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。
So people from all the different subways and all the different neighborhoods come to Union Square.
所以四面八方的人们乘各路地铁到这儿来。
And what I recognized was first of all, how impoverishing that was spiritually to not be able to bring my faith identity into the public square.
而我意识到,第一,我们精神上很枯竭,因为我们不能将自己的宗教身份,带入公共场所。
All right? I mean, I can make money at Harvard Square doing this stuff, right?
对不对?【鼓掌】我意思是,我可以在哈佛广场,靠做这个赚钱对不对?
Well, all this time int on the blackboard I always draw an int as a square.
嗯,向来,我在黑板上用一个正方形表示一个。
And you probably know that Leicester Square is where all the big film premieres happen.
你可能知道,莱斯特广场是所有电影巨作的首映现场。
First of all, it's clear from the Pythagoras' theorem that a is the square root of ^2 + ^2.
首先,根据毕达哥拉斯定理,勾股定理在西方被称为"毕达哥拉斯定理"
so Buckingham Palace, Trafalgar Square, all those places are where the tourists always flock
白金汉宫,特拉法尔加广场,所有这些地方都是游客聚集的地方,
So if we square sigma 1 s star, we flip the amplitude so it's all positive now, but again we still have this node right in the middle.
如果我们平方1s星,我们把振幅翻转所以现在都是正的,但同样在中间有个节点。
Head all the way down in Embarcadero, you hit Ghirardelli Square,
穿过英巴卡迪诺海湾大道,可以去吉尔德利广场,
Leicester Square, Piccadilly, they're where like all the shows are,
莱斯特广场,皮卡迪利广场,所有的演出都在那儿,
And it was all in Trafalgar Square
整个首映会在特拉法加广场举行的。
All right. So we have that square root NR.
好,看看这个NR求平方根方法。
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。
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?
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。
Every time you see a square bracket, put a paren in. All right?
每次你看到一个方括弧,你就得在此添加一个圆括弧,明白了吗?
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。
We know it's going around in a circle because if I find the length of this vector, which is the x-square part, plus the y-square part, I just get r square at all times, because sine square plus cosine square is one.
我们之所以知道它做圆周运动,是因为我求出了这个矢量的模长,也就是 x 的平方加上 y 的平方,我就得到了它在任意时刻的模长平方,因为正弦平方加余弦平方始终等于1
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