Číselné soustavy/Soustava o základu 49
 Tato stránka je součástí databáze a projektu:
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{cs}
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| Příslušnost: Kusurija | |
Neboli devětačtyřicítková 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. Devětačtyřicítková soustava je mocninová, proto většinu informací lze nalézt v sedmičkové soustavě. Připomínky jsou vítány - ale pouze v diskusi. Tam může kdokoliv i přidávat dotazy či tipy na doplnění. Uvítám i obyčejný komentář kteréhokoliv "kolemjdoucího" o tom, zda je/není článek srozumitelný. 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(49) - 48(49).
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, 36, 37*, 38, 39, 40, 41*, 42, 43*, 44, 45, 46, 47*, 48, 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, 01:36, 01:37, 01:38, 01:39, 01:40*, 01:41, 01:42, 01:43, 01:44, 01:45, 01:46, 01:47, 01:48*, 02:00,
02:01, 02:02, 02:03*, 02:04, 02:05*, 02:06, 02:07, 02:08, 02:09*, 02:10, 02:11*, 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 | 36 | 38 | 40 |
| 03 | 03 | 06 | 09 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 | 48 | 01:02 | 01:05 | 01:08 | 01:11 |
| 04 | 04 | 08 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 01:03 | 01:07 | 01:11 | 01:15 | 01:19 | 01:23 | 01:27 | 01:31 |
| 05 | 05 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 01:01 | 01:06 | 01:11 | 01:16 | 01:21 | 01:26 | 01:31 | 01:36 | 01:41 | 01:46 | 02:02 |
| 06 | 06 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 01:05 | 01:11 | 01:17 | 01:23 | 01:29 | 01:35 | 01:41 | 01:47 | 02:04 | 02:10 | 02:16 | 02:22 |
| 07 | 07 | 14 | 21 | 28 | 35 | 42 | 01:00 | 01:07 | 01:14 | 01:21 | 01:28 | 01:35 | 01:42 | 02:00 | 02:07 | 02:14 | 02:21 | 02:28 | 02:35 | 02:42 |
| 08 | 08 | 16 | 24 | 32 | 40 | 48 | 01:07 | 01:15 | 01:23 | 01:31 | 01:39 | 01:47 | 02:06 | 02:14 | 02:22 | 02:30 | 02:38 | 02:46 | 03:05 | 03:13 |
| 09 | 09 | 18 | 27 | 36 | 45 | 01:05 | 01:14 | 01:23 | 01:32 | 01:41 | 02:01 | 02:10 | 02:19 | 02:28 | 02:37 | 02:46 | 03:06 | 03:15 | 03:24 | 03:33 |
| 10 | 10 | 20 | 30 | 40 | 01:01 | 01:11 | 01:21 | 01:31 | 01:41 | 02:02 | 02:12 | 02:22 | 02:32 | 02:42 | 03:03 | 03:13 | 03:23 | 03:33 | 03:43 | 04:04 |
| 11 | 11 | 22 | 33 | 44 | 01:06 | 01:17 | 01:28 | 01:39 | 02:01 | 02:12 | 02:23 | 02:34 | 02:45 | 03:07 | 03:18 | 03:29 | 03:40 | 04:02 | 04:13 | 04:24 |
| 12 | 12 | 24 | 36 | 48 | 01:11 | 01:23 | 01:35 | 01:47 | 02:10 | 02:22 | 02:34 | 02:46 | 03:09 | 03:21 | 03:33 | 03:45 | 04:08 | 04:20 | 04:32 | 04:44 |
| 13 | 13 | 26 | 39 | 01:03 | 01:16 | 01:29 | 01:42 | 02:06 | 02:19 | 02:32 | 02:45 | 03:09 | 03:22 | 03:35 | 03:48 | 04:12 | 04:25 | 04:38 | 05:02 | 05:15 |
| 14 | 14 | 28 | 42 | 01:07 | 01:21 | 01:35 | 02:00 | 02:14 | 02:28 | 02:42 | 03:07 | 03:21 | 03:35 | 04:00 | 04:14 | 04:28 | 04:42 | 05:07 | 05:21 | 05:35 |
| 15 | 15 | 30 | 45 | 01:11 | 01:26 | 01:41 | 02:07 | 02:22 | 02:37 | 03:03 | 03:18 | 03:33 | 03:48 | 04:14 | 04:29 | 04:44 | 05:10 | 05:25 | 05:40 | 06:06 |
| 16 | 16 | 32 | 48 | 01:15 | 01:31 | 01:47 | 02:14 | 02:30 | 02:46 | 03:13 | 03:29 | 03:45 | 04:12 | 04:28 | 04:44 | 05:11 | 05:27 | 05:43 | 06:10 | 06:26 |
| 17 | 17 | 34 | 01:02 | 01:19 | 01:36 | 02:04 | 02:21 | 02:38 | 03:06 | 03:23 | 03:40 | 04:08 | 04:25 | 04:42 | 05:10 | 05:27 | 05:44 | 06:12 | 06:29 | 06:46 |
| 18 | 18 | 36 | 01:05 | 01:23 | 01:41 | 02:10 | 02:28 | 02:46 | 03:15 | 03:33 | 04:02 | 04:20 | 04:38 | 05:07 | 05:25 | 05:43 | 06:12 | 06:30 | 06:48 | 07:17 |
| 19 | 19 | 38 | 01:08 | 01:27 | 01:46 | 02:16 | 02:35 | 03:05 | 03:24 | 03:43 | 04:13 | 04:32 | 05:02 | 05:21 | 05:40 | 06:10 | 06:29 | 06:48 | 07:18 | 07:37 |
| 20 | 20 | 40 | 01:11 | 01:31 | 02:02 | 02:22 | 02:42 | 03:13 | 03:33 | 04:04 | 04:24 | 04:44 | 05:15 | 05:35 | 06:06 | 06:26 | 06:46 | 07:17 | 07:37 | 08:08 |
| 21 | 21 | 42 | 01:14 | 01:35 | 02:07 | 02:28 | 03:00 | 03:21 | 03:42 | 04:14 | 04:35 | 05:07 | 05:28 | 06:00 | 06:21 | 06:42 | 07:14 | 07:35 | 08:07 | 08:28 |
| 22 | 22 | 44 | 01:17 | 01:39 | 02:12 | 02:34 | 03:07 | 03:29 | 04:02 | 04:24 | 04:46 | 05:19 | 05:41 | 06:14 | 06:36 | 07:09 | 07:31 | 08:04 | 08:26 | 08:48 |
| 23 | 23 | 46 | 01:20 | 01:43 | 02:17 | 02:40 | 03:14 | 03:37 | 04:11 | 04:34 | 05:08 | 05:31 | 06:05 | 06:28 | 07:02 | 07:25 | 07:48 | 08:22 | 08:45 | 09:19 |
| 24 | 24 | 48 | 01:23 | 01:47 | 02:22 | 02:46 | 03:21 | 03:45 | 04:20 | 04:44 | 05:19 | 05:43 | 06:18 | 06:42 | 07:17 | 07:41 | 08:16 | 08:40 | 09:15 | 09:39 |
| 25 | 25 | 01:01 | 01:26 | 02:02 | 02:27 | 03:03 | 03:28 | 04:04 | 04:29 | 05:05 | 05:30 | 06:06 | 06:31 | 07:07 | 07:32 | 08:08 | 08:33 | 09:09 | 09:34 | 10:10 |
| 26 | 26 | 01:03 | 01:29 | 02:06 | 02:32 | 03:09 | 03:35 | 04:12 | 04:38 | 05:15 | 05:41 | 06:18 | 06:44 | 07:21 | 07:47 | 08:24 | 09:01 | 09:27 | 10:04 | 10:30 |
| 27 | 27 | 01:05 | 01:32 | 02:10 | 02:37 | 03:15 | 03:42 | 04:20 | 04:47 | 05:25 | 06:03 | 06:30 | 07:08 | 07:35 | 08:13 | 08:40 | 09:18 | 09:45 | 10:23 | 11:01 |
| 28 | 28 | 01:07 | 01:35 | 02:14 | 02:42 | 03:21 | 04:00 | 04:28 | 05:07 | 05:35 | 06:14 | 06:42 | 07:21 | 08:00 | 08:28 | 09:07 | 09:35 | 10:14 | 10:42 | 11:21 |
| 29 | 29 | 01:09 | 01:38 | 02:18 | 02:47 | 03:27 | 04:07 | 04:36 | 05:16 | 05:45 | 06:25 | 07:05 | 07:34 | 08:14 | 08:43 | 09:23 | 10:03 | 10:32 | 11:12 | 11:41 |
| 30 | 30 | 01:11 | 01:41 | 02:22 | 03:03 | 03:33 | 04:14 | 04:44 | 05:25 | 06:06 | 06:36 | 07:17 | 07:47 | 08:28 | 09:09 | 09:39 | 10:20 | 11:01 | 11:31 | 12:12 |
| 31 | 31 | 01:13 | 01:44 | 02:26 | 03:08 | 03:39 | 04:21 | 05:03 | 05:34 | 06:16 | 06:47 | 07:29 | 08:11 | 08:42 | 09:24 | 10:06 | 10:37 | 11:19 | 12:01 | 12:32 |
| 32 | 32 | 01:15 | 01:47 | 02:30 | 03:13 | 03:45 | 04:28 | 05:11 | 05:43 | 06:26 | 07:09 | 07:41 | 08:24 | 09:07 | 09:39 | 10:22 | 11:05 | 11:37 | 12:20 | 13:03 |
| 33 | 33 | 01:17 | 02:01 | 02:34 | 03:18 | 04:02 | 04:35 | 05:19 | 06:03 | 06:36 | 07:20 | 08:04 | 08:37 | 09:21 | 10:05 | 10:38 | 11:22 | 12:06 | 12:39 | 13:23 |
| 34 | 34 | 01:19 | 02:04 | 02:38 | 03:23 | 04:08 | 04:42 | 05:27 | 06:12 | 06:46 | 07:31 | 08:16 | 09:01 | 09:35 | 10:20 | 11:05 | 11:39 | 12:24 | 13:09 | 13:43 |
| 35 | 35 | 01:21 | 02:07 | 02:42 | 03:28 | 04:14 | 05:00 | 05:35 | 06:21 | 07:07 | 07:42 | 08:28 | 09:14 | 10:00 | 10:35 | 11:21 | 12:07 | 12:42 | 13:28 | 14:14 |
| 36 | 36 | 01:23 | 02:10 | 02:46 | 03:33 | 04:20 | 05:07 | 05:43 | 06:30 | 07:17 | 08:04 | 08:40 | 09:27 | 10:14 | 11:01 | 11:37 | 12:24 | 13:11 | 13:47 | 14:34 |
| 37 | 37 | 01:25 | 02:13 | 03:01 | 03:38 | 04:26 | 05:14 | 06:02 | 06:39 | 07:27 | 08:15 | 09:03 | 09:40 | 10:28 | 11:16 | 12:04 | 12:41 | 13:29 | 14:17 | 15:05 |
| 38 | 38 | 01:27 | 02:16 | 03:05 | 03:43 | 04:32 | 05:21 | 06:10 | 06:48 | 07:37 | 08:26 | 09:15 | 10:04 | 10:42 | 11:31 | 12:20 | 13:09 | 13:47 | 14:36 | 15:25 |
| 39 | 39 | 01:29 | 02:19 | 03:09 | 03:48 | 04:38 | 05:28 | 06:18 | 07:08 | 07:47 | 08:37 | 09:27 | 10:17 | 11:07 | 11:46 | 12:36 | 13:26 | 14:16 | 15:06 | 15:45 |
| 40 | 40 | 01:31 | 02:22 | 03:13 | 04:04 | 04:44 | 05:35 | 06:26 | 07:17 | 08:08 | 08:48 | 09:39 | 10:30 | 11:21 | 12:12 | 13:03 | 13:43 | 14:34 | 15:25 | 16:16 |
| 41 | 41 | 01:33 | 02:25 | 03:17 | 04:09 | 05:01 | 05:42 | 06:34 | 07:26 | 08:18 | 09:10 | 10:02 | 10:43 | 11:35 | 12:27 | 13:19 | 14:11 | 15:03 | 15:44 | 16:36 |
| 42 | 42 | 01:35 | 02:28 | 03:21 | 04:14 | 05:07 | 06:00 | 06:42 | 07:35 | 08:28 | 09:21 | 10:14 | 11:07 | 12:00 | 12:42 | 13:35 | 14:28 | 15:21 | 16:14 | 17:07 |
| 43 | 43 | 01:37 | 02:31 | 03:25 | 04:19 | 05:13 | 06:07 | 07:01 | 07:44 | 08:38 | 09:32 | 10:26 | 11:20 | 12:14 | 13:08 | 14:02 | 14:45 | 15:39 | 16:33 | 17:27 |
| 44 | 44 | 01:39 | 02:34 | 03:29 | 04:24 | 05:19 | 06:14 | 07:09 | 08:04 | 08:48 | 09:43 | 10:38 | 11:33 | 12:28 | 13:23 | 14:18 | 15:13 | 16:08 | 17:03 | 17:47 |
| 45 | 45 | 01:41 | 02:37 | 03:33 | 04:29 | 05:25 | 06:21 | 07:17 | 08:13 | 09:09 | 10:05 | 11:01 | 11:46 | 12:42 | 13:38 | 14:34 | 15:30 | 16:26 | 17:22 | 18:18 |
| 46 | 46 | 01:43 | 02:40 | 03:37 | 04:34 | 05:31 | 06:28 | 07:25 | 08:22 | 09:19 | 10:16 | 11:13 | 12:10 | 13:07 | 14:04 | 15:01 | 15:47 | 16:44 | 17:41 | 18:38 |
| 47 | 47 | 01:45 | 02:43 | 03:41 | 04:39 | 05:37 | 06:35 | 07:33 | 08:31 | 09:29 | 10:27 | 11:25 | 12:23 | 13:21 | 14:19 | 15:17 | 16:15 | 17:13 | 18:11 | 19:09 |
| 48 | 48 | 01:47 | 02:46 | 03:45 | 04:44 | 05:43 | 06:42 | 07:41 | 08:40 | 09:39 | 10:38 | 11:37 | 12:36 | 13:35 | 14:34 | 15:33 | 16:32 | 17:31 | 18:30 | 19:29 |
| 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 |
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: 00,24:24:24:24:24:24:24:24:24:24:24:24... l.p. = 1
3: 00,16:16:16:16:16:16:16:16:16:16:16:16... l.p. = 1
4: 00,12:12:12:12:12:12:12:12:12:12:12:12... l.p. = 1
5: 00,09:39:09:39:09:39:09:39:09:39:09:39... l.p. = 2
6: 00,08:08:08:08:08:08:08:08:08:08:08:08... l.p. = 1
7: 00,07:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp
8: 00,06:06:06:06:06:06:06:06:06:06:06:06... l.p. = 1
9: 00,05:21:38:05:21:38:05:21:38:05:21:38... l.p. = 3
10: 00,04:44:04:44:04:44:04:44:04:44:04:44... l.p. = 2
11: 00,04:22:13:17:40:04:22:13:17:40... l.p. = 5
12: 00,04:04:04:04:04:04:04:04:04:04:04:04... l.p. = 1
13: 00,03:37:33:45:11:15:03:37:33:45:11:15... l.p. = 6
16: 00,03:03:03:03:03:03:03:03:03:03:03:03... l.p. = 1
17: 00,02:43:11:25:46:05:37:23... l.p. = 8
19: 00,02:28:18:02:28:18:02:28:18:02:28:18... l.p. = 3
23: 00,02:06:19:08:25:27:34:04:12:38:17:02... l.p. = 11
24: 00,02:02:02:02:02:02:02:02:02:02:02:02... l.p. = 1
25: 00,01:47:01:47:01:47:01:47:01:47:01:47... l.p. = 2
27: 00,01:39:45:18:07:12:34:23:29... l.p. = 9
28: 00,01:36:36:36:36:36:36:36:36:36:36:36... l.p. = 1+1pp
29: 00,01:33:38:42:11:40:27:01:33:38:42:11:40:27... l.p. = 7
31: 00,01:28:22:06:15:39:25:14:11:03:07:44:12:31:30... l.p. = 15
37: 00,01:15:43:34:21:09:13:11:45... l.p. = 9
41: 00,01:09:27:23:44:10:37:02:19:05:47:39... l.p. = 20
43: 00,01:06:41:01:06:41:01:06:41:01:06:41... l.p. = 3
47: 00,01:02:04:08:16:33:17:35:21:43:38:28:07:14:29:09:18:37:26:03:06:12:25... l.p. = 23
48: 00,01:01:01:01:01:01:01:01:01:01:01:01... l.p. = 1
49: 00,01:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp
50: 00,00:48:00:48:00:48:00:48:00:48:00:48... l.p. = 2
53: 00,00:45:14:38:40:33:13:42:25:43:22:09:12... l.p. = 13
59: 00,00:40:34:02:24:04:07:23:12:22:20:37... l.p. = 29
61: 00,00:39:17:32:45:38:27:15:12:41:37:36... l.p. = 30
64: 00,00:37:25:13:00:37:25:13:00:37:25:13... l.p. = 4
67: 00,00:35:40:46:39:24:06:28:25:29:12:21... l.p. = 33
71: 00,00:33:40:01:18:31:02:37:13:05:25:26... l.p. = 35
73: 00,00:32:43:30:42:46:48:16:05:18:06:02... l.p. = 12
79: 00,00:32:43:30:42:46:48:16:05:18:06:02... l.p. = 39
83: 00,00:28:45:22:21:12:19:23:30:05:15:17... l.p. = 41
89: 00,00:26:47:44:02:09:44:29:08:39:31:18... l.p. = 44
97: 00,00:24:36:42:45:47:23:36:18:09:04:26... l.p. = 48
...
Další lze snadno odvodit z údajů o sedmičkové soustavě: délky period jsou poloviční, nežli sudé délky period v sedmičkové soustavě a stejné, jako liché délky period v sedmičkové soustavě...
Sledujte
[editovat]- Předchozí: Číselné soustavy/Soustava o základu 48
- následující: Číselné soustavy/Soustava o základu 50
- také: Číselné soustavy/Soustava o základu 25