WEBVTT 00:00:00.789 --> 00:00:04.600 “自然的律法只是上帝的数学思想。” 00:00:04.862 --> 00:00:07.523 这是欧几里得的一句话。 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。 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。 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, 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, 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。 00:00:27.516 --> 00:00:31.649 自然的规律仅仅是上帝的数学思想, 00:00:31.649 --> 00:00:35.016 而数学是所有自然法则的支柱。 00:00:35.016 --> 00:00:37.802 ”几何学“这个单词本身来自于希腊词根, 00:00:37.802 --> 00:00:40.983 ”Geo“来自于希腊语的”地球“, 00:00:40.983 --> 00:00:44.211 ”Metry“来自于希腊语的”测量“。 00:00:44.211 --> 00:00:47.183 你可能曾经用过某些“测量”系统。 00:00:47.183 --> 00:00:50.132 欧几里得被认为是几何学之父。 00:00:50.132 --> 00:00:52.802 (不是因为他是第一个研究几何学的人) 00:00:52.802 --> 00:00:56.285 你可以想象最初研究几何学的人们, 00:00:56.562 --> 00:01:00.024 他们可能盯着地上的两根树枝看着, 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, 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? 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。 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。” 00:01:18.274 --> 00:01:19.737 或者他们可能问问自己, 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 00:01:26.123 --> 00:01:28.352 这种关系对于所有圆来讲都成立吗 00:01:28.352 --> 00:01:31.812 怎样能让它绝对成立呢? 00:01:31.812 --> 00:01:34.412 一旦你理解了早期希腊人, 00:01:34.412 --> 00:01:39.010 他们开始思考更多几何问题。 00:01:39.010 --> 00:01:43.259 当谈到古希腊数学家,比如毕达哥拉斯 00:01:43.259 --> 00:01:45.535 (他是早于欧几里得的一位数学家) 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) 00:01:54.511 --> 00:01:59.832 00:01:59.832 --> 00:02:05.793 00:02:05.793 --> 00:02:08.383 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》。 00:02:14.397 --> 00:02:21.263 00:02:21.263 --> 00:02:24.773 00:02:24.773 --> 00:02:31.441 00:02:31.441 --> 00:02:37.524 00:02:37.524 --> 00:02:40.682 00:02:40.682 --> 00:02:44.955 00:02:44.955 --> 00:02:47.532 00:02:47.532 --> 00:02:51.851 00:02:51.851 --> 00:02:55.334 00:02:55.334 --> 00:03:02.393 00:03:02.393 --> 00:03:05.806 00:03:05.806 --> 00:03:14.374 00:03:14.374 --> 00:03:18.182 00:03:18.182 --> 00:03:24.475 00:03:24.475 --> 00:03:29.723 00:03:33.215 --> 00:03:37.721 00:03:37.721 --> 00:03:43.747 00:03:43.747 --> 00:03:51.549 00:03:51.549 --> 00:03:55.729 00:03:55.729 --> 00:03:58.492 00:03:58.492 --> 00:04:01.255 00:04:01.255 --> 00:04:04.042 00:04:04.042 --> 00:04:06.155 00:04:06.155 --> 00:04:11.402 00:04:11.402 --> 00:04:14.096 00:04:14.096 --> 00:04:17.068 00:04:17.068 --> 00:04:23.477 00:04:23.477 --> 00:04:30.095 00:04:30.884 --> 00:04:39.692 00:04:39.692 --> 00:04:42.022 00:04:43.069 --> 00:04:47.881 00:04:47.881 --> 00:04:55.427 00:04:55.427 --> 00:04:59.862 00:04:59.862 --> 00:05:01.581 00:05:01.581 --> 00:05:04.344 00:05:04.344 --> 00:05:07.943 00:05:07.943 --> 00:05:09.940 00:05:10.525 --> 00:05:16.606 00:05:16.606 --> 00:05:19.416 00:05:19.816 --> 00:05:23.779 00:05:23.779 --> 00:05:26.612 00:05:26.612 --> 00:05:29.747 00:05:29.747 --> 00:05:35.900 00:05:35.900 --> 00:05:38.872 00:05:38.872 --> 00:05:40.777 00:05:41.207 --> 00:05:43.795 00:05:43.795 --> 00:05:48.415 00:05:48.415 --> 00:05:53.454 00:05:53.454 --> 00:05:59.375 00:05:59.375 --> 00:06:02.580 00:06:02.580 --> 00:06:08.454 00:06:08.454 --> 00:06:13.307 00:06:13.307 --> 00:06:17.998 00:06:17.998 --> 00:06:23.060 00:06:23.060 --> 00:06:28.005 00:06:28.005 --> 00:06:32.649 00:06:32.649 --> 00:06:35.668 00:06:35.668 --> 00:06:41.241 00:06:41.241 --> 00:06:45.676 00:06:45.676 --> 00:06:55.150 00:06:55.150 --> 00:07:00.467 00:07:00.467 --> 00:07:04.345 00:07:04.345 --> 00:07:06.806 00:07:06.806 --> 00:07:11.868 00:07:11.868 --> 00:07:17.348 00:07:17.348 --> 00:07:24.128 00:07:24.128 --> 00:07:30.885 00:07:30.885 --> 00:07:32.954 00:07:33.447 --> 00:07:36.922 00:07:36.922 --> 00:07:42.806 00:07:42.868 --> 00:07:49.624 00:07:49.624 --> 00:07:59.812 00:07:59.812 --> 00:08:01.972 00:08:01.972 --> 00:08:06.388 00:08:06.388 --> 00:08:08.525 00:08:08.525 --> 00:08:12.820 00:08:12.820 --> 00:08:17.000 00:08:17.000 --> 00:08:21.388