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So we've seen one example of this, this idea of walking through all the integers looking for the square root.
现在计算机速度很快了，我可以把这个数字设的更大点,计算机会去很快的做这个事情。
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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？
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You have square root of minus one for something else.
你得到了某个负数的平方根。
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The abandonment of such a study or its adulteration for current political purposes would be a terrible loss for all of humanity, and at the base, at the root of that civilization stood the Greeks.
如果出于政治的目的而对此段历史,视而不见甚至完全摒弃,这对全人类,将是一个巨大的损失,追根溯源,这一切都根植于希腊文明
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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。
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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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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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Looking for the root of this equation.
也就是求这个方程式的根。
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The institutions and the ideas therefore, that provide for freedom and improvement in the material conditions of life, cannot take root and flourish without an understanding of how they came about and what challenges they have had to surmount.
故此,这些机制和理念,为物质生活条件的自由和改善,提供了基础,但在不知道其根源且,无法预料的挑战之前,机制和理念是不可能扎根的
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