
Re: Pi or no Pi ?????????????? 323 molder 08-Feb-18 05:09
Re: Pi or no Pi ?????????????? 332 Sirfiroth 08-Feb-18 06:43
Re: Pi or no Pi ?????????????? 323 DavidK 08-Feb-18 10:48
Re: Pi or no Pi ?????????????? 322 molder 08-Feb-18 11:56
linking egyptian Pi to imperial Pi 268 DavidK 08-Feb-18 15:10
Re: Pi or no Pi ?????????????? 274 DavidK 08-Feb-18 13:58
cubit of 20.25? 236 DavidK 08-Feb-18 14:12
where does Fibonacci Pi come from? 262 DavidK 08-Feb-18 14:49
Re: cubit of 20.25? 323 Sirfiroth 08-Feb-18 15:08
Re: cubit of 20.25? 285 DavidK 08-Feb-18 15:15
Re: cubit of 20.25? 283 molder 09-Feb-18 03:58
Mod Note > Off-Topic Posts 307 Dr. Troglodyte 09-Feb-18 16:38
Re: cubit of 20.25? 434 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 316 drew 09-Feb-18 00:33
Re: Oh...what a shame... 313 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 339 drew 09-Feb-18 06:02
Re: Oh...what a shame... 332 Sirfiroth 09-Feb-18 13:28
Re: Oh...what a shame... 320 DavidK 22-Jun-18 05:58
Re: Oh...what a shame... 262 drew 22-Jun-18 09:54
Re: Oh...what a shame... 326 Sirfiroth 22-Jun-18 13:32
Re: Oh...what a shame... 301 drew 22-Jun-18 22:27
Re: Oh...what a shame... 287 Sirfiroth 23-Jun-18 01:48
Re: well put 263 drew 23-Jun-18 08:08
To put it bluntly! 300 Sirfiroth 23-Jun-18 12:40
Re: well put 287 Manu 23-Jun-18 18:33
Re: extensions of numbers 236 drew 24-Jun-18 00:40
Re: extensions of numbers 294 Sirfiroth 24-Jun-18 04:50
Re: extensions of numbers 238 drew 24-Jun-18 08:36
Re: extensions of numbers 236 Sirfiroth 24-Jun-18 12:22
Re: extensions of numbers 245 drew 24-Jun-18 20:53
Re: extensions of numbers 245 Sirfiroth 25-Jun-18 16:06
Re: extensions of numbers 227 DavidK 25-Jun-18 16:13
Re: extensions of numbers 230 Sirfiroth 25-Jun-18 16:46
the primitive calculator 230 drew 25-Jun-18 23:23
Re: the primitive calculator 276 Sirfiroth 26-Jun-18 02:24
Re: the primitive calculator 212 drew 26-Jun-18 07:06
Mod Note > Duplicate Post Removed 241 Dr. Troglodyte 26-Jun-18 12:45
Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 258 rodz111 26-Jun-18 13:55
Re: Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 191 drew 27-Jun-18 05:18
Re: the primitive calculator 247 Sirfiroth 26-Jun-18 17:00
Re: the primitive calculator 246 drew 27-Jun-18 00:01
Re: the primitive calculator 234 Sirfiroth 27-Jun-18 00:18
Re: the primitive calculator 215 drew 27-Jun-18 01:56
Re: well put 209 cloister 24-Jun-18 09:43
Re: well put 238 Manu 24-Jun-18 12:59
Re: well put 231 cloister 24-Jun-18 18:14
Re: well put 281 cloister 29-Jun-18 08:48
Re: well put 219 drew 27-Jun-18 05:11
Re: Oh...what a shame... 286 Sirfiroth 22-Jun-18 12:21
Re: Oh...what a shame... 308 molder 23-Jun-18 00:24
Re: Oh...what a shame... 294 DavidK 23-Jun-18 21:06
Re: Oh...what a shame... 246 DavidK 24-Jun-18 07:41
Understanding the differences! 237 Sirfiroth 24-Jun-18 12:50
No pie for jacob 290 DavidK 24-Jun-18 08:54
Re: No pie for jacob 238 Sirfiroth 25-Jun-18 16:44
Re: No pie for jacob 254 DavidK 25-Jun-18 20:21
Re: No pie for jacob 237 Sirfiroth 25-Jun-18 23:19
Re: 5 values for pi in GP here are 3 223 molder 26-Jun-18 00:51
Re: what value for pi? 220 drew 26-Jun-18 14:11
Re: what value for pi? 257 molder 26-Jun-18 21:30
Re: what value for pi? 213 drew 26-Jun-18 23:42
Re: 5 values for pi in GP here are 3 212 Sirfiroth 26-Jun-18 14:55
Re: 5 values for pi in GP here are 3 259 molder 26-Jun-18 21:18
Re: No pie for jacob 247 DavidK 26-Jun-18 10:34
Re: No pie for jacob 210 Sirfiroth 26-Jun-18 15:02
Re: No pie for jacob 205 DavidK 26-Jun-18 16:46
Re: No pie for jacob 220 Sirfiroth 26-Jun-18 17:12
Re: No pie for jacob 230 DavidK 26-Jun-18 18:58
Re: No pie for jacob 255 Sirfiroth 26-Jun-18 22:59
Re: No pie for jacob 216 DUNE 26-Jun-18 19:52
Re: No pie for jacob 206 DavidK 26-Jun-18 21:18
Re: No pie for jacob 220 Sirfiroth 26-Jun-18 23:10
Hard evidence for base 100 using egyptian maths 231 DavidK 27-Jun-18 05:37
Re: Hard evidence for base 100 using egyptian maths 256 drew 27-Jun-18 06:16
Re: Hard evidence for base 100 using egyptian maths 232 DavidK 27-Jun-18 10:25
Re: Hard evidence for base 100 using egyptian maths 238 drew 27-Jun-18 21:18
Re: Pi or no Pi ?????????????? 262 rodz111 25-Jun-18 17:48
Re: Pi or no Pi ?????????????? 261 Sirfiroth 25-Jun-18 19:54
Re: Pi or no Pi ?????????????? 218 rodz111 26-Jun-18 03:13
Re: Pi or no Pi ?????????????? 253 molder 26-Jun-18 03:19
Re: Pi or no Pi ?????????????? 240 rodz111 26-Jun-18 03:30
Re: Pi or no Pi ?????????????? 234 molder 26-Jun-18 21:52
Re: Pi or no Pi ?????????????? 296 rodz111 28-Jun-18 07:44
Re: Pi or no Pi ?????????????? 232 drew 28-Jun-18 09:56
Re: Pi or no Pi ?????????????? 264 rodz111 28-Jun-18 11:09
Re: Pi or no Pi ?????????????? 249 drew 28-Jun-18 17:13
Re: Pi or no Pi ?????????????? 266 DavidK 28-Jun-18 20:00
Tripping over museum rods 255 drew 28-Jun-18 23:52
Museum rods 230 drew 29-Jun-18 00:20
Re: Pi or no Pi ?????????????? 253 rodz111 29-Jun-18 00:37
You're as much as a complainer as anyone but you're not... 243 drew 29-Jun-18 01:24
Re: Pi or no Pi ?????????????? 307 rodz111 30-Jun-18 01:21
You down and dirty so-n-so 253 drew 27-Jun-18 05:29
Re: You down and dirty so-n-so 198 Sirfiroth 27-Jun-18 08:17
Re: You down and dirty so-n-so 203 drew 27-Jun-18 09:49
Re: You down and dirty so-n-so 313 Sirfiroth 27-Jun-18 17:12
The math or the pyramid? 268 drew 27-Jun-18 20:46
Re: You down and dirty so-n-so 187 DavidK 17-Jul-18 23:04
Re: You down and dirty so-n-so 217 Sirfiroth 17-Jul-18 23:16
Re: You down and dirty so-n-so 207 DavidK 17-Jul-18 23:20
Re: Pi or no Pi ?????????????? 302 spaceyhippie 19-Jul-18 10:32
Re: Pi or no Pi ?????????????? 234 molder 19-Jul-18 11:21
Re: Pi or no Pi ?????????????? 276 Sirfiroth 19-Jul-18 12:05
Re: Pi or no Pi ?????????????? 382 spaceyhippie 19-Jul-18 23:57
Re: Pi or no Pi ?????????????? 240 DavidK 20-Jul-18 08:20
Re: Pi or no Pi ?????????????? 303 spaceyhippie 20-Jul-18 21:58
Re: Pi or no Pi ?????????????? 196 DavidK 22-Jul-18 09:41
Re: Pi or no Pi ?????????????? 289 spaceyhippie 23-Jul-18 02:15
Re: Pi or no Pi ?????????????? 233 DavidK 23-Jul-18 08:09
Re: Pi or no Pi ?????????????? 247 Sirfiroth 23-Jul-18 13:49
Re: Pi or no Pi ?????????????? 225 DavidK 23-Jul-18 22:23
Re: Pi or no Pi ?????????????? 250 Sirfiroth 23-Jul-18 23:52
Re: Pi or no Pi ?????????????? 235 DavidK 24-Jul-18 09:11
Re: Pi or no Pi ?????????????? 194 Sirfiroth 24-Jul-18 13:11
Re: Pi or no Pi ?????????????? 177 DavidK 27-Jul-18 06:13
Re: Pi or no Pi ?????????????? 218 Sirfiroth 27-Jul-18 15:45
Re: Pi or no Pi ?????????????? 284 spaceyhippie 24-Jul-18 02:44
Re: Pi or no Pi ?????????????? 279 DavidK 24-Jul-18 17:10
Re: Pi or no Pi ?????????????? 324 spaceyhippie 27-Jul-18 00:51
Re: Pi or no Pi ?????????????? 259 spaceyhippie 27-Jul-18 14:36
Re: Pi or no Pi ?????????????? 362 spaceyhippie 29-Jul-18 11:01
Re: Pi or no Pi ?????????????? 248 DavidK 06-Aug-18 19:15
Re: Pi or no Pi ?????????????? 229 DavidK 07-Aug-18 05:16
Re: Pi or no Pi ?????????????? 236 spaceyhippie 08-Aug-18 09:20
Re: Pi or no Pi ?????????????? 236 DavidK 08-Aug-18 09:39
Re: Pi or no Pi ?????????????? 275 spaceyhippie 09-Aug-18 02:32
Re: Pi or no Pi ?????????????? 292 DavidK 09-Aug-18 08:00
ROTFLMAO! 195 Sirfiroth 09-Aug-18 13:22
Re: ROTFLMAO! 191 DavidK 09-Aug-18 14:12
Re: ROTFLMAO! 214 Sirfiroth 09-Aug-18 14:28
Re: ROTFLMAO! 184 DavidK 09-Aug-18 14:49
Re: ROTFLMAO! 189 Sirfiroth 09-Aug-18 15:03
Re: ROTFLMAO! 211 DavidK 09-Aug-18 21:39
Re: ROTFLMAO! 221 Sirfiroth 10-Aug-18 02:06
Re: Pi or no Pi ?????????????? 235 spaceyhippie 09-Aug-18 20:40
Re: Pi or no Pi ?????????????? 297 DavidK 10-Aug-18 07:59
Re: Pi or no Pi ?????????????? 304 Steve Clayton 12-Aug-18 18:16
Re: Pi or no Pi ?????????????? 96 DavidK 27-Dec-19 23:13
Re: Pi or no Pi ?????????????? 87 Sirfiroth 28-Dec-19 03:46
Pi. All Pi. All The Time. 96 thinkitover 28-Dec-19 04:59
Re: Pi. All Pi. All The Time. 75 molder 28-Dec-19 10:35
Re: Pi or no Pi ?????????????? 71 DavidK 28-Dec-19 10:20
Re: Pi or no Pi ?????????????? 84 Sirfiroth 28-Dec-19 15:13
Re: Pi or no Pi ?????????????? 96 Thanos5150 28-Dec-19 16:30
Re: Pi or no Pi ?????????????? 86 thinkitover 28-Dec-19 21:49
Re: Pi or no Pi ?????????????? 81 Thanos5150 29-Dec-19 04:35
Re: Pi or no Pi ?????????????? 84 Sirfiroth 29-Dec-19 02:17
Re: Pi or no Pi ?????????????? 73 molder 29-Dec-19 04:14
Re: Pi or no Pi ?????????????? 81 Sirfiroth 29-Dec-19 12:51
Re: Pi or no Pi ?????????????? 69 molder 29-Dec-19 22:31
Re: Pi or no Pi ?????????????? 71 Sirfiroth 30-Dec-19 14:11
Re: Pi or no Pi ?????????????? 102 magisterchessmutt 30-Dec-19 15:16
Re: Pi or no Pi ?????????????? 70 Sirfiroth 31-Dec-19 03:33
Re: Pi or no Pi ?????????????? 103 magisterchessmutt 31-Dec-19 04:33
Re: Pi or no Pi ?????????????? 82 Sirfiroth 31-Dec-19 15:04
Re: Pi or no Pi ?????????????? 84 spaceyhippie 31-Dec-19 23:37
Re: Pi or no Pi ?????????????? 86 Thanos5150 29-Dec-19 04:29
Re: Pi or no Pi ?????????????? 79 DavidK 29-Dec-19 09:32
Re: Pi or no Pi ?????????????? 84 Sirfiroth 29-Dec-19 14:09
Re: Pi or no Pi ?????????????? 71 spaceyhippie 01-Jan-20 23:18
Re: Pi or no Pi ?????????????? 93 Sirfiroth 02-Jan-20 01:33
Pi vs Pudding 90 thinkitover 02-Jan-20 21:45
Re: Pi vs Pudding 70 spaceyhippie 03-Jan-20 00:06
Re: Pi vs Pudding 78 seasmith 03-Jan-20 00:24
Re: Pi vs Pudding 75 spaceyhippie 07-Jan-20 23:06
Re: Pi vs Pudding 109 seasmith 08-Jan-20 02:54
Re: Pi vs Pudding 80 Sirfiroth 03-Jan-20 03:36
Re: Pi vs Pudding 76 molder 03-Jan-20 06:56
Re: Pi vs Pudding 81 Sirfiroth 03-Jan-20 18:25
Re: Pi vs Pudding 72 spaceyhippie 04-Jan-20 00:02
LOL, now that was hilarious ! 73 Sirfiroth 04-Jan-20 05:51
Re: LOL, now that was hilarious ! 92 hendrik dirker 04-Jan-20 09:32
Re: LOL, now that was hilarious ! 65 spaceyhippie 04-Jan-20 23:37
Re: LOL, now that was hilarious ! 73 spaceyhippie 04-Jan-20 23:39
Re: Pi vs Pudding 94 molder 04-Jan-20 11:03
Re: Pi vs Pudding 82 Sirfiroth 05-Jan-20 20:11
Re: Pi vs Pudding 67 molder 06-Jan-20 02:55
Re: Pi vs Pudding 96 magisterchessmutt 06-Jan-20 02:58
Re: Pi vs Pudding 67 molder 06-Jan-20 05:26
Re: Pi vs Pudding 74 spaceyhippie 07-Jan-20 01:32
Re: Pi vs Pudding 63 DavidK 07-Jan-20 02:02
Re: Pi vs Pudding 83 thinkitover 06-Jan-20 06:13
Re: Pi vs Pudding 87 Sirfiroth 07-Jan-20 02:18
Re: Pi vs Pudding 64 DavidK 07-Jan-20 14:25
Re: Pi vs Pudding 74 Sirfiroth 07-Jan-20 15:16
Re: Pi vs Pudding 76 DavidK 07-Jan-20 19:03
Re: Pi vs Pudding 64 Sirfiroth 07-Jan-20 20:08
Re: Pi vs Pudding 70 DavidK 07-Jan-20 20:11
Re: Pi or no Pi ?????????????? 93 DavidK 28-Dec-19 11:21
Re: Pi or no Pi ?????????????? 86 engbren 28-Dec-19 12:34
Re: Pi or no Pi ?????????????? 93 Sirfiroth 28-Dec-19 15:55
Re: Pi or no Pi ?????????????? 80 engbren 29-Dec-19 01:14
Re: Pi or no Pi ?????????????? 79 Sirfiroth 30-Dec-19 16:52
Re: Pi or no Pi ?????????????? 80 engbren 30-Dec-19 22:23
Re: Pi or no Pi ?????????????? 128 magisterchessmutt 30-Dec-19 23:24
Re: Pi or no Pi ?????????????? 98 engbren 31-Dec-19 11:31
Re: Pi or no Pi ?????????????? 84 spaceyhippie 04-Jan-20 00:42


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