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my modern math professors also typically care less about exactitudes,
and more about the concept getting through, the student understanding
- an interesting concept to get across, that gives an insight into the culture
- to what historical applications would this mere approximation suffice?

so, the classical Egyptian method for calculating the area of a circle
is 8/9 the diameter squared... which is only a rough approximation,
in this case giving you 64, from 8x8, for a circle with a diameter of 9
when the actual answer is pi (d/2)2 = pi (4.5)2 ~= 63.617 251 24...
which 64 is a little off, but possibly the difference is interesting
- if we want to be more exact, with a more modern tolerance,
maybe there's an interesting number we can adjust it with...

.. . 128 / 127 ~= 1.00 787 401...
. . . 129 / 128 = 1.00 781 25
64 / 63.617... ~= 1.00 6016 43... ***
.. . 192 / 191 ~= 1.00 5235 60209...
.. . 193 / 192 ~= 1.00 5208 333...
.. . 256 / 255 ~= 1.00 392 1568...
. . . 257 / 256 = 1.00 390 625

.. . 256 / 257 ~= 0.99 610 894...
. . . 255 / 256 = 0.99 609 375
.. . 192 / 193 ~= 0.99 4818 6528...
.. . 191 / 192 ~= 0.99 4791 666...
63.617... / 64 ~= 0.99 4019 5506... ***
.. . 128 / 129 ~= 0.99 2248 06201...
. . . 127 / 128 = 0.99 218 75

this is where i get the 192 from
128 x (3/2) = 128 x 1.5 = 192
just looking for a good fit

or if that's not producing interest enough,
128 x (4/3) = 128 x 1.333... ~= 170.666...
in which case, 170.666... = 172 - (4/3) would be something
or it could be also (4/3) up from 169 + (1/3) = 132 + (1/3)

and it's potentially interesting these fractions are so close
. . . . . 256 / 255 = 1.0039215686274 509803921568627451...
170.666... / 170 = 1.0039215686274 117647058823529412...
(could be the calculator, we'll analyze it later)

but pi remains elusive
or just not conspicuous

there are many groovy formulae for pi
my chief favorite among them being:

1
- (1/3) + (1/5)
- (1/7) + (1/9)
- (1/11) + (1/13)
- (1/15) + (1/17)
- ... + ...

...observe the wonder
and beauty of nature:



the stated solution above relies on a circle's area
being 8/9 that of a square with side = circle diameter
which, of course, 64 is not exactly 63.617...
but 8/9 is an interesting number
8/9 = 23 / 32

pi = C / d

knowing this, it seems to us
that pi can be easily discovered
and was certainly known very early on
...it's the number you come up with
if you want to know how much fabric
will wrap a person, given their width ;o)

"measure twice, cut once;
measure once, cut twice"
- ben franklin

so, here's a table of interesting numbers...
a little sideways, but exponents of 2 and 3

^ : 1 . 2 . 3 .. 4 . 5 .. 6 .. 7 ... 8 ..: (exponent)
2 : 2 . 4 . 8 . 16 32 64 128 256 ...of
3 : 3 . 9 . 27 81 243 . . . . .

256/81
= 28 / 34
= 44 / 34
= (4/3)4
= [(4/3)2]2
= (16/9)2

4/3 is the pythagorean ratio of a perfect fifth
which is the basis for a western musical scale
though today we use an even tempered scale
which is based on exponents: 2(n/12)
maybe we could try something like that
but fractions as exponents
might be a little deep

4/3 is also found in the formula for a sphere
V = 4/3 pi r3

it is also the distance from any south pole
to the magical tetrahedral latitude of 19.47°N

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Subject Views Written By Posted
Pi or no Pi ?????????????? 3228 Sirfiroth 06-Feb-18 03:26
Re: Pi or no Pi ?????????????? 568 drew 06-Feb-18 04:18
Re: Pi or no Pi ?????????????? 530 Sirfiroth 06-Feb-18 17:37
Re: Pi or no Pi ?????????????? 433 drew 06-Feb-18 23:32
Re: Pi or no Pi ???????????????? 493 Dr. Troglodyte 07-Feb-18 14:44
Re: Pi or no Pi ?????????????? 421 molder 08-Feb-18 05:09
Re: Pi or no Pi ?????????????? 417 Sirfiroth 08-Feb-18 06:43
Re: Pi or no Pi ?????????????? 420 DavidK 08-Feb-18 10:48
Re: Pi or no Pi ?????????????? 421 molder 08-Feb-18 11:56
linking egyptian Pi to imperial Pi 355 DavidK 08-Feb-18 15:10
Re: Pi or no Pi ?????????????? 358 DavidK 08-Feb-18 13:58
cubit of 20.25? 326 DavidK 08-Feb-18 14:12
where does Fibonacci Pi come from? 360 DavidK 08-Feb-18 14:49
Re: cubit of 20.25? 415 Sirfiroth 08-Feb-18 15:08
Re: cubit of 20.25? 378 DavidK 08-Feb-18 15:15
Re: cubit of 20.25? 377 molder 09-Feb-18 03:58
Mod Note > Off-Topic Posts 394 Dr. Troglodyte 09-Feb-18 16:38
Re: cubit of 20.25? 579 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 407 drew 09-Feb-18 00:33
Re: Oh...what a shame... 407 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 425 drew 09-Feb-18 06:02
Re: Oh...what a shame... 510 Sirfiroth 09-Feb-18 13:28
Re: Oh...what a shame... 413 DavidK 22-Jun-18 05:58
Re: Oh...what a shame... 350 drew 22-Jun-18 09:54
Re: Oh...what a shame... 431 Sirfiroth 22-Jun-18 13:32
Re: Oh...what a shame... 507 drew 22-Jun-18 22:27
Re: Oh...what a shame... 380 Sirfiroth 23-Jun-18 01:48
Re: well put 350 drew 23-Jun-18 08:08
To put it bluntly! 392 Sirfiroth 23-Jun-18 12:40
Re: well put 372 Manu 23-Jun-18 18:33
Re: extensions of numbers 325 drew 24-Jun-18 00:40
Re: extensions of numbers 386 Sirfiroth 24-Jun-18 04:50
Re: extensions of numbers 336 drew 24-Jun-18 08:36
Re: extensions of numbers 327 Sirfiroth 24-Jun-18 12:22
Re: extensions of numbers 331 drew 24-Jun-18 20:53
Re: extensions of numbers 332 Sirfiroth 25-Jun-18 16:06
Re: extensions of numbers 308 DavidK 25-Jun-18 16:13
Re: extensions of numbers 316 Sirfiroth 25-Jun-18 16:46
the primitive calculator 312 drew 25-Jun-18 23:23
Re: the primitive calculator 367 Sirfiroth 26-Jun-18 02:24
Re: the primitive calculator 300 drew 26-Jun-18 07:06
Mod Note > Duplicate Post Removed 442 Dr. Troglodyte 26-Jun-18 12:45
Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 368 rodz111 26-Jun-18 13:55
Re: Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 269 drew 27-Jun-18 05:18
Re: the primitive calculator 354 Sirfiroth 26-Jun-18 17:00
Re: the primitive calculator 334 drew 27-Jun-18 00:01
Re: the primitive calculator 331 Sirfiroth 27-Jun-18 00:18
Re: the primitive calculator 303 drew 27-Jun-18 01:56
Re: well put 291 cloister 24-Jun-18 09:43
Re: well put 332 Manu 24-Jun-18 12:59
Re: well put 320 cloister 24-Jun-18 18:14
Re: well put 409 cloister 29-Jun-18 08:48
Re: well put 308 drew 27-Jun-18 05:11
Re: Oh...what a shame... 372 Sirfiroth 22-Jun-18 12:21
Re: Oh...what a shame... 401 molder 23-Jun-18 00:24
Re: Oh...what a shame... 382 DavidK 23-Jun-18 21:06
Re: Oh...what a shame... 341 DavidK 24-Jun-18 07:41
Understanding the differences! 385 Sirfiroth 24-Jun-18 12:50
No pie for jacob 379 DavidK 24-Jun-18 08:54
Re: No pie for jacob 317 Sirfiroth 25-Jun-18 16:44
Re: No pie for jacob 341 DavidK 25-Jun-18 20:21
Re: No pie for jacob 351 Sirfiroth 25-Jun-18 23:19
Re: 5 values for pi in GP here are 3 303 molder 26-Jun-18 00:51
Re: what value for pi? 305 drew 26-Jun-18 14:11
Re: what value for pi? 354 molder 26-Jun-18 21:30
Re: what value for pi? 308 drew 26-Jun-18 23:42
Re: 5 values for pi in GP here are 3 294 Sirfiroth 26-Jun-18 14:55
Re: 5 values for pi in GP here are 3 349 molder 26-Jun-18 21:18
Re: No pie for jacob 344 DavidK 26-Jun-18 10:34
Re: No pie for jacob 304 Sirfiroth 26-Jun-18 15:02
Re: No pie for jacob 302 DavidK 26-Jun-18 16:46
Re: No pie for jacob 317 Sirfiroth 26-Jun-18 17:12
Re: No pie for jacob 338 DavidK 26-Jun-18 18:58
Re: No pie for jacob 348 Sirfiroth 26-Jun-18 22:59
Re: No pie for jacob 297 DUNE 26-Jun-18 19:52
Re: No pie for jacob 302 DavidK 26-Jun-18 21:18
Re: No pie for jacob 305 Sirfiroth 26-Jun-18 23:10
Hard evidence for base 100 using egyptian maths 313 DavidK 27-Jun-18 05:37
Re: Hard evidence for base 100 using egyptian maths 370 drew 27-Jun-18 06:16
Re: Hard evidence for base 100 using egyptian maths 314 DavidK 27-Jun-18 10:25
Re: Hard evidence for base 100 using egyptian maths 329 drew 27-Jun-18 21:18
Re: Pi or no Pi ?????????????? 374 rodz111 25-Jun-18 17:48
Re: Pi or no Pi ?????????????? 345 Sirfiroth 25-Jun-18 19:54
Re: Pi or no Pi ?????????????? 315 rodz111 26-Jun-18 03:13
Re: Pi or no Pi ?????????????? 336 molder 26-Jun-18 03:19
Re: Pi or no Pi ?????????????? 332 rodz111 26-Jun-18 03:30
Re: Pi or no Pi ?????????????? 328 molder 26-Jun-18 21:52
Re: Pi or no Pi ?????????????? 378 rodz111 28-Jun-18 07:44
Re: Pi or no Pi ?????????????? 325 drew 28-Jun-18 09:56
Re: Pi or no Pi ?????????????? 354 rodz111 28-Jun-18 11:09
Re: Pi or no Pi ?????????????? 397 drew 28-Jun-18 17:13
Re: Pi or no Pi ?????????????? 358 DavidK 28-Jun-18 20:00
Tripping over museum rods 353 drew 28-Jun-18 23:52
Museum rods 320 drew 29-Jun-18 00:20
Re: Pi or no Pi ?????????????? 345 rodz111 29-Jun-18 00:37
You're as much as a complainer as anyone but you're not... 335 drew 29-Jun-18 01:24
Re: Pi or no Pi ?????????????? 408 rodz111 30-Jun-18 01:21
You down and dirty so-n-so 341 drew 27-Jun-18 05:29
Re: You down and dirty so-n-so 287 Sirfiroth 27-Jun-18 08:17
Re: You down and dirty so-n-so 282 drew 27-Jun-18 09:49
Re: You down and dirty so-n-so 422 Sirfiroth 27-Jun-18 17:12
The math or the pyramid? 358 drew 27-Jun-18 20:46
Re: You down and dirty so-n-so 277 DavidK 17-Jul-18 23:04
Re: You down and dirty so-n-so 300 Sirfiroth 17-Jul-18 23:16
Re: You down and dirty so-n-so 293 DavidK 17-Jul-18 23:20
Re: Pi or no Pi ?????????????? 401 spaceyhippie 19-Jul-18 10:32
Re: Pi or no Pi ?????????????? 320 molder 19-Jul-18 11:21
Re: Pi or no Pi ?????????????? 363 Sirfiroth 19-Jul-18 12:05
Re: Pi or no Pi ?????????????? 489 spaceyhippie 19-Jul-18 23:57
Re: Pi or no Pi ?????????????? 342 DavidK 20-Jul-18 08:20
Re: Pi or no Pi ?????????????? 395 spaceyhippie 20-Jul-18 21:58
Re: Pi or no Pi ?????????????? 276 DavidK 22-Jul-18 09:41
Re: Pi or no Pi ?????????????? 381 spaceyhippie 23-Jul-18 02:15
Re: Pi or no Pi ?????????????? 316 DavidK 23-Jul-18 08:09
Re: Pi or no Pi ?????????????? 338 Sirfiroth 23-Jul-18 13:49
Re: Pi or no Pi ?????????????? 312 DavidK 23-Jul-18 22:23
Re: Pi or no Pi ?????????????? 669 Sirfiroth 23-Jul-18 23:52
Re: Pi or no Pi ?????????????? 331 DavidK 24-Jul-18 09:11
Re: Pi or no Pi ?????????????? 279 Sirfiroth 24-Jul-18 13:11
Re: Pi or no Pi ?????????????? 268 DavidK 27-Jul-18 06:13
Re: Pi or no Pi ?????????????? 304 Sirfiroth 27-Jul-18 15:45
Re: Pi or no Pi ?????????????? 366 spaceyhippie 24-Jul-18 02:44
Re: Pi or no Pi ?????????????? 376 DavidK 24-Jul-18 17:10
Re: Pi or no Pi ?????????????? 426 spaceyhippie 27-Jul-18 00:51
Re: Pi or no Pi ?????????????? 337 spaceyhippie 27-Jul-18 14:36
Re: Pi or no Pi ?????????????? 456 spaceyhippie 29-Jul-18 11:01
Re: Pi or no Pi ?????????????? 340 DavidK 06-Aug-18 19:15
Re: Pi or no Pi ?????????????? 313 DavidK 07-Aug-18 05:16
Re: Pi or no Pi ?????????????? 315 spaceyhippie 08-Aug-18 09:20
Re: Pi or no Pi ?????????????? 323 DavidK 08-Aug-18 09:39
Re: Pi or no Pi ?????????????? 351 spaceyhippie 09-Aug-18 02:32
Re: Pi or no Pi ?????????????? 380 DavidK 09-Aug-18 08:00
ROTFLMAO! 272 Sirfiroth 09-Aug-18 13:22
Re: ROTFLMAO! 279 DavidK 09-Aug-18 14:12
Re: ROTFLMAO! 414 Sirfiroth 09-Aug-18 14:28
Re: ROTFLMAO! 265 DavidK 09-Aug-18 14:49
Re: ROTFLMAO! 273 Sirfiroth 09-Aug-18 15:03
Re: ROTFLMAO! 286 DavidK 09-Aug-18 21:39
Re: ROTFLMAO! 311 Sirfiroth 10-Aug-18 02:06
Re: Pi or no Pi ?????????????? 324 spaceyhippie 09-Aug-18 20:40
Re: Pi or no Pi ?????????????? 378 DavidK 10-Aug-18 07:59
Re: Pi or no Pi ?????????????? 384 Steve Clayton 12-Aug-18 18:16
Re: Pi or no Pi ?????????????? 170 DavidK 27-Dec-19 23:13
Re: Pi or no Pi ?????????????? 155 Sirfiroth 28-Dec-19 03:46
Pi. All Pi. All The Time. 170 thinkitover 28-Dec-19 04:59
Re: Pi. All Pi. All The Time. 144 molder 28-Dec-19 10:35
Re: Pi or no Pi ?????????????? 142 DavidK 28-Dec-19 10:20
Re: Pi or no Pi ?????????????? 152 Sirfiroth 28-Dec-19 15:13
Re: Pi or no Pi ?????????????? 171 Thanos5150 28-Dec-19 16:30
Re: Pi or no Pi ?????????????? 160 thinkitover 28-Dec-19 21:49
Re: Pi or no Pi ?????????????? 157 Thanos5150 29-Dec-19 04:35
Re: Pi or no Pi ?????????????? 149 Sirfiroth 29-Dec-19 02:17
Re: Pi or no Pi ?????????????? 153 molder 29-Dec-19 04:14
Re: Pi or no Pi ?????????????? 146 Sirfiroth 29-Dec-19 12:51
Re: Pi or no Pi ?????????????? 146 molder 29-Dec-19 22:31
Re: Pi or no Pi ?????????????? 138 Sirfiroth 30-Dec-19 14:11
Re: Pi or no Pi ?????????????? 185 magisterchessmutt 30-Dec-19 15:16
Re: Pi or no Pi ?????????????? 144 Sirfiroth 31-Dec-19 03:33
Re: Pi or no Pi ?????????????? 190 magisterchessmutt 31-Dec-19 04:33
Re: Pi or no Pi ?????????????? 162 Sirfiroth 31-Dec-19 15:04
Re: Pi or no Pi ?????????????? 170 spaceyhippie 31-Dec-19 23:37
Re: Pi or no Pi ?????????????? 164 Thanos5150 29-Dec-19 04:29
Re: Pi or no Pi ?????????????? 150 DavidK 29-Dec-19 09:32
Re: Pi or no Pi ?????????????? 156 Sirfiroth 29-Dec-19 14:09
Re: Pi or no Pi ?????????????? 154 spaceyhippie 01-Jan-20 23:18
Re: Pi or no Pi ?????????????? 169 Sirfiroth 02-Jan-20 01:33
Pi vs Pudding 158 thinkitover 02-Jan-20 21:45
Re: Pi vs Pudding 149 spaceyhippie 03-Jan-20 00:06
Re: Pi vs Pudding 167 seasmith 03-Jan-20 00:24
Re: Pi vs Pudding 149 spaceyhippie 07-Jan-20 23:06
Re: Pi vs Pudding 192 seasmith 08-Jan-20 02:54
Re: Pi vs Pudding 157 Sirfiroth 03-Jan-20 03:36
Re: Pi vs Pudding 157 molder 03-Jan-20 06:56
Re: Pi vs Pudding 159 Sirfiroth 03-Jan-20 18:25
Re: Pi vs Pudding 154 spaceyhippie 04-Jan-20 00:02
LOL, now that was hilarious ! 152 Sirfiroth 04-Jan-20 05:51
Re: LOL, now that was hilarious ! 197 hendrik dirker 04-Jan-20 09:32
Re: LOL, now that was hilarious ! 142 spaceyhippie 04-Jan-20 23:37
Re: LOL, now that was hilarious ! 152 spaceyhippie 04-Jan-20 23:39
Re: Pi vs Pudding 170 molder 04-Jan-20 11:03
Re: Pi vs Pudding 160 Sirfiroth 05-Jan-20 20:11
Re: Pi vs Pudding 150 molder 06-Jan-20 02:55
Re: Pi vs Pudding 179 magisterchessmutt 06-Jan-20 02:58
Re: Pi vs Pudding 145 molder 06-Jan-20 05:26
Re: Pi vs Pudding 148 spaceyhippie 07-Jan-20 01:32
Re: Pi vs Pudding 136 DavidK 07-Jan-20 02:02
Re: Pi vs Pudding 150 thinkitover 06-Jan-20 06:13
Re: Pi vs Pudding 165 Sirfiroth 07-Jan-20 02:18
Re: Pi vs Pudding 134 DavidK 07-Jan-20 14:25
Re: Pi vs Pudding 147 Sirfiroth 07-Jan-20 15:16
Re: Pi vs Pudding 146 DavidK 07-Jan-20 19:03
Re: Pi vs Pudding 140 Sirfiroth 07-Jan-20 20:08
Re: Pi vs Pudding 139 DavidK 07-Jan-20 20:11
Re: Pi or no Pi ?????????????? 166 DavidK 28-Dec-19 11:21
Re: Pi or no Pi ?????????????? 161 engbren 28-Dec-19 12:34
Re: Pi or no Pi ?????????????? 161 Sirfiroth 28-Dec-19 15:55
Re: Pi or no Pi ?????????????? 150 engbren 29-Dec-19 01:14
Re: Pi or no Pi ?????????????? 150 Sirfiroth 30-Dec-19 16:52
Re: Pi or no Pi ?????????????? 151 engbren 30-Dec-19 22:23
Re: Pi or no Pi ?????????????? 209 magisterchessmutt 30-Dec-19 23:24
Re: Pi or no Pi ?????????????? 175 engbren 31-Dec-19 11:31
Re: Pi or no Pi ?????????????? 158 spaceyhippie 04-Jan-20 00:42


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