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And that's going to be valuable to me when I want to get back to using these things, right?
时髦的东西,这代表了它的种类是,笛卡尔坐标？
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And if I go look at the polar form of this, OK, good, looks right, right?
现在它有一个不同的坐标，以及跟原来相同的角度？
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On the vertical axis I'll put two vertical axes in, just for the sake of things on the vertical axis I'll put my expected payoffs.
坐标系的纵轴,由于种种原因,我花了两个纵轴,纵轴表示我的预期收益
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But you agree that there is no reason why somebody else couldn't come along and say, "You know what, I want to use a different set of axes.
但是你们得认识到,没有人会站出来说,"我想要用一套不同的坐标系
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That was Cartesian space. When I plot r as a distance out from the nucleus that is sort of our simple-minded planetary model. Now let's look at energy.
笛卡尔坐标系，当我用r表示,离原子核的距离时，那只是我们头脑中简单的,类似行星的模型，现在我们看一下能量问题。
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And similarly, actually, if we're looking at our polar coordinates here, what we see is it's any place where theta is equal to is what's going to put up on the x-y plane.
类似的，如果我们,看这里的极坐标系，我们能看到只要在theta等于,多少的地方就是ｘｙ平面。
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And so the slope of this thing is f at the triple point, which is this point here, this is the temperature of the triple point of water, f divided by 273.16. That's the slope of that line.
除以x轴的坐标,这就是斜率，而直线,经过原点，因此斜率乘上T就得到。
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If I want to get out right now the versions of these things, I can ask what's the value of c p 1 x, and it returns it back out.
你可以在那里看到那些,代表笛卡尔坐标点的东西，如果我想要得到现在，这个类的版本的东西的话。
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And then I could do things like again, say, okay having done, that let me just run it here, run that, so I've now got polar point 1, and polar point 2.
然后给它们赋值半径和角度，然后我可以进行刚才的操作，也就是说，对刚才的笛卡尔坐标进行的操作，让我们来运行下它吧，运行下，现在我有一个极坐标点。
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That's the picture we just had, except I've changed the numbers a bit.
除了坐标变了,其它的和以前一样
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The equation for the y coordinate is the height of the building.
坐标的方程是楼的高度
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And then from that start point, get the x-value. Same thing, from that instance, get the endpoint, from that end point get the x-value, square.
取得结束点，然后取得结束点的y坐标，然后求差开平方，然后同样求的y坐标。
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What I want to do is I want to draw a picture here, in which on the horizontal axis, I'm going to put the probability of the other guy choosing Right.
我要在这里画一张图,坐标系的横轴,表示对手选右的概率
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And so I'm going to go back to this idea of a class, and let's build the first of these, and that is shown right here on this piece of your handout.
你把半径加到一起,你不会把角度加到一起，你需要再笛卡尔坐标下，进行这个操作,那么我这里在讲的就是。
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Well you know what a point is, it's got an x- and a y- coordinate, it's natural to think about those two things as belonging as a single entity.
把这两个坐标认为，是属于一个独立的实体，是理所当然的事情,因此实现这个目的的。
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And so this doesn't know how to do it, it doesn't have a method to deal with it, so it complains.
因为，我原来是期望做什么来着？,我原来是要对x坐标，和y坐标进行对比的。
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How do the components of A in the new rotated coordinate system relate to the components of the old coordinate system?
在旋转后的新坐标系中 A 的分量,和原始坐标系中 A 的分量有什么关联呢
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Right, and just to get a sense of this, let's look at a simple little example, so on your hand-out, you'll see I've got a little piece of code that says assuming I've got one of these points, I want to do things with it, for example I might want to add them together.
这些数组中的一个，你怎么能够知道，它是哪种类型的呢？,你怎么知道它是以笛卡尔坐标,表示的还是以极坐标,形式表示的呢？,你没有可以用来区分的东西，你没有说明这种信息,聚集实际上的意义。
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It says if I want to get the length of a segment, going to pass in that instance, it says from that instance, get the start point, that's the thing I just found.
它的意思是如果我想要,得到一个线段的长度，首先要把这个实例传进来，然后对于这个实例，从开始点，取得x坐标，然后通过同样的操作。
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OK, for example, I might say point p1 is that list, x is 1, y is 2.
和y坐标的数组是很简单的1,那么，例如，我可能会说点。
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And I originally decided I was going to have as points, it's going to have internal values of an x and a y.
写了一堆代码,然后我以开始决定，是要把值放到点里面的,点有内部的x坐标和y坐标。
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It's easy to think of a point as just a list of an x- and a y- coordinate.
或者说有两个元素的数组,把一个点认为是含有x坐标。
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And I'll give it an x value of 3 3 and a y value of 4.
一个笛卡尔坐标3,然后给p2的x坐标赋值为。
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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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So I don't know don't, John, I would argue if I'd written this better, I would have had a method that returned the x- and the y- value, and it would be cleaner to go after it that way.
我会去辩论这么写是不是更好，我也可以写一个，返回x坐标和y坐标的方法,这么做可能会更清楚一点，这是很棒的缩写，好。
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You've got to be very used to the notion of taking a vector in some oblique direction and writing it in terms of i and j.
你们应该已经很熟悉,倾斜的坐标系中矢量的概念,和用 i 和 j 来表示该矢量的方法
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At that time t, the x coordinate must have a certain value.
在该时刻,x 坐标一定是个确定的值
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The way we read this graph, is you give me an S2, I read across to the pink line and drop down, and that tells me the best response for Player I.
这个图的作用是,给定一个S2,找到粉线对应的坐标,然后就能找出参与人I的最佳对策
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So x is not really the coordinate of the end point.
其实并不是弹簧端点的坐标
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The components come in the minute you pick your axis.
但它的分量由你所选择的坐标系确定
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