1 00:00:04,420 --> 00:00:07,221 Tasavvur qiling, milodan avvalgi yillar. 2 00:00:07,221 --> 00:00:09,468 O'ylab ko'ring: 3 00:00:09,468 --> 00:00:12,721 Qanday qilib soatsiz, vaqtni aniqlashgan? 4 00:00:12,721 --> 00:00:15,315 Barcha soatlar, vaqt oqimini teng bo'laklarga bo'luvchi 5 00:00:15,315 --> 00:00:18,890 qandaydir takroriy shaklga asoslangan. 6 00:00:18,890 --> 00:00:20,688 Bunday takroriy shakillarni topish uchun 7 00:00:20,688 --> 00:00:22,918 samolarga yuzlanamiz. 8 00:00:22,918 --> 00:00:24,902 Har kuni, quyoshning chiqishi va botishi 9 00:00:24,902 --> 00:00:26,184 bunday shakllarning eng oddiysidir. 10 00:00:26,184 --> 00:00:28,760 Lekin, uzoqroq vaqt bo'lagini kuzatish uchun, 11 00:00:28,760 --> 00:00:30,811 uzoqroq takrorlanishlarga e'tibor beramiz. 12 00:00:30,811 --> 00:00:32,512 Buning uchun esa, oyga yuzlanamiz. 13 00:00:32,512 --> 00:00:33,853 E'tibor bergan bo'lsangiz, 14 00:00:33,853 --> 00:00:36,578 oy kunlar osha to'lishadi va kichrayadi. 15 00:00:36,578 --> 00:00:37,894 To'lin oylar orasidagi kunlar sonini 16 00:00:37,894 --> 00:00:38,978 sanaydigan bo'lsak, 17 00:00:38,978 --> 00:00:40,910 u 29 kunga teng. 18 00:00:40,910 --> 00:00:42,833 Bir oydagi kunlar soni shundan kelib chiqqan bo'lsa kerak. 19 00:00:42,833 --> 00:00:45,873 Ammo, 29 ni teng bo'laklarga bo'lishga harakat qilsak 20 00:00:45,873 --> 00:00:49,227 bir muammoga duch kelamiz: buning iloji yo'q. 21 00:00:49,227 --> 00:00:51,676 29 ni teng bo'laklarga bo'lishning yagona yo'li 22 00:00:51,676 --> 00:00:54,819 uni 29 ta teng bo'lakka bo'lishdan iborat. 23 00:00:54,819 --> 00:00:57,102 29 soni tub son hisoblanadi. 24 00:00:57,102 --> 00:00:59,061 Uni bo'linmas deb tasavvur qiling. 25 00:00:59,061 --> 00:01:00,879 Agar son birdan boshqa 26 00:01:00,879 --> 00:01:02,814 teng bo'laklarga bo'linsa, 27 00:01:02,814 --> 00:01:04,621 biz uni 'murakkab son' deb ataymiz. 28 00:01:04,621 --> 00:01:06,608 Endi biz qiziqishimiz mumkin, 29 00:01:06,608 --> 00:01:08,450 "Dunyoda nechta tub son bo'lishi mumkin - 30 00:01:08,450 --> 00:01:10,398 va ularning eng kattasi nechaga teng ekan?" 31 00:01:10,398 --> 00:01:13,744 Keling, barcha sonlarni ikkita guruhga bo'lamiz. 32 00:01:13,744 --> 00:01:15,611 Tub sonlar chap tomonda 33 00:01:15,611 --> 00:01:17,648 va murakkab sonlar o'ng tomonda. 34 00:01:17,648 --> 00:01:20,379 Boshida, u tomondan bu tomonga raqs tushayotganga o'xshaydilar. 35 00:01:20,379 --> 00:01:23,017 Ammo, ularning joylashuvida aniq bir shakl mavjud emas. 36 00:01:23,017 --> 00:01:24,439 Keling, bunday shaklni ko'rish uchun 37 00:01:24,439 --> 00:01:26,077 zamonaviy usuldan foydalanamiz. 38 00:01:26,077 --> 00:01:29,047 Bu usul "Ulam spirali" deb nomlanadi. 39 00:01:29,047 --> 00:01:32,011 Boshida, barcha raqamlarni tartib bilan, o'sayotgan spiral 40 00:01:32,011 --> 00:01:34,043 ichiga joylab chiqamiz. 41 00:01:34,043 --> 00:01:37,164 Keyin, barcha tub sonlarni ko'k ranga bo'yab chiqamiz. 42 00:01:37,164 --> 00:01:41,290 Nihoyat, biz millionlab raqamlarni ko'rish uchun uzoqlashamiz. 43 00:01:41,290 --> 00:01:42,860 Mana bu tugalmas tub sonlarning 44 00:01:42,860 --> 00:01:45,365 shakli hisoblanadi. 45 00:01:45,365 --> 00:01:47,967 Hayratlanarlisi shuki, bu shaklning tuliq strukturasi 46 00:01:47,967 --> 00:01:50,314 haligacha topilmagan. 47 00:01:50,314 --> 00:01:51,843 Nimanidir kashf etish arafasida turganga o'xshaymiz. 48 00:01:51,843 --> 00:01:52,987 Keling, m.a. 300 yillarga 49 00:01:52,987 --> 00:01:55,526 Qadimgi Gretsiyaga sayr qilamiz. 50 00:01:55,526 --> 00:01:58,183 Buyuk faylasuf Aleksandryalik Evklid 51 00:01:58,183 --> 00:01:59,411 barcha sonlarni 52 00:01:59,411 --> 00:02:02,607 bu ikki guruhga ajralishini anglab yetadi. 53 00:02:02,607 --> 00:02:04,896 Dastlab, u istalgan sonni 54 00:02:04,896 --> 00:02:07,078 eng kichik teng sonlar guruhlarigacha 55 00:02:07,078 --> 00:02:10,599 bo'lish mumkinligini anglab yetadi. 56 00:02:10,599 --> 00:02:12,921 Va bu eng kichik sonlar esa, har doim, 57 00:02:12,921 --> 00:02:15,760 tub sonlardir. 58 00:02:15,760 --> 00:02:17,148 Shunday qilib u, barcha sonlar 59 00:02:17,148 --> 00:02:20,542 tub sonlardan qurilganini tushunib yetadi. 60 00:02:20,542 --> 00:02:23,317 Aniqrog'i, barcha sonlar olamini tasavvur qiling. 61 00:02:23,317 --> 00:02:25,674 tub sonlar haqida unuting. 62 00:02:25,674 --> 00:02:28,037 Endi, istalgan murakkab sonni olamiz, 63 00:02:28,037 --> 00:02:30,518 va bo'laklarga ajratamiz, 64 00:02:30,518 --> 00:02:33,354 va bu bo'laklar har doim tub sonlardir. 65 00:02:33,354 --> 00:02:34,774 Demak, Evklid istalgan raqam 66 00:02:34,774 --> 00:02:37,675 kichikroq tub sonlar guruhi orqali ifodalanishi mumkinligin tushunib yetgan. 67 00:02:37,675 --> 00:02:38,675 Ularni g'ishtlar deb tasavvur qiling. 68 00:02:38,675 --> 00:02:40,221 Qaysi son bo'lishidan qat'iy nazar 69 00:02:40,221 --> 00:02:41,996 uni kichiroq tub sonlarni qo'shish bilan yasash mumkin. 70 00:02:41,996 --> 00:02:46,157 Mana shu Evklid kashfiyotining asosi bo'lib, 71 00:02:46,157 --> 00:02:48,032 "Arifmetikaning asosiy nazariyasi" deb nomlanadi. 72 00:02:48,032 --> 00:02:50,759 73 00:02:50,759 --> 00:02:52,013 74 00:02:52,013 --> 00:02:53,934 75 00:02:53,934 --> 00:02:55,501 76 00:02:55,501 --> 00:02:57,233 77 00:02:57,233 --> 00:02:59,763 78 00:02:59,763 --> 00:03:01,624 79 00:03:01,624 --> 00:03:05,811 80 00:03:05,811 --> 00:03:07,906 81 00:03:07,906 --> 00:03:10,714 82 00:03:10,714 --> 00:03:12,739 83 00:03:12,739 --> 00:03:13,780 84 00:03:13,780 --> 00:03:16,178 85 00:03:16,178 --> 00:03:20,158 86 00:03:20,158 --> 00:03:23,153 87 00:03:23,153 --> 00:03:24,887 88 00:03:24,887 --> 00:03:27,110 89 00:03:27,110 --> 00:03:28,792 90 00:03:28,792 --> 00:03:31,276 91 00:03:31,276 --> 00:03:34,046 92 00:03:34,046 --> 00:03:36,299 93 00:03:36,299 --> 00:03:38,017 94 00:03:38,033 --> 00:03:39,722 95 00:03:39,722 --> 00:03:42,054 96 00:03:42,054 --> 00:03:43,937 97 00:03:43,937 --> 00:03:47,889