1 00:00:00,789 --> 00:00:04,600 “自然的律法只是上帝的数学思想。” 2 00:00:04,862 --> 00:00:07,523 这是欧几里得的一句话。 3 00:00:07,523 --> 00:00:12,655 欧几里得是一个生于约公元前300唸的一个希腊数学家和哲学家。 4 00:00:12,655 --> 00:00:19,691 我之所以引用这句话,是因为欧几里得被认为是几何学之父。 5 00:00:19,691 --> 00:00:22,663 这句名言简洁明了,无论你怎样看待上帝, 6 00:00:22,663 --> 00:00:25,054 不管上帝是否存在,或者上帝的本质是什么, 7 00:00:25,054 --> 00:00:27,516 它都揭露了关于自然的最重要的一些东西。 8 00:00:27,516 --> 00:00:31,649 自然的规律仅仅是上帝的数学思想, 9 00:00:31,649 --> 00:00:35,016 而数学是所有自然法则的支柱。 10 00:00:35,016 --> 00:00:37,802 ”几何学“这个单词本身来自于希腊词根, 11 00:00:37,802 --> 00:00:40,983 ”Geo“来自于希腊语的”地球“, 12 00:00:40,983 --> 00:00:44,211 ”Metry“来自于希腊语的”测量“。 13 00:00:44,211 --> 00:00:47,183 你可能曾经用过某些“测量”系统。 14 00:00:47,183 --> 00:00:50,132 欧几里得被认为是几何学之父。 15 00:00:50,132 --> 00:00:52,802 (不是因为他是第一个研究几何学的人) 16 00:00:52,802 --> 00:00:56,285 你可以想象最初研究几何学的人们, 17 00:00:56,562 --> 00:01:00,024 他们可能盯着地上的两根树枝看着, 18 00:01:00,024 --> 00:01:02,462 他们可能盯着另外一对树枝一样的东西看着, 19 00:01:02,462 --> 00:01:05,178 然后说,这个开口更大。它们的关系是什么? 20 00:01:05,178 --> 00:01:13,654 或者他们可能看着一棵树枝像这样的树。 21 00:01:13,654 --> 00:01:18,274 然后他们会说,“嗯,这个开口和这个开口有点像。” 22 00:01:18,274 --> 00:01:19,737 或者他们可能问问自己, 23 00:01:19,737 --> 00:01:26,123 这个比例是多少,或者圆的周长和直径有什么关系 24 00:01:26,123 --> 00:01:28,352 这种关系对于所有圆来讲都成立吗 25 00:01:28,352 --> 00:01:31,812 怎样能让它绝对成立呢? 26 00:01:31,812 --> 00:01:34,412 一旦你理解了早期希腊人, 27 00:01:34,412 --> 00:01:39,010 他们开始思考更多几何问题。 28 00:01:39,010 --> 00:01:43,259 当谈到古希腊数学家,比如毕达哥拉斯 29 00:01:43,259 --> 00:01:45,535 (他是早于欧几里得的一位数学家) 30 00:01:45,535 --> 00:01:54,511 但是人们之所以认为认为欧几里得是几何学之父(我们常常谈到欧式几何) 31 00:01:54,511 --> 00:01:59,832 32 00:01:59,832 --> 00:02:05,793 33 00:02:05,793 --> 00:02:08,383 34 00:02:08,383 --> 00:02:14,397 但是让欧几里得成为几何学之父的,是他的代表作《几何原本》。 35 00:02:14,397 --> 00:02:21,263 36 00:02:21,263 --> 00:02:24,773 37 00:02:24,773 --> 00:02:31,441 38 00:02:31,441 --> 00:02:37,524 39 00:02:37,524 --> 00:02:40,682 40 00:02:40,682 --> 00:02:44,955 41 00:02:44,955 --> 00:02:47,532 42 00:02:47,532 --> 00:02:51,851 43 00:02:51,851 --> 00:02:55,334 44 00:02:55,334 --> 00:03:02,393 45 00:03:02,393 --> 00:03:05,806 46 00:03:05,806 --> 00:03:14,374 47 00:03:14,374 --> 00:03:18,182 48 00:03:18,182 --> 00:03:24,475 49 00:03:24,475 --> 00:03:29,723 50 00:03:33,215 --> 00:03:37,721 51 00:03:37,721 --> 00:03:43,747 52 00:03:43,747 --> 00:03:51,549 53 00:03:51,549 --> 00:03:55,729 54 00:03:55,729 --> 00:03:58,492 55 00:03:58,492 --> 00:04:01,255 56 00:04:01,255 --> 00:04:04,042 57 00:04:04,042 --> 00:04:06,155 58 00:04:06,155 --> 00:04:11,402 59 00:04:11,402 --> 00:04:14,096 60 00:04:14,096 --> 00:04:17,068 61 00:04:17,068 --> 00:04:23,477 62 00:04:23,477 --> 00:04:30,095 63 00:04:30,884 --> 00:04:39,692 64 00:04:39,692 --> 00:04:42,022 65 00:04:43,069 --> 00:04:47,881 66 00:04:47,881 --> 00:04:55,427 67 00:04:55,427 --> 00:04:59,862 68 00:04:59,862 --> 00:05:01,581 69 00:05:01,581 --> 00:05:04,344 70 00:05:04,344 --> 00:05:07,943 71 00:05:07,943 --> 00:05:09,940 72 00:05:10,525 --> 00:05:16,606 73 00:05:16,606 --> 00:05:19,416 74 00:05:19,816 --> 00:05:23,779 75 00:05:23,779 --> 00:05:26,612 76 00:05:26,612 --> 00:05:29,747 77 00:05:29,747 --> 00:05:35,900 78 00:05:35,900 --> 00:05:38,872 79 00:05:38,872 --> 00:05:40,777 80 00:05:41,207 --> 00:05:43,795 81 00:05:43,795 --> 00:05:48,415 82 00:05:48,415 --> 00:05:53,454 83 00:05:53,454 --> 00:05:59,375 84 00:05:59,375 --> 00:06:02,580 85 00:06:02,580 --> 00:06:08,454 86 00:06:08,454 --> 00:06:13,307 87 00:06:13,307 --> 00:06:17,998 88 00:06:17,998 --> 00:06:23,060 89 00:06:23,060 --> 00:06:28,005 90 00:06:28,005 --> 00:06:32,649 91 00:06:32,649 --> 00:06:35,668 92 00:06:35,668 --> 00:06:41,241 93 00:06:41,241 --> 00:06:45,676 94 00:06:45,676 --> 00:06:55,150 95 00:06:55,150 --> 00:07:00,467 96 00:07:00,467 --> 00:07:04,345 97 00:07:04,345 --> 00:07:06,806 98 00:07:06,806 --> 00:07:11,868 99 00:07:11,868 --> 00:07:17,348 100 00:07:17,348 --> 00:07:24,128 101 00:07:24,128 --> 00:07:30,885 102 00:07:30,885 --> 00:07:32,954 103 00:07:33,447 --> 00:07:36,922 104 00:07:36,922 --> 00:07:42,806 105 00:07:42,868 --> 00:07:49,624 106 00:07:49,624 --> 00:07:59,812 107 00:07:59,812 --> 00:08:01,972 108 00:08:01,972 --> 00:08:06,388 109 00:08:06,388 --> 00:08:08,525 110 00:08:08,525 --> 00:08:12,820 111 00:08:12,820 --> 00:08:17,000 112 00:08:17,000 --> 00:08:21,388