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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。
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Square root of 16, and my plot basically shows it crosses at 4 and-- well, I think that's minus 4.
我的图清楚的显示这个函数,在4和-4两个点和x轴交合。
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60 If we look at 435 times 160, take the square root of that, we will end up with 264 kilojoules per mole, which sensibly lies between these two values.
35乘以，取平方根，我们会得到264千焦每摩，很合理地落在两数值之间。
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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。
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So the square root of n squared r e over r h.
这里的n值是什么呢？
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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。
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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。
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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？
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Add the same thing to the y-values, squared, take the square root.
的差的平方，然后加起来开平方。
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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。
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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。
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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。
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What we want to do now is compute the mean and variance of the portfolio-- or the mean and standard deviation, since standard deviation is the square root of the variance-- for different combinations of the portfolios.
我们现在要做的是,计算这个投资组合的均值和方差-,或者均值和标准差，因为标准差的平方就等于方差-,这对任何投资组合都是一样的。
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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。
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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？
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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。
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I take the difference in the x-values, squared, the difference in the y-values, squared, add them up, take the square root of that.
好，是毕达哥拉斯定力对不对？,求x坐标的差，然后平方，求y坐标的差，然后平方，把它们加起来，开平方。
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Look, part of the reason I'm flaming at you is, something like square root, it seems dumb to write specs on it. Everybody knows what this is going to do. But you want to get into that discipline of good hygiene, good style.
也是非常重要的，我在这里说的,一些理由就是像平方根,为它写规范听上去很傻,每个人都知道它是干什么的。
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So you take the square root of the product.
你应该用乘积的平方根。
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Is the square root ever going to be less than 0?
一个数的平方根会小于0么？
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OK, once it gets to the end of that, what's it going to do? It's going to come down here and, oh. What's that doing? Well I cheated when I started. I said, somebody's giving me a perfect square, I'm looking for the square root of it. But suppose 15 I gave this thing 15, and asked it to run.
好，一旦到了循环的最后，程序会去做什么？程序会跳到这里来,噢，这是干什么的？好吧,当我开始的时候我有点小作弊的意思,我说过，我得到了一个完美的平方数,我要求这个数的平方根,但是假设下我得到的数是。
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I'm checking that I didn't leave my program because I didn't find an answer. Well this is a good thing, it's better than my program running forever, but it's a bad thing because I don't have it the square root of 0.25.
我对计数器要做个验证,因为我不会没得到答案就退出程序,好，这其实是个好事,因为它不会让我的程序永远跑下去，但这也是件坏事因为,我没得到0。25的平方根。
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All right. So we have that square root NR.
好，看看这个NR求平方根方法。
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5 Right. Sure. Square root of 16 is 5.
是的，那么ANS为5，AND的平方等于。
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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。
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