I wanted to show you that, so, first thing I'm going to do is say, all right, I know I'm going to need square root in here, so I'm going to, in fact, import math.

我们可以开始完成这个方法了，我想让你们看到完成这个方法的过程，第一件事情就是,我们在这儿需要一个求平方根的方法，实际上我将引入math包。

麻省理工公开课 - 计算机科学及编程导论课程节选

Then if I'm looking for the square root of something less than 1, I know it will be in my region, right?

如果我要求平方根的数小于,我就知道我们的答案应该,在0-1这个区间了，对不对？

麻省理工公开课 - 计算机科学及编程导论课程节选

So because so much popular music and particularly rock music has those chords in root position we can track them more readily.

因为很多流行音乐尤其是摇滚乐会在原位上添加这样的和弦,这样听起来会比较悦耳。

耶鲁公开课 - 聆听音乐课程节选

But you do, in fact, have to worry about long-term exposure, cyanide poisoning in terms of long-term effects in certain populations that do get the bulk of their carbohydrates from this root, from the root of the Cassava plant.

但是你确实，不得不担心长时间的接触，氰化物的慢性中毒会对,从木薯根中获取大部分,碳水化合物的部分人群产生影响。

麻省理工公开课 - 化学原理课程节选

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

If you had one negative number in it, then the product would be a negative number and, if you took a root of that, then you might get an imaginary number.

如果这当中有一个负数,乘积就会变成负的,如果你对一个负数开根号,你就会得到一个虚数

耶鲁公开课 - 金融市场课程节选

And I was talking about the fact that for Deuteronomy the election of Israel, God's election of Israel means or entails the idea that Israel is a holy people, holy in the sense of separated to God that root meaning of holiness which means to be separated from the common or the ordinary.

我上次提到了《申命记》中的一个事实,以色列被选择，上帝选择以色列意味着,以色列是神圣的民族，对于上帝他们是分离的,这便是神圣的根本意义,意味着与一般和普通分离。

耶鲁公开课 - 旧约导论课程节选

And it is precisely this desire to be self-governing, you might say to rule directly, to have a direct part in political rule, that Hobbes saw as one of the great root causes of civil war.

正是这种自我统治的愿望，直接统治的愿望，在政治统治中直接参与的愿望，霍布斯视为是,内战一个很重要的原因。

耶鲁公开课 - 政治哲学导论课程节选

There is one exception. In the sixth century, I think it's around--imagine around 550 or something like that, the Greeks settle a single colony in the Delta of the Nile of Egypt at a place called Naucratis, and the root of that word is ship.

但有一个例外,在公元前六世纪,我想大概是,在公元前550年左右,希腊在埃及尼罗河三角洲,一个叫诺克拉提斯的地方建立了殖民地,Naucratis的意思就是船

耶鲁公开课 - 古希腊历史简介课程节选

I first tested it on the square root of 4 and in one iteration it found 2.

我首先测了下求4的平方根4,它只迭代了一次并返回了2。

麻省理工公开课 - 计算机科学及编程导论课程节选

In a high-level language, square root might simply be a primitive that you can use rather than you having to go over and code it.

一个高级的语言，平方根可能仅仅,只是你能使用的一个基本要素,而不是你需要去编译它。

麻省理工公开课 - 计算机科学及编程导论课程节选

Computing square root. I'm going to capture it in a piece of code, I'm going to be able to refer to it by a name, and I'm going to suppress the details, meaning inside of that computation, you don't need to know what it does. You just need to know, if I give it the right kind of input, it'll give me back an input that satisfies the contract that I set up.

比如计算平方根,我会用一段代码来说明,我将给它命名,并且忽略细节,意思就是在这一段计算过程中,你不用知道它做了什么，你只需知道，如果我进行了正确的输入,它将会给我符合条件的输出。

麻省理工公开课 - 计算机科学及编程导论课程节选

Well,here's one other that you might not have thought of, and that is that most of the chords in rock music in particular tend to be root-position chords, and for that reason they're easier to hear.

还有另外一点也许大家还没有想到，那就是摇滚乐的主要和弦尤其倾向于变成根和弦，因此他们听起来也更加容易。

耶鲁公开课 - 聆听音乐课程节选

So we've looked at how to solve square root we've, looked at two problems, I've tried to instill in you this sense of paranoia which is so valuable, and now we're going to pull back Python and return to something much simpler than numbers, and that's Python. All right?

我们已经研究了如何去求平方根,研究了两种方法,我一直在尝试着给你们逐渐灌输,要偏执的理念，这样的理念非常有价值，现在我们回过头来去学习一些,比数字更简单的东西，也就是,对不对？数学问题很难？

麻省理工公开课 - 计算机科学及编程导论课程节选

We've talked about some of these already, having to do with the nature of the harmony-- that pop music tends to have simpler harmonies, and that those harmonies tend to be more repetitious, that they tend to have harmonies that have chords in root position.

我们以前说过，这个问题与和声的性质有关-,流行乐通常用较为简单的和声，流行乐通常用较为简单的和声，流行乐手也大多喜欢用原位和弦。

耶鲁公开课 - 聆听音乐课程节选

We're not going to get into that 'cause that takes us into heavy-duty music theory, but it's--if we don't have root position then we've got some other note of the triad in the bass, and we've got some kind of chord inversion, so that's what that particular term means up there.

我们就不深究这个问题了，这是一个冗长的音乐理论，但是如果没有了原位，三和弦的低音被另一个音所替代，这就是一种和弦转位，这就是这个词在这里的意思。

耶鲁公开课 - 聆听音乐课程节选