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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 ?????????????? 3195 Sirfiroth 06-Feb-18 03:26
Re: Pi or no Pi ?????????????? 549 drew 06-Feb-18 04:18
Re: Pi or no Pi ?????????????? 512 Sirfiroth 06-Feb-18 17:37
Re: Pi or no Pi ?????????????? 415 drew 06-Feb-18 23:32
Re: Pi or no Pi ???????????????? 476 Dr. Troglodyte 07-Feb-18 14:44
Re: Pi or no Pi ?????????????? 401 molder 08-Feb-18 05:09
Re: Pi or no Pi ?????????????? 399 Sirfiroth 08-Feb-18 06:43
Re: Pi or no Pi ?????????????? 400 DavidK 08-Feb-18 10:48
Re: Pi or no Pi ?????????????? 399 molder 08-Feb-18 11:56
linking egyptian Pi to imperial Pi 337 DavidK 08-Feb-18 15:10
Re: Pi or no Pi ?????????????? 340 DavidK 08-Feb-18 13:58
cubit of 20.25? 306 DavidK 08-Feb-18 14:12
where does Fibonacci Pi come from? 341 DavidK 08-Feb-18 14:49
Re: cubit of 20.25? 398 Sirfiroth 08-Feb-18 15:08
Re: cubit of 20.25? 356 DavidK 08-Feb-18 15:15
Re: cubit of 20.25? 357 molder 09-Feb-18 03:58
Mod Note > Off-Topic Posts 376 Dr. Troglodyte 09-Feb-18 16:38
Re: cubit of 20.25? 518 Sirfiroth 09-Feb-18 21:02
Oh...what a shame... 388 drew 09-Feb-18 00:33
Re: Oh...what a shame... 389 Sirfiroth 09-Feb-18 04:47
Re: Oh...what a shame... 409 drew 09-Feb-18 06:02
Re: Oh...what a shame... 411 Sirfiroth 09-Feb-18 13:28
Re: Oh...what a shame... 396 DavidK 22-Jun-18 05:58
Re: Oh...what a shame... 334 drew 22-Jun-18 09:54
Re: Oh...what a shame... 412 Sirfiroth 22-Jun-18 13:32
Re: Oh...what a shame... 490 drew 22-Jun-18 22:27
Re: Oh...what a shame... 361 Sirfiroth 23-Jun-18 01:48
Re: well put 333 drew 23-Jun-18 08:08
To put it bluntly! 376 Sirfiroth 23-Jun-18 12:40
Re: well put 354 Manu 23-Jun-18 18:33
Re: extensions of numbers 308 drew 24-Jun-18 00:40
Re: extensions of numbers 365 Sirfiroth 24-Jun-18 04:50
Re: extensions of numbers 319 drew 24-Jun-18 08:36
Re: extensions of numbers 310 Sirfiroth 24-Jun-18 12:22
Re: extensions of numbers 313 drew 24-Jun-18 20:53
Re: extensions of numbers 313 Sirfiroth 25-Jun-18 16:06
Re: extensions of numbers 290 DavidK 25-Jun-18 16:13
Re: extensions of numbers 297 Sirfiroth 25-Jun-18 16:46
the primitive calculator 295 drew 25-Jun-18 23:23
Re: the primitive calculator 350 Sirfiroth 26-Jun-18 02:24
Re: the primitive calculator 282 drew 26-Jun-18 07:06
Mod Note > Duplicate Post Removed 352 Dr. Troglodyte 26-Jun-18 12:45
Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 350 rodz111 26-Jun-18 13:55
Re: Newton's problem solved(the relation between the Roman foot and the Egyptian foot ) 251 drew 27-Jun-18 05:18
Re: the primitive calculator 324 Sirfiroth 26-Jun-18 17:00
Re: the primitive calculator 314 drew 27-Jun-18 00:01
Re: the primitive calculator 310 Sirfiroth 27-Jun-18 00:18
Re: the primitive calculator 284 drew 27-Jun-18 01:56
Re: well put 273 cloister 24-Jun-18 09:43
Re: well put 313 Manu 24-Jun-18 12:59
Re: well put 299 cloister 24-Jun-18 18:14
Re: well put 358 cloister 29-Jun-18 08:48
Re: well put 288 drew 27-Jun-18 05:11
Re: Oh...what a shame... 353 Sirfiroth 22-Jun-18 12:21
Re: Oh...what a shame... 383 molder 23-Jun-18 00:24
Re: Oh...what a shame... 364 DavidK 23-Jun-18 21:06
Re: Oh...what a shame... 322 DavidK 24-Jun-18 07:41
Understanding the differences! 321 Sirfiroth 24-Jun-18 12:50
No pie for jacob 359 DavidK 24-Jun-18 08:54
Re: No pie for jacob 298 Sirfiroth 25-Jun-18 16:44
Re: No pie for jacob 325 DavidK 25-Jun-18 20:21
Re: No pie for jacob 328 Sirfiroth 25-Jun-18 23:19
Re: 5 values for pi in GP here are 3 285 molder 26-Jun-18 00:51
Re: what value for pi? 288 drew 26-Jun-18 14:11
Re: what value for pi? 334 molder 26-Jun-18 21:30
Re: what value for pi? 286 drew 26-Jun-18 23:42
Re: 5 values for pi in GP here are 3 275 Sirfiroth 26-Jun-18 14:55
Re: 5 values for pi in GP here are 3 330 molder 26-Jun-18 21:18
Re: No pie for jacob 326 DavidK 26-Jun-18 10:34
Re: No pie for jacob 286 Sirfiroth 26-Jun-18 15:02
Re: No pie for jacob 286 DavidK 26-Jun-18 16:46
Re: No pie for jacob 293 Sirfiroth 26-Jun-18 17:12
Re: No pie for jacob 321 DavidK 26-Jun-18 18:58
Re: No pie for jacob 332 Sirfiroth 26-Jun-18 22:59
Re: No pie for jacob 281 DUNE 26-Jun-18 19:52
Re: No pie for jacob 285 DavidK 26-Jun-18 21:18
Re: No pie for jacob 286 Sirfiroth 26-Jun-18 23:10
Hard evidence for base 100 using egyptian maths 297 DavidK 27-Jun-18 05:37
Re: Hard evidence for base 100 using egyptian maths 323 drew 27-Jun-18 06:16
Re: Hard evidence for base 100 using egyptian maths 297 DavidK 27-Jun-18 10:25
Re: Hard evidence for base 100 using egyptian maths 310 drew 27-Jun-18 21:18
Re: Pi or no Pi ?????????????? 354 rodz111 25-Jun-18 17:48
Re: Pi or no Pi ?????????????? 327 Sirfiroth 25-Jun-18 19:54
Re: Pi or no Pi ?????????????? 297 rodz111 26-Jun-18 03:13
Re: Pi or no Pi ?????????????? 318 molder 26-Jun-18 03:19
Re: Pi or no Pi ?????????????? 314 rodz111 26-Jun-18 03:30
Re: Pi or no Pi ?????????????? 310 molder 26-Jun-18 21:52
Re: Pi or no Pi ?????????????? 361 rodz111 28-Jun-18 07:44
Re: Pi or no Pi ?????????????? 306 drew 28-Jun-18 09:56
Re: Pi or no Pi ?????????????? 337 rodz111 28-Jun-18 11:09
Re: Pi or no Pi ?????????????? 325 drew 28-Jun-18 17:13
Re: Pi or no Pi ?????????????? 340 DavidK 28-Jun-18 20:00
Tripping over museum rods 338 drew 28-Jun-18 23:52
Museum rods 303 drew 29-Jun-18 00:20
Re: Pi or no Pi ?????????????? 327 rodz111 29-Jun-18 00:37
You're as much as a complainer as anyone but you're not... 318 drew 29-Jun-18 01:24
Re: Pi or no Pi ?????????????? 388 rodz111 30-Jun-18 01:21
You down and dirty so-n-so 324 drew 27-Jun-18 05:29
Re: You down and dirty so-n-so 271 Sirfiroth 27-Jun-18 08:17
Re: You down and dirty so-n-so 265 drew 27-Jun-18 09:49
Re: You down and dirty so-n-so 402 Sirfiroth 27-Jun-18 17:12
The math or the pyramid? 340 drew 27-Jun-18 20:46
Re: You down and dirty so-n-so 258 DavidK 17-Jul-18 23:04
Re: You down and dirty so-n-so 281 Sirfiroth 17-Jul-18 23:16
Re: You down and dirty so-n-so 274 DavidK 17-Jul-18 23:20
Re: Pi or no Pi ?????????????? 381 spaceyhippie 19-Jul-18 10:32
Re: Pi or no Pi ?????????????? 297 molder 19-Jul-18 11:21
Re: Pi or no Pi ?????????????? 344 Sirfiroth 19-Jul-18 12:05
Re: Pi or no Pi ?????????????? 466 spaceyhippie 19-Jul-18 23:57
Re: Pi or no Pi ?????????????? 325 DavidK 20-Jul-18 08:20
Re: Pi or no Pi ?????????????? 376 spaceyhippie 20-Jul-18 21:58
Re: Pi or no Pi ?????????????? 259 DavidK 22-Jul-18 09:41
Re: Pi or no Pi ?????????????? 364 spaceyhippie 23-Jul-18 02:15
Re: Pi or no Pi ?????????????? 298 DavidK 23-Jul-18 08:09
Re: Pi or no Pi ?????????????? 320 Sirfiroth 23-Jul-18 13:49
Re: Pi or no Pi ?????????????? 292 DavidK 23-Jul-18 22:23
Re: Pi or no Pi ?????????????? 447 Sirfiroth 23-Jul-18 23:52
Re: Pi or no Pi ?????????????? 310 DavidK 24-Jul-18 09:11
Re: Pi or no Pi ?????????????? 259 Sirfiroth 24-Jul-18 13:11
Re: Pi or no Pi ?????????????? 249 DavidK 27-Jul-18 06:13
Re: Pi or no Pi ?????????????? 287 Sirfiroth 27-Jul-18 15:45
Re: Pi or no Pi ?????????????? 348 spaceyhippie 24-Jul-18 02:44
Re: Pi or no Pi ?????????????? 356 DavidK 24-Jul-18 17:10
Re: Pi or no Pi ?????????????? 408 spaceyhippie 27-Jul-18 00:51
Re: Pi or no Pi ?????????????? 319 spaceyhippie 27-Jul-18 14:36
Re: Pi or no Pi ?????????????? 439 spaceyhippie 29-Jul-18 11:01
Re: Pi or no Pi ?????????????? 320 DavidK 06-Aug-18 19:15
Re: Pi or no Pi ?????????????? 294 DavidK 07-Aug-18 05:16
Re: Pi or no Pi ?????????????? 298 spaceyhippie 08-Aug-18 09:20
Re: Pi or no Pi ?????????????? 305 DavidK 08-Aug-18 09:39
Re: Pi or no Pi ?????????????? 334 spaceyhippie 09-Aug-18 02:32
Re: Pi or no Pi ?????????????? 362 DavidK 09-Aug-18 08:00
ROTFLMAO! 255 Sirfiroth 09-Aug-18 13:22
Re: ROTFLMAO! 260 DavidK 09-Aug-18 14:12
Re: ROTFLMAO! 313 Sirfiroth 09-Aug-18 14:28
Re: ROTFLMAO! 248 DavidK 09-Aug-18 14:49
Re: ROTFLMAO! 254 Sirfiroth 09-Aug-18 15:03
Re: ROTFLMAO! 270 DavidK 09-Aug-18 21:39
Re: ROTFLMAO! 294 Sirfiroth 10-Aug-18 02:06
Re: Pi or no Pi ?????????????? 309 spaceyhippie 09-Aug-18 20:40
Re: Pi or no Pi ?????????????? 364 DavidK 10-Aug-18 07:59
Re: Pi or no Pi ?????????????? 371 Steve Clayton 12-Aug-18 18:16
Re: Pi or no Pi ?????????????? 154 DavidK 27-Dec-19 23:13
Re: Pi or no Pi ?????????????? 141 Sirfiroth 28-Dec-19 03:46
Pi. All Pi. All The Time. 155 thinkitover 28-Dec-19 04:59
Re: Pi. All Pi. All The Time. 130 molder 28-Dec-19 10:35
Re: Pi or no Pi ?????????????? 128 DavidK 28-Dec-19 10:20
Re: Pi or no Pi ?????????????? 138 Sirfiroth 28-Dec-19 15:13
Re: Pi or no Pi ?????????????? 151 Thanos5150 28-Dec-19 16:30
Re: Pi or no Pi ?????????????? 146 thinkitover 28-Dec-19 21:49
Re: Pi or no Pi ?????????????? 144 Thanos5150 29-Dec-19 04:35
Re: Pi or no Pi ?????????????? 135 Sirfiroth 29-Dec-19 02:17
Re: Pi or no Pi ?????????????? 139 molder 29-Dec-19 04:14
Re: Pi or no Pi ?????????????? 132 Sirfiroth 29-Dec-19 12:51
Re: Pi or no Pi ?????????????? 131 molder 29-Dec-19 22:31
Re: Pi or no Pi ?????????????? 124 Sirfiroth 30-Dec-19 14:11
Re: Pi or no Pi ?????????????? 171 magisterchessmutt 30-Dec-19 15:16
Re: Pi or no Pi ?????????????? 130 Sirfiroth 31-Dec-19 03:33
Re: Pi or no Pi ?????????????? 175 magisterchessmutt 31-Dec-19 04:33
Re: Pi or no Pi ?????????????? 148 Sirfiroth 31-Dec-19 15:04
Re: Pi or no Pi ?????????????? 155 spaceyhippie 31-Dec-19 23:37
Re: Pi or no Pi ?????????????? 149 Thanos5150 29-Dec-19 04:29
Re: Pi or no Pi ?????????????? 136 DavidK 29-Dec-19 09:32
Re: Pi or no Pi ?????????????? 138 Sirfiroth 29-Dec-19 14:09
Re: Pi or no Pi ?????????????? 139 spaceyhippie 01-Jan-20 23:18
Re: Pi or no Pi ?????????????? 152 Sirfiroth 02-Jan-20 01:33
Pi vs Pudding 143 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 133 spaceyhippie 07-Jan-20 23:06
Re: Pi vs Pudding 176 seasmith 08-Jan-20 02:54
Re: Pi vs Pudding 142 Sirfiroth 03-Jan-20 03:36
Re: Pi vs Pudding 142 molder 03-Jan-20 06:56
Re: Pi vs Pudding 144 Sirfiroth 03-Jan-20 18:25
Re: Pi vs Pudding 135 spaceyhippie 04-Jan-20 00:02
LOL, now that was hilarious ! 135 Sirfiroth 04-Jan-20 05:51
Re: LOL, now that was hilarious ! 176 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 ! 133 spaceyhippie 04-Jan-20 23:39
Re: Pi vs Pudding 153 molder 04-Jan-20 11:03
Re: Pi vs Pudding 144 Sirfiroth 05-Jan-20 20:11
Re: Pi vs Pudding 135 molder 06-Jan-20 02:55
Re: Pi vs Pudding 165 magisterchessmutt 06-Jan-20 02:58
Re: Pi vs Pudding 128 molder 06-Jan-20 05:26
Re: Pi vs Pudding 133 spaceyhippie 07-Jan-20 01:32
Re: Pi vs Pudding 121 DavidK 07-Jan-20 02:02
Re: Pi vs Pudding 136 thinkitover 06-Jan-20 06:13
Re: Pi vs Pudding 151 Sirfiroth 07-Jan-20 02:18
Re: Pi vs Pudding 119 DavidK 07-Jan-20 14:25
Re: Pi vs Pudding 132 Sirfiroth 07-Jan-20 15:16
Re: Pi vs Pudding 131 DavidK 07-Jan-20 19:03
Re: Pi vs Pudding 126 Sirfiroth 07-Jan-20 20:08
Re: Pi vs Pudding 125 DavidK 07-Jan-20 20:11
Re: Pi or no Pi ?????????????? 153 DavidK 28-Dec-19 11:21
Re: Pi or no Pi ?????????????? 148 engbren 28-Dec-19 12:34
Re: Pi or no Pi ?????????????? 148 Sirfiroth 28-Dec-19 15:55
Re: Pi or no Pi ?????????????? 136 engbren 29-Dec-19 01:14
Re: Pi or no Pi ?????????????? 136 Sirfiroth 30-Dec-19 16:52
Re: Pi or no Pi ?????????????? 138 engbren 30-Dec-19 22:23
Re: Pi or no Pi ?????????????? 194 magisterchessmutt 30-Dec-19 23:24
Re: Pi or no Pi ?????????????? 160 engbren 31-Dec-19 11:31
Re: Pi or no Pi ?????????????? 141 spaceyhippie 04-Jan-20 00:42


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