Číselné soustavy/Soustava o základu 36
 Tato stránka je součástí databáze a projektu:
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{cs}
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| Příslušnost: Kusurija | |
Neboli šestatřicítková soustava. Toto je 100 % vlastní výzkum. Ne, že by informace, zde uvedené, nebyly dosud známy (naprostá většina z nich je známa od starověku, většina malého zbytku je známa z počátků novověku a nepatrný zbytek v posledních desetiletích); vlastním výzkumem je seřazení/prezentace těch informací a naznačené souvislosti mezi nimi. Šestatřicítková soustava je mocninová, nejmenší z mocninových, jejichž kořenem není prvočíslo; proto většinu informací lze nalézt v šestkové soustavě. kusurija.
Pro číslice menší než 10(10) jsou (počínaje osmnáctkovou soustavou) používány náhradní symboly s přidanou nulou (0) vpředu a i pro číslice vyšší jsou používány dvojčíselné symboly. Navzájem jsou symboly odděleny dvojtečkou s výjimkou čísel jednosymbolových, tedy 00(36) - 35(36).
Číselná řada
[editovat]- Číselná řada
00, 01, 02*, 03*, 04**, 05*, 06, 07*, 08**, 09**, 10, 11*, 12, 13*, 14, 15, 16**, 17*, 18, 19*, 20, 21, 22, 23*, 24, 25**, 26, 27**, 28, 29*, 30, 31*, 32**, 33, 34, 35, 01:00,
01:01*, 01:02, 01:03, 01:04, 01:05*, 01:06, 01:07*, 01:08, 01:09, 01:10, 01:11*, 01:12, 01:13**, 01:14, 01:15, 01:16, 01:17*, 01:18, 01:19, 01:20, 01:21, 01:22, 01:23*, 01:24, 01:25*, 01:26, 01:27, 01:28**, 01:29, 01:30, 01:31*, 01:32, 01:33, 01:34, 01:35, 02:00,
02:01*, 02:02, 02:03, 02:04, 02:05, 02:06, 02:07*, 02:08, 02:09**, další členy řady viz tabulky ...
Malá násobilka
[editovat]| × | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 01 | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 02 | 02 | 04 | 06 | 08 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 01:00 | 01:02 | 01:04 |
| 03 | 03 | 06 | 09 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 01:00 | 01:03 | 01:06 | 01:09 | 01:12 | 01:15 | 01:18 | 01:21 | 01:24 |
| 04 | 04 | 08 | 12 | 16 | 20 | 24 | 28 | 32 | 01:00 | 01:04 | 01:08 | 01:12 | 01:16 | 01:20 | 01:24 | 01:28 | 01:32 | 02:00 | 02:04 | 02:08 |
| 05 | 05 | 10 | 15 | 20 | 25 | 30 | 35 | 01:04 | 01:09 | 01:14 | 01:19 | 01:24 | 01:29 | 01:34 | 02:03 | 02:08 | 02:13 | 02:18 | 02:23 | 02:28 |
| 06 | 06 | 12 | 18 | 24 | 30 | 01:00 | 01:06 | 01:12 | 01:18 | 01:24 | 01:30 | 02:00 | 02:06 | 02:12 | 02:18 | 02:24 | 02:30 | 03:00 | 03:06 | 03:12 |
| 07 | 07 | 14 | 21 | 28 | 35 | 01:06 | 01:13 | 01:20 | 01:27 | 01:34 | 02:05 | 02:12 | 02:19 | 02:26 | 02:33 | 03:04 | 03:11 | 03:18 | 03:25 | 03:32 |
| 08 | 08 | 16 | 24 | 32 | 01:04 | 01:12 | 01:20 | 01:28 | 02:00 | 02:08 | 02:16 | 02:24 | 02:32 | 03:04 | 03:12 | 03:20 | 03:28 | 04:00 | 04:18 | 04:16 |
| 09 | 09 | 18 | 27 | 01:00 | 01:09 | 01:18 | 01:27 | 02:00 | 02:09 | 02:18 | 02:27 | 03:00 | 03:09 | 03:18 | 03:27 | 04:00 | 04:09 | 04:18 | 04:27 | 05:00 |
| 10 | 10 | 20 | 30 | 01:04 | 01:14 | 01:24 | 01:34 | 02:08 | 02:18 | 02:28 | 03:02 | 03:12 | 03:22 | 03:32 | 04:06 | 04:16 | 04:26 | 05:00 | 05:10 | 05:20 |
| 11 | 11 | 22 | 33 | 01:08 | 01:19 | 01:30 | 02:05 | 02:16 | 02:27 | 03:02 | 03:13 | 03:24 | 03:35 | 04:10 | 04:21 | 04:32 | 05:07 | 05:18 | 05:29 | 06:04 |
| 12 | 12 | 24 | 01:00 | 01:12 | 01:24 | 02:00 | 02:12 | 02:24 | 03:00 | 03:12 | 03:24 | 04:00 | 04:12 | 04:24 | 05:00 | 05:12 | 05:24 | 06:00 | 06:12 | 06:24 |
| 13 | 13 | 26 | 01:03 | 01:16 | 01:29 | 02:06 | 02:19 | 02:32 | 03:09 | 03:22 | 03:35 | 04:12 | 04:25 | 05:02 | 05:15 | 05:28 | 06:05 | 06:18 | 06:31 | 07:08 |
| 14 | 14 | 28 | 01:06 | 01:20 | 01:34 | 02:12 | 02:26 | 03:04 | 03:18 | 03:32 | 04:10 | 04:24 | 05:02 | 05:16 | 05:30 | 06:08 | 06:22 | 07:00 | 07:14 | 07:28 |
| 15 | 15 | 30 | 01:09 | 01:24 | 02:03 | 02:18 | 02:33 | 03:12 | 03:27 | 04:06 | 04:21 | 05:00 | 05:15 | 05:30 | 06:09 | 06:24 | 07:03 | 07:18 | 07:33 | 08:12 |
| 16 | 16 | 32 | 01:12 | 01:28 | 02:08 | 02:24 | 03:04 | 03:20 | 04:00 | 04:16 | 04:32 | 05:12 | 05:28 | 06:08 | 06:24 | 07:04 | 07:20 | 08:00 | 08:16 | 08:32 |
| 17 | 17 | 34 | 01:15 | 01:32 | 02:13 | 02:30 | 03:11 | 03:28 | 04:09 | 04:26 | 05:07 | 05:24 | 06:05 | 06:22 | 07:03 | 07:20 | 08:01 | 08:18 | 08:35 | 09:16 |
| 18 | 18 | 01:00 | 01:18 | 02:00 | 02:18 | 03:00 | 03:18 | 04:00 | 04:18 | 05:00 | 05:18 | 06:00 | 06:18 | 07:00 | 07:18 | 08:00 | 08:18 | 09:00 | 09:18 | 10:00 |
| 19 | 19 | 01:02 | 01:21 | 02:04 | 02:23 | 03:06 | 03:25 | 04:08 | 04:27 | 05:10 | 05:29 | 06:12 | 06:31 | 07:14 | 07:33 | 08:16 | 08:35 | 09:18 | 10:01 | 10:20 |
| 20 | 20 | 01:04 | 01:24 | 02:08 | 02:28 | 03:12 | 03:32 | 04:16 | 05:00 | 05:20 | 06:04 | 06:24 | 07:08 | 07:28 | 08:12 | 08:32 | 09:16 | 10:00 | 10:20 | 11:04 |
| 21 | 21 | 01:06 | 01:27 | 02:12 | 02:33 | 03:18 | 04:03 | 04:24 | 05:09 | 05:30 | 06:15 | 07:00 | 07:21 | 08:06 | 08:27 | 09:12 | 09:33 | 10:18 | 11:03 | 11:24 |
| 22 | 22 | 01:08 | 01:30 | 02:16 | 03:02 | 03:24 | 04:10 | 04:32 | 05:18 | 06:04 | 06:26 | 07:12 | 07:34 | 08:20 | 09:06 | 09:28 | 10:14 | 11:00 | 11:22 | 12:08 |
| 23 | 23 | 01:10 | 01:33 | 02:20 | 03:07 | 03:30 | 04:17 | 05:04 | 05:27 | 06:14 | 07:01 | 07:24 | 08:11 | 08:34 | 09:21 | 10:08 | 10:31 | 11:18 | 12:05 | 12:28 |
| 24 | 24 | 01:12 | 02:00 | 02:24 | 03:12 | 04:00 | 04:24 | 05:12 | 06:00 | 06:24 | 07:12 | 08:00 | 08:24 | 09:12 | 10:00 | 10:24 | 11:12 | 12:00 | 12:24 | 13:12 |
| 25 | 25 | 01:14 | 02:03 | 02:28 | 03:17 | 04:06 | 04:31 | 05:20 | 06:09 | 06:34 | 07:23 | 08:12 | 09:01 | 09:26 | 10:15 | 11:04 | 11:29 | 12:18 | 13:07 | 13:32 |
| 26 | 26 | 01:16 | 02:06 | 02:32 | 03:22 | 04:12 | 05:02 | 05:28 | 06:18 | 07:08 | 07:34 | 08:24 | 09:14 | 10:04 | 10:30 | 11:20 | 12:10 | 13:00 | 13:26 | 14:16 |
| 27 | 27 | 01:18 | 02:09 | 03:00 | 03:27 | 04:18 | 05:09 | 06:00 | 06:27 | 07:18 | 08:09 | 09:00 | 09:27 | 10:18 | 11:09 | 12:00 | 12:27 | 13:18 | 14:09 | 15:00 |
| 28 | 28 | 01:20 | 02:12 | 03:04 | 03:32 | 04:24 | 05:16 | 06:08 | 07:00 | 07:28 | 08:20 | 09:12 | 10:04 | 10:32 | 11:24 | 12:16 | 13:08 | 14:00 | 14:28 | 15:20 |
| 29 | 29 | 01:22 | 02:15 | 03:08 | 04:01 | 04:30 | 05:23 | 06:16 | 07:09 | 08:02 | 08:31 | 09:24 | 10:17 | 11:10 | 12:03 | 12:32 | 13:25 | 14:18 | 15:11 | 16:04 |
| 30 | 30 | 01:24 | 02:18 | 03:12 | 04:06 | 05:00 | 05:30 | 06:24 | 07:18 | 08:12 | 09:06 | 10:00 | 10:30 | 11:24 | 12:18 | 13:12 | 14:06 | 15:00 | 15:30 | 16:24 |
| 31 | 31 | 01:26 | 02:21 | 03:16 | 04:11 | 05:06 | 06:01 | 06:32 | 07:27 | 08:22 | 09:17 | 10:12 | 11:07 | 12:02 | 12:33 | 13:28 | 14:23 | 15:18 | 16:13 | 17:08 |
| 32 | 32 | 01:28 | 02:24 | 03:20 | 04:16 | 05:12 | 06:08 | 07:04 | 08:00 | 08:32 | 09:28 | 10:24 | 11:20 | 12:16 | 13:12 | 14:08 | 15:04 | 16:00 | 16:32 | 17:28 |
| 33 | 33 | 01:30 | 02:27 | 03:24 | 04:21 | 05:18 | 06:15 | 07:12 | 08:09 | 09:06 | 10:03 | 11:00 | 11:33 | 12:30 | 13:27 | 14:24 | 15:21 | 16:18 | 17:15 | 18:12 |
| 34 | 34 | 01:32 | 02:30 | 03:28 | 04:26 | 05:24 | 06:22 | 07:20 | 08:18 | 09:16 | 10:14 | 11:12 | 12:10 | 13:08 | 14:06 | 15:04 | 16:02 | 17:00 | 17:34 | 18:32 |
| 35 | 35 | 01:34 | 02:33 | 03:32 | 04:31 | 05:30 | 06:29 | 07:28 | 08:27 | 09:26 | 10:25 | 11:24 | 12:23 | 13:22 | 14:21 | 15:20 | 16:19 | 17:18 | 18:17 | 19:16 |
| 01:00 | 01:00 | 02:00 | 03:00 | 04:00 | 05:00 | 06:00 | 07:00 | 08:00 | 09:00 | 10:00 | 11:00 | 12:00 | 13:00 | 14:00 | 15:00 | 16:00 | 17:00 | 18:00 | 19:00 | 20:00 |
Repunitová prvočísla
[editovat]Prvočíslo, které se v šestatřicítkové soustavě skládá ze dvou jedniček, je pouze toto jediné: 37(10) = 01:01(36).
Převrácené hodnoty prvočísel
[editovat]- Převrácené hodnoty prvočísel (1/p); do 13 všech čísel (1/n) a vybraných součinů.
l.p. - délka periody; pp=předperioda
2: 00,18:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp
3: 00,12:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp
4: 00,09:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp
5: 00,07:07:07:07:07:07:07:07:07:07:07:07... l.p. = 1
6: 00,06:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp
7: 00,05:05:05:05:05:05:05:05:05:05:05:05... l.p. = 1
8: 00,04:18:00:00:00:00:00:00:00:00:00:00... l.p. = 0+2pp
9: 00,04:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp
10: 00,03:21:21:21:21:21:21:21:21:21:21:21... l.p. = 1+1pp
11: 00,03:09:29:16:13:03:09:29:16:13... l.p. = 5
12: 00,03:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp
13: 00,02:27:24:33:08:11:02:27:24:33:08:11... l.p. = 6
17: 00,02:04:08:16:33:31:27:19:02:04:08:16:33:31:27:19... l.p. = 8
19: 00,01:32:07:20:30:11:13:09:17... l.p. = 9
23: 00,01:20:12:18:28:06:09:14:03:04:25... l.p. = 11
27: 00,01:12:00:00:00:00:00:00:00:00:00:00... l.p. = 0+2pp
29: 00,01:08:24:29:28:19:31:01:08:24:29:28:19:31... l.p. = 7
31: 00,01:05:29:01:05:29:01:05:29:01:05:29... l.p. = 3
35: 00,01:01:01:01:01:01:01:01:01:01:01:01... l.p. = 1
36: 00,01:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp
37: 00,00:35:00:35:00:35:00:35:00:35:00:35... l.p. = 2
41: 00,00:31:21:34:08:28:03:18:15:28:35:04... l.p. = 20
43: 00,00:30:05:00:30:05:00:30:05:00:30:05... l.p. = 3
47: 00,00:27:20:24:18:13:28:12:09:06:32:06... l.p. = 23
49: 00,00:26:16:05:31:21:11:00:26:16:05:31:21:11... l.p. = 7
53: 00,00:24:16:10:31:08:29:31:33:10:06:28:19... l.p. = 13
59: 00,00:21:34:28:02:15:31:04:09:27:16:17... l.p. = 29
61: 00,00:21:08:30:24:28:11:28:33:01:27:26... l.p. = 30
67: 00,00:19:12:12:32:08:21:17:26:11:29:19... l.p. = 33
71: 00,00:18:09:04:20:10:05:02:19:09:22:29... l.p. = 35
...
Další lze snadno odvodit z údajů o šestkové soustavě: délky period jsou poloviční, nežli sudé délky period v šestkové soustavě a stejné, jako liché délky period v šestkové soustavě...