-
What is that? It's the piece of code we wrote for computing square roots, square roots of actually perfect squares.
对吧？这是什么呢？,这是我们写的计算平方根的代码，计算完全全平方根的。
-
I like that answer. I then tested it on the square root of 9, and as I mentioned last time, I didn't find 3. I was not crushed.
我喜欢这个答案,然后我又试了试9的平方根，跟我上次说的一样，答案不是3。
-
But he said the energy of an X-Y bond is going to be equal to the square root.
但他说ＸＹ键的键能,会等于ＸＸ键与ＹＹ键键能乘积的平方根。
-
Because the square root of 10,000 is 100, whatever the standard deviation of the portfolio is, you would divide it by 100 and it would become really small.
因为一万的平方根是一百，无论这个投资组合的标准差是多大，当除以100后就都变得很小很小了。
-
So, if we just rearrange this equation, what we find is that z effective is equal to n squared times the ionization energy, IE all over the Rydberg constant and the square root of this.
我们可以发现有效的z等于n的平凡，乘以电离能除以里德堡常数,这些所有再开方，所以等于n乘以,除以RH整体的平方根。
-
All right, this is actually a very old piece of imperative knowledge for computing square roots, it's attributed to Heron of Alexandria, although I believe that the Babylonians are suspected of knowing it beforehand.
好，这是一个很古老的,关于计算平方根的程序性知识，是亚历山大的海伦提出的，不过我怀疑在那之前,巴比伦人就已经猜想过了。
-
You know, if you're wandering through Harvard Square and you see an out-of-work Harvard grad, they're handing out examples of square roots, they'll give you an example and you can test it to see is the square root of 2, 1.41529 or whatever.
你知道，如果你从哈佛校园里穿过去,你看见了一个失业校友，正在派发平方根的示例，他们会给你一个例子,而你会检查2的平方根是1。41529或者别的什么。
-
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。
-
Suppose I want to find all the divisors of some integer, I want to figure out what all the divisors are that go evenly into it.
也就是遍历所有的整数来寻找,一个数的平方根，让我们再来看一个例子吧,为了找出另外一种的解决方法。
-
So you take the square root of the product.
你应该用乘积的平方根。
-
It was over here. Because the square root of a quarter is not smaller than a quarter it's bigger than a quarter. Right?
答案超出了这个区间,因为0。25的平方根会比0。25大,是应该比0。25大对不对？
-
I can check it, so if this was part of some other computation, I want to know, did it find a perfect square or not?
我可以检验它,因此如果这是其它计算的一部分我想知道，它能否找到一个完全平方根呢？
-
All right. I tried it on 2, I surely didn't expect a precise and exact answer to that but I got something, and if you square this, you'll find the answer kept pretty darn close to 2.
好，我试试求2的平方根,我当然不希望得到一个完全准确的答案了,但是我得到了一个近似值，试试将这个数平方一下,你会发现结果和2相当接近。
-
I'm not supposed to make bad jokes like that.
6的平方根是5吧，这是布什经济学对不对？
-
Remember, I said when we do a bisection method, we're assuming the answer lies somewhere between Well, what is the square root of a quarter? It is a half.
记住，我提过当我们用二分法的时候,我们假设答案处于,上边界和下边界之间,0。25的平方根是多少？,是0。5。
-
Or, it could act like a square root machine.
或者，它可以表现的像个开平方根的机器。
-
The standard deviation is the square root of the variance.
标准差是方差的平方根
-
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？
-
I want to then do, I need to find the square root b squared plus h squared, right?
我接下来要求b的平方和h的平方,的和的平方根对不对？
-
This was using something called a bisection method, which is related to something called binary search, which we'll see lots more of later, to find square roots.
你应该想起来,我们是以一个,叫做二分法求平方根的问题结束的，它运用了二分法去求一个数的平方根，二分法和我们将要花很多时间。
-
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。
-
You have square root of minus one for something else.
你得到了某个负数的平方根。
-
And I'm looking here at 16.
现在我要求一下16的平方根。
-
I'm given an integer that's a perfect square, and I want to write a little piece of code that's going to find the square root of it. All right so I'm cheating a little, I know it's a perfect square, somebody's given it to me, we'll come back in a second to generalizing it, so what would the steps be that I'd use to walk through it?
完美平方数的整数，我想写一段代码来求这个数的平方根,好，我这儿有点儿作弊了,我知道这是一个完美的平方数了,他们给我的，我们后面会讲怎么产生这个数的，那么我想解决这个问题,需要什么步骤呢？
-
In some sense, strictly speaking they shouldn't be necessary because the fact that my specification starts with an assumption, says, hey you, who might call square root make sure that the things you call me with obey the assumption.
在某种意义上严格的来讲,它们不是必要的,因为我已经对假设做了声明,也就是说，如果你要调用我的，求平方根的函数,请确保你传递给我的,参数满足假设条件。
-
Let's call x the thing I'm trying to find the square root of. Let's start at 1. Square it.
让我们把求平方根的对象,这个数称为x，让我们从1开始。
-
I'm using it as an abstraction, saying I'm going to have square root from somewhere, maybe I'll build it myself, maybe somebody gives it to me a s part of a library, so I'm burying the details inside of it.
我把这个方法作为一个抽象来引用，意味着我将会从另外一个,地方去求一个数的平方根，可能我会自己写这个方法,也可能我会从别人写的lib中去引用,因此我将实现的细节放到了其他地方。
-
If I say x is 2, I want to know, what's the square root of 2, well if you're enough of a geek, you'll say 1.41529 or whatever the heck it is, but in general, this doesn't help you find the square root.
如果我说X等于，我想知道，2的平方根是多少，那么如果你足够书呆子你就会说,1。41529或者随便什么玩意儿，但是大体上，它不会帮你算出平方根。
-
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。
-
Well I'm relying on the contract, if you like, that the manufacturer of square root put together, which is, if I know I'm giving it two floats, which I do because I make sure they're floats, the contract, if you like, of square root says I'll give you back a float.
好吧我能靠一些类似合约来保证，如果这么说你喜欢的话,其实就是当求平方根的方法,获得了两个我已经确认了是浮点数的数后,这个类似合约的东西就会保证，返回一个浮点数。
应用推荐