STUDENT: Right, we're going to do that in a second, but the answer is Fibonacci numbers, we define the first two.

学生：听不见：,我们马上会试一试，但是答案是斐波那契数列，我们可以定义下最初的两个数。

麻省理工公开课 - 计算机科学及编程导论课程节选

And all this is, is saying that when you take a mixed second derivative, it doesn't matter in which order you take the two derivatives.

麦克斯韦关系的本质是,当你考虑混合的二阶导数时，求导的顺序不影响最后的结果,现在，我们利用这些关系。

麻省理工公开课 - 热力学与动力学课程节选

And I'm going to show you an example in a 1 second, just to drive this home, but notice the characteristics. In the first two cases, the problem reduced by 1 at each step.

在前面两个例子里,每一部问题的规模缩小了,不管是迭代的还是递归的，这表明这个问题的复杂性可能是线性的。

麻省理工公开课 - 计算机科学及编程导论课程节选

He was trying to describe electrons, but the theory said there are two roots in the quadratic equation and the second root is mathematically as interesting as the first one.

他当时只是想去描述电子,但是数学理论告诉我们,二次方程有两个根,而第二个根在数学上和第一个根一样有趣

耶鲁公开课 - 基础物理课程节选

And what you will give me in return is on the first day, one cent-- one penny; on the second day, two cents; third day, 4 cents... Every day, twice as much as the previous day, starting with one.

你们给我的是，第一天，一分钱;,第二天，二分钱，第三天，四分钱。,每天给我前一天的两倍钱，从一分钱开始。

哈佛公开课 - 幸福课课程节选

And there is this heartbreaking love that Sal has for Dean, and, if you track that through, the major turning points in the second two thirds of the novel are moments when Sal makes it clear to Dean that he actually cares about him.

而且萨尔对迪安有着令人悲痛的爱情，如果你追踪这一点，你就会发现小说里,三分之二的时间萨尔都在,向迪安说明他有多在乎迪安。

耶鲁公开课 - 1945年后的美国小说课程节选

If you see a problem that asks you, for example, the third ionization energy versus taking a second electron out of the 2 s in a photoelectron spectroscopy experiment, those are two very different things.

如果你遇到一个题目问你的是，比如说，是第三电离能,还是在光电子能谱实验中从，2，s，轨道中,拿走第二个电子，这可是两个完全不同的问题。

麻省理工公开课 - 化学原理课程节选

At the end of the first round, I've got the smallest element at the front. At the end of the second round, I've got the smallest two elements at the front, in fact I got all of them sorted out. And it actually runs through the loop multiple times, making sure that it's in the right form.

看看发生了什么，在第一轮结束后,我把最小的元素移到了前面,第二轮结束后，我把最小的,两个元素移到了前面，实际上,所有的元素都排好序了,实际上，这个算法运行了几次循环，确认下这是正确的形式。

麻省理工公开课 - 计算机科学及编程导论课程节选

And runners proved the doctors and scientists-- proved that they were right and ran the mile in two seconds and 4 minutes, one second, but no runner could run the mile in under 4 minutes, ever since the mile was actually timed-- when they started to time runs.

跑手们证明了医生和科学家…,证明了他们是对的,一英里跑四分钟两秒，四分钟一秒，但没有跑手能少于四分钟，从一英里跑计时以来-,当人们开始计时跑时。

哈佛公开课 - 幸福课课程节选