Little explorations with HP calculators (no Prime)
11-05-2017, 04:05 PM (This post was last modified: 11-05-2017 07:19 PM by pier4r.)
Post: #247
 pier4r Senior Member Posts: 2,067 Joined: Nov 2014
RE: Little explorations with HP calculators (no Prime)
I am slowly continuing to explore the "integer numerator ranges that enclose pi" (I post it here and not in another thread because I already mentioned the exploration here).

At the moment I'd like to see how the numerators approaches pi keeping a dynamic TopX of approximations. The program I assembled so far does a lot of list processing and the listExt library of DavidM is super helpful. Especially KSORT is great.

The program has the following idea:

create a list that contains quintuplets
{ D NL NH VL VH }
D: denominator
NL: numerator low (minimum of the range given the denominator)
NH: numerator high (maximum of the range given the denominator)
VL: value NL/D
VH: value NH/D

I do not just add to the result all the quintuplets between firstDenominator (say 1) and maxDenominator (say 10).
Instead I want to add those approximations that make it to the "actual top5", where actual means: considering the quintuplets computed so far. This excluding quintuplets that produce the same best approximation.

For example
14 43 44 3.071... 3.14285...
is considered equal to
7 21 22 3 3.14285...
because the best approximation produced ( 44/14 ) is already in the top 5, since 22/7 was the first instance found for that approximation. (I may later on check if also the second approximation is worth the top5)

The program is the following
Code:
 gpIntegerRangeEnclosePiAttempt201711051450   \<<     @use the listExt of davidM     1               "lvFirstDenominator"                  DROP     10              "lvLastDenominator"                   DROP     0               "lvCountElements"                     DROP     { }             "lvCurrentTopApproximations"          DROP     { }             "lvCurrentTopApproxDist"              DROP     5               "lvNumberTopApproxSave"               DROP     0               "lvValueMin"                          DROP     0               "lvValueMax"                          DROP     0               "lvApproxInIteration"                 DROP     0               "lvDistInIteration"                   DROP               \->     lvFirstDenominator     lvLastDenominator     lvCountElements     lvCurrentTopApproximations     lvCurrentTopApproxDist     lvNumberTopApproxSave     lvValueMin     lvValueMax     lvApproxInIteration     lvDistInIteration               \<<       0 lvNumberTopApproxSave NDUPN \->LIST        DUP 'lvCurrentTopApproximations' STO       \pi - ABS 'lvCurrentTopApproxDist' STO                   lvFirstDenominator lvLastDenominator       FOR lvDenominator         lvDenominator @den         DUP \pi * IP @min num         DUP 1 + @max num           @see explanation in other attemps         OVER lvDenominator / @min num/den          DUP 'lvValueMin' STO                  OVER lvDenominator / @max num/den         DUP 'lvValueMax' STO                  IF           @if there is not already the best approximation inside the top list           lvValueMin lvValueMax 2 \->LIST @make a list of value           DUP 'lvApproxInIteration' STO           DUP \pi - ABS @distance from pi in absolute value           DUP 'lvDistInIteration' STO           KSORT @sort by distance           DROP @drop the distance           HEAD @pick the approx with the closest distance to PI           lvCurrentTopApproximations SWAP POS 0 ==             @the best value is not in the list         THEN           @see if any of those two values is in the best approximations           @optimizations come later           lvCurrentTopApproximations lvApproxInIteration +           lvCurrentTopApproxDist lvDistInIteration +                      @ sort by the absolute distance from PI           KSORT                      @save the distance           lvNumberTopApproxSave LFRST 'lvCurrentTopApproxDist' STO           @save the list of the 5 best approx           lvNumberTopApproxSave LFRST 'lvCurrentTopApproximations' STO                      IF             lvCurrentTopApproximations lvValueMin POS 0 >             lvCurrentTopApproximations lvValueMax POS 0 >             OR             @ if Any approximation made it in the top list           THEN             @save the computations             'lvCountElements' 5 STO+           ELSE             @discard             5 DROPN           END         ELSE           @discard           5 DROPN         END       NEXT              @we have on the stack many values now, let's pack them in a list       lvCountElements       \->LIST            \>>   \>>

The program runs on my hp50g in 646 seconds for the first 1000 denominators.

And uses 10232 seconds for the first 10k denominators. Seeing the fraction slowly closing in pi is satisfying.

The values so far:
Code:
 { 1. 3. 4. 3. 4. 4. 12. 13. 3. 3.25 5. 15. 16. 3. 3.2 6. 18. 19. 3. 3.16666666667  7. 21. 22. 3. 3.14285714286 8. 25. 26. 3.125 3.25  9. 28. 29. 3.11111111111 3.22222222222 10. 31. 32. 3.1 3.2  11. 34. 35. 3.09090909091 3.18181818182  13. 40. 41. 3.07692307692 3.15384615385  15. 47. 48. 3.13333333333 3.2 17. 53. 54. 3.11764705882 3.17647058824  19. 59. 60. 3.10526315789 3.15789473684 20. 62. 63. 3.1 3.15  22. 69. 70. 3.13636363636 3.18181818182 23. 72. 73. 3.13043478261 3.17391304348  27. 84. 85. 3.11111111111 3.14814814815 29. 91. 92. 3.13793103448 3.1724137931  34. 106. 107. 3.11764705882 3.14705882353 36. 113. 114. 3.13888888889 3.16666666667  41. 128. 129. 3.12195121951 3.14634146341 43. 135. 136. 3.13953488372 3.16279069767  48. 150. 151. 3.125 3.14583333333 50. 157. 158. 3.14 3.16  57. 179. 180. 3.14035087719 3.15789473684 64. 201. 202. 3.140625 3.15625  71. 223. 224. 3.14084507042 3.15492957746 78. 245. 246. 3.14102564103 3.15384615385  85. 267. 268. 3.14117647059 3.15294117647 92. 289. 290. 3.14130434783 3.15217391304  99. 311. 312. 3.14141414141 3.15151515152 106. 333. 334. 3.14150943396 3.15094339623  113. 354. 355. 3.13274336283 3.14159292035 120. 376. 377. 3.13333333333 3.14166666667  127. 398. 399. 3.13385826772 3.14173228346 205. 644. 645. 3.14146341463 3.14634146341  219. 688. 689. 3.14155251142 3.14611872146 233. 731. 732. 3.13733905579 3.14163090129  325. 1021. 1022. 3.14153846154 3.14461538462 332. 1043. 1044. 3.14156626506 3.14457831325  346. 1086. 1087. 3.1387283237 3.14161849711 445. 1398. 1399. 3.14157303371 3.14382022472  459. 1441. 1442. 3.1394335512 3.14161220044 558. 1753. 1754. 3.14157706093 3.14336917563  572. 1796. 1797. 3.13986013986 3.14160839161 671. 2108. 2109. 3.14157973174 3.14307004471  685. 2151. 2152. 3.1401459854 3.14160583942 784. 2463. 2464. 3.14158163265 3.14285714286  798. 2506. 2507. 3.14035087719 3.14160401003 897. 2818. 2819. 3.14158305463 3.14269788183  911. 2861. 2862. 3.14050493963 3.14160263447 1010. 3173. 3174. 3.14158415842 3.14257425743  1024. 3216. 3217. 3.140625 3.1416015625 1123. 3528. 3529. 3.14158504007 3.14247551202  1137. 3571. 3572. 3.14072119613 3.14160070361 1236. 3883. 3884. 3.14158576052 3.14239482201  1250. 3926. 3927. 3.1408 3.1416 1349. 4238. 4239. 3.14158636027 3.14232765011  1363. 4281. 4282. 3.14086573734 3.14159941306 1462. 4593. 4594. 3.14158686731 3.14227086183  1476. 4636. 4637. 3.14092140921 3.14159891599 1575. 4948. 4949. 3.14158730159 3.14222222222  1589. 4991. 4992. 3.140969163 3.14159848962 1688. 5303. 5304. 3.14158767773 3.14218009479  1702. 5346. 5347. 3.14101057579 3.14159811986 1801. 5658. 5659. 3.14158800666 3.14214325375  1815. 5701. 5702. 3.14104683196 3.14159779614 1914. 6013. 6014. 3.14158829676 3.1421107628  1928. 6056. 6057. 3.14107883817 3.14159751037 2027. 6368. 6369. 3.14158855451 3.14208189443  2041. 6411. 6412. 3.14110730034 3.14159725625 2140. 6723. 6724. 3.14158878505 3.14205607477  2154. 6766. 6767. 3.14113277623 3.14159702878 2253. 7078. 7079. 3.14158899245 3.1420328451  2267. 7121. 7122. 3.1411557124 3.141596824 2366. 7433. 7434. 3.14158918005 3.14201183432  2380. 7476. 7477. 3.14117647059 3.14159663866 2479. 7788. 7789. 3.14158935054 3.14199273901  2493. 7831. 7832. 3.14119534697 3.14159647012 2592. 8143. 8144. 3.14158950617 3.14197530864  2705. 8498. 8499. 3.1415896488 3.14195933457 2818. 8853. 8854. 3.14158977999 3.14194464159  2931. 9208. 9209. 3.14158990106 3.14193108154 3044. 9563. 9564. 3.14159001314 3.14191852825  3157. 9918. 9919. 3.1415901172 3.14190687361 3270. 10273. 10274. 3.14159021407 3.14189602446  3383. 10628. 10629. 3.14159030446 3.14188590009 3496. 10983. 10984. 3.14159038902 3.14187643021  3609. 11338. 11339. 3.14159046827 3.14186755334 3722. 11693. 11694. 3.14159054272 3.14185921548  3835. 12048. 12049. 3.14159061278 3.14185136897 3948. 12403. 12404. 3.14159067882 3.14184397163  4061. 12758. 12759. 3.1415907412 3.14183698596 4174. 13113. 13114. 3.14159080019 3.14183037853  4287. 13468. 13469. 3.14159085608 3.14182411943 4400. 13823. 13824. 3.14159090909 3.14181818182  4513. 14178. 14179. 3.14159095945 3.14181254155 4626. 14533. 14534. 3.14159100735 3.14180717683  4739. 14888. 14889. 3.14159105296 3.14180206795 4852. 15243. 15244. 3.14159109646 3.14179719703  4965. 15598. 15599. 3.14159113797 3.14179254783 5078. 15953. 15954. 3.14159117763 3.14178810555  5191. 16308. 16309. 3.14159121557 3.14178385668 5304. 16663. 16664. 3.14159125189 3.14177978884  5417. 17018. 17019. 3.14159128669 3.14177589071 5530. 17373. 17374. 3.14159132007 3.1417721519  5643. 17728. 17729. 3.14159135212 3.14176856282 5756. 18083. 18084. 3.1415913829 3.14176511466  5869. 18438. 18439. 3.14159141251 3.14176179928 5982. 18793. 18794. 3.14159144099 3.14175860916  6095. 19148. 19149. 3.14159146842 3.14175553733 6208. 19503. 19504. 3.14159149485 3.14175257732  6321. 19858. 19859. 3.14159152033 3.14174972315 6434. 20213. 20214. 3.14159154492 3.14174696923  6547. 20568. 20569. 3.14159156866 3.14174431037 6660. 20923. 20924. 3.14159159159 3.14174174174  6773. 21278. 21279. 3.14159161376 3.14173925882 6886. 21633. 21634. 3.1415916352 3.14173685739  6999. 21988. 21989. 3.14159165595 3.1417345335 7112. 22343. 22344. 3.14159167604 3.14173228346  7225. 22698. 22699. 3.1415916955 3.14173010381 7338. 23053. 23054. 3.14159171436 3.14172799128  7451. 23408. 23409. 3.14159173265 3.14172594283 7564. 23763. 23764. 3.1415917504 3.14172395558  7677. 24118. 24119. 3.14159176762 3.14172202683 7790. 24473. 24474. 3.14159178434 3.14172015404  7903. 24828. 24829. 3.14159180058 3.14171833481 8016. 25183. 25184. 3.14159181637 3.14171656687  8129. 25538. 25539. 3.14159183171 3.14171484807 8242. 25893. 25894. 3.14159184664 3.14171317641  8355. 26248. 26249. 3.14159186116 3.14171154997 8468. 26603. 26604. 3.1415918753 3.14170996693  8581. 26958. 26959. 3.14159188906 3.14170842559 8694. 27313. 27314. 3.14159190246 3.14170692432  8807. 27668. 27669. 3.14159191552 3.14170546156 8920. 28023. 28024. 3.14159192825 3.14170403587  9033. 28378. 28379. 3.14159194066 3.14170264585 9146. 28733. 28734. 3.14159195277 3.14170129018  9259. 29088. 29089. 3.14159196458 3.1416999676 9372. 29443. 29444. 3.1415919761 3.14169867691  9485. 29798. 29799. 3.14159198735 3.14169741697 9598. 30153. 30154. 3.14159199833 3.14169618671  9711. 30508. 30509. 3.14159200906 3.14169498507 9824. 30863. 30864. 3.14159201954 3.14169381107  9937. 31218. 31219. 3.14159202979 3.14169266378 }

I do not use heavy stack manipulations, although I use them more than before. For example I build the list only at the end of the iterations, as suggested by John Keith. I avoid too much stack acrobatics due to readability of the code but I am pretty sure other people could make the program way faster.

Therefore I posted it because I am curious to see how it can be optimized.

Wikis are great, Contribute :)
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 Messages In This Thread Little explorations with HP calculators (no Prime) - pier4r - 03-15-2017, 11:11 PM RE: Little explorations with the HP calculators - Thomas Okken - 03-15-2017, 11:56 PM RE: Little explorations with the HP calculators - pier4r - 03-16-2017, 12:01 AM RE: Little explorations with the HP calculators - Logan - 03-16-2017, 11:06 AM RE: Little explorations with the HP calculators - ekubaskie - 03-16-2017, 02:07 AM RE: Little explorations with the HP calculators - Csaba Tizedes - 03-16-2017, 08:09 AM RE: Little explorations with the HP calculators - TASP - 03-16-2017, 06:29 PM RE: Little explorations with the HP calculators - pier4r - 03-21-2017, 10:40 PM RE: Little explorations with the HP calculators - Joe Horn - 03-21-2017, 11:41 PM RE: Little explorations with the HP calculators - Dieter - 03-28-2017, 05:46 PM RE: Little explorations with the HP calculators - pier4r - 03-28-2017, 06:17 PM RE: Little explorations with the HP calculators - pier4r - 03-22-2017, 08:37 AM RE: Little explorations with the HP calculators - John Keith - 03-22-2017, 12:14 PM RE: Little explorations with the HP calculators - Joe Horn - 03-22-2017, 03:27 PM RE: Little explorations with the HP calculators - pier4r - 03-22-2017, 04:45 PM RE: Little explorations with the HP calculators - John Keith - 03-22-2017, 11:11 PM RE: Little explorations with the HP calculators - pier4r - 03-23-2017, 08:07 AM RE: Little explorations with the HP calculators - Simone Cerica - 03-23-2017, 08:58 AM RE: Little explorations with the HP calculators - John Keith - 03-22-2017, 11:25 PM RE: Little explorations with the HP calculators - pier4r - 03-23-2017, 08:28 AM RE: Little explorations with the HP calculators - pier4r - 03-23-2017, 10:00 AM RE: Little explorations with the HP calculators - Joe Horn - 03-23-2017, 12:19 PM RE: Little explorations with the HP calculators - pier4r - 03-23-2017, 01:23 PM RE: Little explorations with the HP calculators - pier4r - 03-24-2017, 01:45 PM RE: Little explorations with the HP calculators - pier4r - 03-24-2017, 03:23 PM RE: Little explorations with the HP calculators - pier4r - 03-24-2017, 10:04 PM RE: Little explorations with the HP calculators - Dieter - 03-24-2017, 10:54 PM RE: Little explorations with the HP calculators - pier4r - 03-25-2017, 08:17 AM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 12:14 PM RE: Little explorations with the HP calculators - Dieter - 03-27-2017, 06:01 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 06:14 PM RE: Little explorations with the HP calculators - Han - 03-27-2017, 06:30 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 06:57 PM RE: Little explorations with the HP calculators - Han - 03-27-2017, 07:07 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 07:22 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 03-27-2017, 07:39 PM RE: Little explorations with the HP calculators - Dieter - 03-27-2017, 08:55 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 03-27-2017, 10:35 PM RE: Little explorations with HP calculators (no Prime) - RMollov - 05-06-2018, 06:13 AM RE: Little explorations with HP calculators (no Prime) - Gerson W. Barbosa - 05-22-2018, 03:03 AM RE: Little explorations with HP calculators (no Prime) - RMollov - 05-23-2018, 11:04 AM RE: Little explorations with the HP calculators - Thomas Okken - 03-27-2017, 12:54 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 02:27 PM RE: Little explorations with the HP calculators - Thomas Okken - 03-27-2017, 03:44 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 03:55 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 05:29 PM RE: Little explorations with the HP calculators - Joe Horn - 03-27-2017, 07:24 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 07:35 PM RE: Little explorations with the HP calculators - Han - 03-27-2017, 08:01 PM RE: Little explorations with the HP calculators - Joe Horn - 03-27-2017, 08:08 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 08:14 PM RE: Little explorations with the HP calculators - Han - 03-27-2017, 08:36 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 08:44 PM RE: Little explorations with the HP calculators - Han - 03-27-2017, 08:07 PM RE: Little explorations with the HP calculators - pier4r - 03-27-2017, 07:58 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 03-27-2017, 10:12 PM RE: Little explorations with the HP calculators - pier4r - 03-28-2017, 10:44 AM RE: Little explorations with the HP calculators - pier4r - 03-28-2017, 11:07 AM RE: Little explorations with the HP calculators - Dieter - 03-28-2017, 05:33 PM RE: Little explorations with the HP calculators - pier4r - 03-28-2017, 06:13 PM RE: Little explorations with the HP calculators - Han - 03-28-2017, 07:32 PM RE: Little explorations with the HP calculators - pier4r - 03-28-2017, 08:15 PM RE: Little explorations with the HP calculators - Dieter - 03-29-2017, 07:54 AM RE: Little explorations with the HP calculators - pier4r - 03-29-2017, 08:48 AM RE: Little explorations with the HP calculators - Dieter - 03-29-2017, 01:07 PM RE: Little explorations with the HP calculators - Han - 03-28-2017, 07:36 PM RE: Little explorations with the HP calculators - pier4r - 03-28-2017, 09:32 PM RE: Little explorations with the HP calculators - Han - 03-29-2017, 01:58 AM RE: Little explorations with the HP calculators - pier4r - 03-29-2017, 06:02 AM RE: Little explorations with the HP calculators - Simone Cerica - 03-29-2017, 09:51 AM RE: Little explorations with the HP calculators - pier4r - 03-29-2017, 11:04 AM RE: Little explorations with the HP calculators - Han - 03-29-2017, 11:31 AM RE: Little explorations with the HP calculators - pier4r - 03-29-2017, 11:49 AM RE: Little explorations with the HP calculators - Han - 03-29-2017, 06:15 PM RE: Little explorations with the HP calculators - Dieter - 03-30-2017, 12:26 PM RE: Little explorations with the HP calculators - Han - 03-30-2017, 04:14 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 03-30-2017, 05:47 PM RE: Little explorations with the HP calculators - Han - 03-30-2017, 06:36 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 03-30-2017, 07:33 PM RE: Little explorations with the HP calculators - pier4r - 03-29-2017, 06:35 PM RE: Little explorations with the HP calculators - Isaac S. Friedman - 03-29-2017, 06:58 PM RE: Little explorations with the HP calculators - pier4r - 03-30-2017, 08:30 AM RE: Little explorations with the HP calculators - Dieter - 03-30-2017, 12:13 PM RE: Little explorations with the HP calculators - pier4r - 03-30-2017, 06:02 PM RE: Little explorations with the HP calculators - Han - 03-30-2017, 08:19 PM RE: Little explorations with the HP calculators - Dieter - 03-30-2017, 09:22 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 03-30-2017, 10:38 PM RE: Little explorations with the HP calculators - pier4r - 03-30-2017, 08:41 PM RE: Little explorations with the HP calculators - Han - 03-30-2017, 10:41 PM RE: Little explorations with the HP calculators - pier4r - 03-31-2017, 07:35 AM RE: Little explorations with the HP calculators - SlideRule - 04-06-2017, 12:47 AM RE: Little explorations with the HP calculators - pier4r - 04-07-2017, 10:30 AM RE: Little explorations with the HP calculators - pier4r - 03-31-2017, 10:01 AM RE: Little explorations with the HP calculators - DavidM - 03-31-2017, 03:12 PM RE: Little explorations with the HP calculators - pier4r - 03-31-2017, 05:27 PM RE: Little explorations with the HP calculators - DavidM - 03-31-2017, 06:34 PM RE: Little explorations with the HP calculators - pier4r - 03-31-2017, 07:34 PM RE: Little explorations with the HP calculators - pier4r - 03-31-2017, 08:33 PM RE: Little explorations with the HP calculators - DavidM - 03-31-2017, 09:41 PM RE: Little explorations with the HP calculators - pier4r - 03-31-2017, 09:51 PM RE: Little explorations with the HP calculators - DavidM - 04-01-2017, 02:27 PM RE: Little explorations with the HP calculators - Csaba Tizedes - 04-01-2017, 11:45 PM RE: Little explorations with the HP calculators - Han - 03-31-2017, 09:19 PM RE: Little explorations with the HP calculators - pier4r - 03-31-2017, 09:42 PM RE: Little explorations with the HP calculators - pier4r - 04-01-2017, 07:58 PM RE: Little explorations with the HP calculators - DavidM - 04-01-2017, 09:45 PM RE: Little explorations with the HP calculators - pier4r - 04-02-2017, 08:34 AM RE: Little explorations with the HP calculators - DavidM - 04-02-2017, 04:01 PM RE: Little explorations with the HP calculators - pier4r - 04-03-2017, 06:24 PM RE: Little explorations with the HP calculators - DavidM - 04-02-2017, 06:19 PM RE: Little explorations with the HP calculators - pier4r - 04-03-2017, 08:52 AM RE: Little explorations with the HP calculators - DavidM - 04-03-2017, 03:03 PM RE: Little explorations with the HP calculators - pier4r - 04-03-2017, 06:47 PM RE: Little explorations with the HP calculators - DavidM - 04-03-2017, 09:59 PM RE: Little explorations with the HP calculators - pier4r - 04-03-2017, 10:12 PM RE: Little explorations with the HP calculators - pier4r - 04-02-2017, 06:00 PM RE: Little explorations with the HP calculators - pier4r - 04-03-2017, 07:17 AM RE: Little explorations with the HP calculators - pier4r - 04-03-2017, 05:05 PM RE: Little explorations with the HP calculators - DavidM - 04-03-2017, 06:50 PM RE: Little explorations with the HP calculators - pier4r - 04-03-2017, 06:57 PM RE: Little explorations with the HP calculators - pier4r - 04-04-2017, 08:25 AM RE: Little explorations with the HP calculators - pier4r - 04-04-2017, 12:22 PM RE: Little explorations with the HP calculators - DavidM - 04-04-2017, 06:26 PM RE: Little explorations with the HP calculators - pier4r - 04-04-2017, 06:36 PM RE: Little explorations with the HP calculators - ttw - 04-14-2017, 08:53 AM RE: Little explorations with the HP calculators - John Keith - 04-14-2017, 12:26 PM RE: Little explorations with the HP calculators - Joe Horn - 04-15-2017, 05:34 AM RE: Little explorations with the HP calculators - pier4r - 04-05-2017, 10:49 AM RE: Little explorations with the HP calculators - pier4r - 04-06-2017, 10:43 PM RE: Little explorations with the HP calculators - SlideRule - 04-06-2017, 11:24 PM RE: Little explorations with the HP calculators - rprosperi - 04-06-2017, 11:37 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 05:12 PM RE: Little explorations with the HP calculators - pier4r - 04-07-2017, 07:54 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017, 02:29 AM RE: Little explorations with the HP calculators - pier4r - 04-07-2017, 09:46 AM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017, 02:37 PM RE: Little explorations with the HP calculators - SlideRule - 04-07-2017, 12:57 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017, 02:52 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 10:09 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 05:19 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017, 05:41 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 06:00 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017, 08:52 PM RE: Little explorations with the HP calculators - pier4r - 04-07-2017, 09:26 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017, 10:04 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 10:19 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017, 11:39 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 11:52 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-08-2017, 12:40 AM RE: Little explorations with the HP calculators - Han - 04-08-2017, 01:17 AM RE: Little explorations with the HP calculators - pier4r - 04-08-2017, 09:45 AM RE: Little explorations with the HP calculators - Han - 04-07-2017, 10:00 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 02:38 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017, 02:57 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 04:11 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017, 05:01 PM RE: Little explorations with the HP calculators - Dieter - 04-07-2017, 05:40 PM RE: Little explorations with the HP calculators - pier4r - 04-07-2017, 07:59 PM RE: Little explorations with the HP calculators - SlideRule - 04-07-2017, 06:58 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 07:19 PM RE: Little explorations with the HP calculators - Han - 04-07-2017, 10:23 PM RE: Little explorations with the HP calculators - Han - 04-08-2017, 02:44 AM RE: Little explorations with the HP calculators - Han - 04-08-2017, 03:37 AM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-08-2017, 03:01 PM RE: Little explorations with the HP calculators - Han - 04-08-2017, 05:19 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-08-2017, 09:17 PM RE: Little explorations with the HP calculators - Han - 04-08-2017, 10:16 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-08-2017, 10:53 PM RE: Little explorations with the HP calculators - pier4r - 04-09-2017, 07:55 AM RE: Little explorations with the HP calculators - SlideRule - 04-09-2017, 02:18 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-09-2017, 03:40 PM RE: Little explorations with the HP calculators - pier4r - 04-08-2017, 06:23 PM RE: Little explorations with the HP calculators - pier4r - 04-09-2017, 05:44 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-09-2017, 07:17 PM RE: Little explorations with the HP calculators - brickviking - 04-10-2017, 02:22 AM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-10-2017, 03:39 AM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-10-2017, 12:37 AM RE: Little explorations with the HP calculators - pier4r - 04-10-2017, 08:00 AM RE: Little explorations with the HP calculators - Dieter - 04-10-2017, 09:30 AM RE: Little explorations with the HP calculators - Dieter - 04-10-2017, 10:53 AM RE: Little explorations with the HP calculators - pier4r - 04-10-2017, 12:11 PM RE: Little explorations with the HP calculators - SlideRule - 04-10-2017, 01:01 PM RE: Little explorations with the HP calculators - pier4r - 04-10-2017, 02:30 PM RE: Little explorations with the HP calculators - pier4r - 04-10-2017, 09:51 AM RE: Little explorations with the HP calculators - Dieter - 04-10-2017, 10:05 AM RE: Little explorations with the HP calculators - telemachos - 04-10-2017, 03:22 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-10-2017, 04:49 PM RE: Little explorations with the HP calculators - pier4r - 04-10-2017, 09:20 PM RE: Little explorations with the HP calculators - pier4r - 04-14-2017, 08:30 PM RE: Little explorations with the HP calculators - pier4r - 04-15-2017, 06:59 AM RE: Little explorations with the HP calculators - pier4r - 04-18-2017, 04:15 PM RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-18-2017, 05:52 PM RE: Little explorations with the HP calculators - pier4r - 04-18-2017, 06:10 PM RE: Little explorations with the HP calculators - pier4r - 04-19-2017, 12:22 PM RE: Little explorations with the HP calculators - DavidM - 04-19-2017, 02:49 PM RE: Little explorations with the HP calculators - pier4r - 04-19-2017, 03:56 PM RE: Little explorations with the HP calculators - DavidM - 04-19-2017, 06:40 PM RE: Little explorations with the HP calculators - John Keith - 04-28-2017, 01:24 PM RE: Little explorations with the HP calculators - pier4r - 04-19-2017, 07:23 PM RE: Little explorations with the HP calculators - ttw - 04-19-2017, 09:58 PM RE: Little explorations with the HP calculators - pier4r - 04-23-2017, 07:24 PM RE: Little explorations with the HP calculators - ttw - 04-24-2017, 05:01 AM RE: Little explorations with the HP calculators - peacecalc - 04-24-2017, 07:23 PM RE: Little explorations with the HP calculators - pier4r - 04-24-2017, 08:29 PM RE: Little explorations with the HP calculators - pier4r - 04-28-2017, 03:01 PM RE: Little explorations with the HP calculators - Gene - 04-28-2017, 05:22 PM RE: Little explorations with the HP calculators - pier4r - 04-30-2017, 02:01 PM RE: Little explorations with the HP calculators - pier4r - 05-01-2017, 05:36 PM RE: Little explorations with the HP calculators - DavidM - 05-02-2017, 03:45 PM RE: Little explorations with the HP calculators - pier4r - 05-02-2017, 03:51 PM RE: Little explorations with the HP calculators - DavidM - 05-02-2017, 04:17 PM RE: Little explorations with the HP calculators - pier4r - 05-02-2017, 09:51 AM RE: Little explorations with the HP calculators - pier4r - 05-28-2017, 10:50 PM RE: Little explorations with the HP calculators - rprosperi - 05-29-2017, 12:04 AM RE: Little explorations with the HP calculators - pier4r - 05-29-2017, 02:54 PM RE: Little explorations with the HP calculators - rprosperi - 05-29-2017, 04:32 PM RE: Little explorations with the HP calculators - pier4r - 05-06-2017, 03:27 PM RE: Little explorations with the HP calculators - DavidM - 05-06-2017, 04:51 PM RE: Little explorations with the HP calculators - pier4r - 05-06-2017, 05:14 PM RE: Little explorations with the HP calculators - pier4r - 05-14-2017, 04:12 PM RE: Little explorations with the HP calculators - grsbanks - 05-29-2017, 08:26 PM RE: Little explorations with the HP calculators - pier4r - 05-29-2017, 10:35 PM RE: Little explorations with the HP calculators - pier4r - 06-01-2017, 07:00 PM RE: Little explorations with the HP calculators - Vtile - 06-01-2017, 07:44 PM RE: Little explorations with the HP calculators - pier4r - 06-01-2017, 10:19 PM RE: Little explorations with the HP calculators - pier4r - 06-13-2017, 09:49 AM RE: Little explorations with the HP calculators - pier4r - 06-15-2017, 01:09 PM RE: Little explorations with the HP calculators - pier4r - 09-09-2017, 09:21 PM RE: Little explorations with the HP calculators - Joe Horn - 09-09-2017, 10:03 PM RE: Little explorations with the HP calculators - pier4r - 09-10-2017, 09:55 AM RE: Little explorations with the HP calculators - AlexFekken - 09-10-2017, 10:46 AM RE: Little explorations with the HP calculators - Gilles59 - 09-11-2017, 09:21 PM RE: Little explorations with HP calculators (pre Prime) - pier4r - 09-24-2017, 08:17 PM RE: Little explorations with HP calculators (pre Prime) - brickviking - 09-25-2017, 12:12 AM RE: Little explorations with HP calculators (pre Prime) - rprosperi - 09-25-2017, 12:23 AM RE: Little explorations with HP calculators (pre Prime) - pier4r - 10-17-2017, 08:18 AM RE: Little explorations with HP calculators (pre Prime) - pier4r - 10-17-2017, 01:34 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 10-17-2017, 04:46 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 10-22-2017, 08:50 AM RE: Little explorations with HP calculators (no Prime) - John Keith - 10-22-2017, 01:52 PM RE: Little explorations with HP calculators (no Prime) - brickviking - 10-22-2017, 08:30 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 10-22-2017, 03:51 PM RE: Little explorations with HP calculators (no Prime) - John Keith - 10-22-2017, 11:05 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 10-30-2017, 08:46 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 10-31-2017, 09:54 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 10-31-2017, 02:22 PM RE: Little explorations with HP calculators (no Prime) - Claudio L. - 10-31-2017, 03:12 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 10-31-2017, 05:50 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 10-31-2017, 06:23 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 11-05-2017 04:05 PM RE: Little explorations with HP calculators (no Prime) - Joe Horn - 11-05-2017, 10:28 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 11-07-2017, 07:33 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 11-07-2017, 09:26 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 11-07-2017, 09:33 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-12-2017, 10:30 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-17-2017, 10:05 AM RE: Little explorations with HP calculators (no Prime) - Joe Horn - 12-18-2017, 02:26 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-18-2017, 07:08 AM RE: Little explorations with HP calculators (no Prime) - Joe Horn - 12-19-2017, 04:20 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-19-2017, 09:15 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-19-2017, 09:27 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 02-19-2018, 08:03 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 02-19-2018, 09:25 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 02-19-2018, 09:40 PM RE: Little explorations with HP calculators (no Prime) - John Keith - 02-19-2018, 10:30 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-10-2018, 11:36 AM RE: Little explorations with HP calculators (no Prime) - DavidM - 03-10-2018, 05:14 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-11-2018, 12:07 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 03-11-2018, 06:25 PM RE: Little explorations with HP calculators (no Prime) - Neve - 03-11-2018, 06:47 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-11-2018, 07:30 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-12-2018, 09:03 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-16-2018, 07:48 PM RE: Little explorations with HP calculators (no Prime) - Thomas Okken - 03-16-2018, 08:24 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-16-2018, 09:10 PM RE: Little explorations with HP calculators (no Prime) - 3298 - 03-17-2018, 12:27 PM RE: Little explorations with HP calculators (no Prime) - Csaba Tizedes - 03-17-2018, 01:22 PM RE: Little explorations with HP calculators (no Prime) - John Keith - 03-17-2018, 08:00 PM RE: Little explorations with HP calculators (no Prime) - grsbanks - 03-17-2018, 02:37 PM RE: Little explorations with HP calculators (no Prime) - Dieter - 03-16-2018, 08:29 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-17-2018, 08:55 PM RE: Little explorations with HP calculators (no Prime) - 3298 - 03-18-2018, 12:14 PM RE: Little explorations with HP calculators (no Prime) - grsbanks - 03-18-2018, 12:27 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 04-02-2018, 08:55 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-18-2018, 09:54 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-18-2018, 12:50 PM RE: Little explorations with Casio 9750/9860 calculators - brickviking - 03-20-2018, 11:59 PM RE: Little explorations with HP calculators (no Prime) - 3298 - 03-21-2018, 10:45 AM RE: Little explorations with Casio 9750/9860 calculators - brickviking - 03-22-2018, 02:16 AM RE: Little explorations with HP calculators (no Prime) - 3298 - 03-22-2018, 11:32 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-21-2018, 11:23 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-21-2018, 08:37 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 03-21-2018, 11:27 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-22-2018, 11:15 AM RE: Little explorations with HP calculators (no Prime) - rprosperi - 03-23-2018, 02:02 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-23-2018, 08:20 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 04-02-2018, 09:29 AM RE: Little explorations with HP calculators (no Prime) - rprosperi - 04-02-2018, 01:50 PM RE: Little explorations with HP calculators (no Prime) - Zaphod - 04-02-2018, 02:24 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 04-02-2018, 05:34 PM RE: Little explorations with HP calculators (no Prime) - Zaphod - 04-02-2018, 06:17 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 04-02-2018, 08:53 PM RE: Little explorations with HP calculators (no Prime) - Zaphod - 04-02-2018, 09:16 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-25-2018, 05:01 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 03-25-2018, 07:34 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 03-25-2018, 08:00 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 03-25-2018, 08:45 PM RE: Little explorations with HP calculators (no Prime) - Dave Frederickson - 03-25-2018, 09:40 PM RE: Little explorations with HP calculators (no Prime) - Dave Frederickson - 03-25-2018, 09:43 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 04-02-2018, 01:53 PM RE: Little explorations with HP calculators (no Prime) - John Keith - 04-02-2018, 09:11 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 05-05-2018, 02:22 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 05-21-2018, 12:53 PM RE: Little explorations with HP calculators (no Prime) - grsbanks - 05-21-2018, 01:04 PM RE: Little explorations with HP calculators (no Prime) - rprosperi - 05-21-2018, 06:02 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-26-2018, 09:34 PM RE: Little explorations with HP calculators (no Prime) - ijabbott - 12-26-2018, 11:41 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-27-2018, 03:22 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-27-2018, 04:59 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 12-31-2018, 07:59 PM RE: Little explorations with HP calculators (no Prime) - brickviking - 12-28-2018, 09:42 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-28-2018, 09:53 PM RE: Little explorations with HP calculators (no Prime) - 3298 - 12-28-2018, 11:21 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 12-29-2018, 12:10 AM RE: Little explorations with HP calculators (no Prime) - 3298 - 12-29-2018, 02:05 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-27-2018, 06:52 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-27-2018, 08:31 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-27-2018, 08:47 PM RE: Little explorations with HP calculators (no Prime) - Thomas Klemm - 12-27-2018, 10:20 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-27-2018, 11:58 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 12-28-2018, 01:38 AM RE: Little explorations with HP calculators (no Prime) - Thomas Klemm - 12-28-2018, 04:04 AM RE: Little explorations with HP calculators (no Prime) - ijabbott - 12-28-2018, 09:06 AM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-28-2018, 02:00 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 12-28-2018, 03:41 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-29-2018, 04:06 PM RE: Little explorations with HP calculators (no Prime) - Thomas Klemm - 12-29-2018, 07:35 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-29-2018, 10:02 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-30-2018, 01:26 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-31-2018, 04:30 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 12-31-2018, 08:20 PM RE: Little explorations with HP calculators (no Prime) - DavidM - 12-31-2018, 08:36 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 01-13-2019, 10:48 AM RE: Little explorations with HP calculators (no Prime) - DavidM - 01-13-2019, 05:05 PM RE: Little explorations with HP calculators (no Prime) - John Keith - 01-13-2019, 08:27 PM RE: Little explorations with HP calculators (no Prime) - Thomas Klemm - 01-13-2019, 01:44 PM RE: Little explorations with HP calculators (no Prime) - Albert Chan - 01-13-2019, 01:48 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 01-13-2019, 07:00 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 01-28-2019, 01:38 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 01-31-2019, 04:07 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 05-27-2019, 04:47 PM RE: Little explorations with HP calculators (no Prime) - pier4r - 05-27-2019, 06:06 PM RE: Little explorations with HP calculators (no Prime) - 3298 - 05-28-2019, 11:09 AM RE: Little explorations with HP calculators (no Prime) - pier4r - 05-28-2019, 07:18 PM

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