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If it's in polar form I passed in a radius and angle and I'll compute what the x- and y- value is.
以及半径和角度,但是现在是这样的,不管我是以哪种形式。
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OK, as I said, I want equality in the case of points to be, are the x- and y- coordinates the same?
好，正如我所说，我想要这个例子中的，点相等的意思是？
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It might turn out if I had X-ray vision that what I see is this... Then the answer'd be there's not one train here.
有可能是,我看到的是这样。,答案就不是同一辆火车。
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I think it becomes 30 degrees for the freezing of water and 22.5 x 4, which I don't know what it is, 90 100 or something -- no, it's 90 I think.
我想水的冰点,应该变成了30度,22。5，4，我不知道是多少，大概100左右--不，我想是。
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It's like I've got ESP or I'm some character out of the X-Men, Is that what it's called? The X-Men right?
好像我有超能力或者我是X-Men,是叫X-Men吧
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x 4 x 4--possibilities, because I could have here, here, , , - 4 x 4 = 16.
x4x4种可能性,因为这有AGCU四种,这也是四种,4x4=16.
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- The fact that I've called it X, is really just a programming -- it's a feature of the programming language that I, the human, can now refer to it.
事实是我叫它为X，它实际上只是一个程序-,它是程序的一个特写，我们可以参考使用它。
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Then, I gave you one other very important example of a particle moving in the x-y plane.
下面我再拿一个重要的例子,质点在 x-y 平面内的运动
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Funny story, I met him because at MIT they signed us all up for chest x-rays alphabetically-- that's the way MIT does things, an orderly way.
有趣的是,我在MIT遇到他是因为,我们按姓氏字母顺序,排队去照胸透,MIT做事总是用这种有条理的方式
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Take many of you through graduation When you leave Yale, what do you want--like, "I had X sexual partners, " and that's what I wanted" ? Or your lifetime?
如果你们多数都毕业了,当你们离开耶鲁时想要什么，诸如，“我有过X个性伴侣，那就是我想要的“,在你这一生呢？
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Another way to represent a point in a plane is I've got a radius and I've got an angle from the x-axis, right, and that's a standard thing you might do.
平面上面的点的方法,也就是极坐标,上面那种方法其实是，如果你们喜欢我这么说的话,笛卡尔坐标表示法。
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Right now it's a simple template, but it's a template for creating what a class looks like, and I now have an x- and y- value associated with each instance of this.
那么大家明白了为什么，我说类是一个模板了，对不对？,现在它只是一个简单的模板，但是它是一个用来-,创建形成一个类的模板。
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I was expecting to compare x- and y- values, not radius and angle.
噢，发生了什么？,好吧有错误了。
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OK? And in fact, if you look at the code up here, and it's on your handout, the very first one, x 1, right here- if I could ask you to look at it-- is a piece of code to do it. And I'm less interested in the code than how we're going to analyze it, but let's look at it for a second.
实际上，如果你看看,你们课堂发的材料上面的代码，第一页上的，就是那-,大家请看看实现的这一部分代码,我不太关心,我们会怎么解释这个代码,首先让我们先看看。
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And so this time when you hand it back, this value, I store it in -- we'll say X, and now we actually have retained the value.
这次当你拿回这个值时，我把它存储在X中，现在我们把这个值保存了。
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How do I posit-- why do I believe in x-rays, even though I don't see them?
我如何证实,我为什么会相信X射线是存在的,尽管我压根看不见它
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0 This time I called it X. I hard-coded into it the value 10.
这一次我声明它为X，我把它赋值为。
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Even if I was that guy in the X-Men or the Matrix or whatever it was, who could reason his way into making people do things.
就算我是X-Men或者尼奥,我能影响到别人的推理
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I'm plotting--this is the probability of various values of x/n.
这里是x/n等于各个值的概率
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So this first little piece of code right here says, ok you give me 2 points, I'll create another 1 of these lists and I'll simply take the x, sorry I shouldn't say x, I'm going to assume it's the x, the x-values are the two points, add them together, just right there, the y-values, add them together and return that list.
好，为了来认识到这一点,让我们来看一个简单的小例子，在你们的课堂手册上，你可以看到我写了一个小程序,它假设我得到了，这些点中的一些，我想对它们做一些操作，例如我想把它们加到一起，那么这里的第一小片，代码的意思是，好给我两个点，我会再创建一个数组。
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It says, if I want to print out something I built in Cartesian form up here, says, again, I'm going to pass it in a pointer to the instance, that self thing, and then I'm going to return a string that I combine together with an open self and close paren, a comma in the middle, and getting the x-value and the y-value and converting them into strings before I put the whole thing together.
这不仅仅是个列表,它是怎么来做的？,流程是：如果我想要返回,一些已经在笛卡尔模式下建好的值，好，再说一遍，我首先要传入一个,指向实例的指针,也就是，然后我会返回一个,由开括号，闭括号,中间的一个逗号,以及提前转换为字符串格式的。
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I'm taking advantage of the fact that start is going to be a point, and I'm just directly saying, John give me your x-value.
我利用了开始是一个点这个事实,然后我就直接说，返回给我你的x值，因此我不知道。
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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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And keep going, until the square of one of those integers is greater than or equal to - sorry, just greater than x. OK, why am I doing that? When I get greater than x, I've gone past the place where I want to be.
如果还是比x小的话，跳到3，这么继续下去,直到一个整数的平方大于或者等于,对不起，是大于x，好,为什么我要这么做呢？,让我得到的整数的平方和。
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The idea is that for any amount of money-- if this x is the amount of money that I receive-- utility as the function of the amount of money I receive is downwardly-concave.
这种观点是对于任何数量的货币,假设我得到x数量的货币,随着货币的增加,边际效用呈,向下凹进去的曲线
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Pardon? I could square x but maybe I should just do something pretty simple here. Suppose-- whoops.
对不起我没听清，我可以求x的平方,但是好像这里我做点简单的,改动就可以解决问题了。
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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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All right, we're-- well actually, I should say that better, we first check to see, is x 0 greater than or equal to zero, if it's not, then we come down here and we print something out, otherwise we run through a little loop to get the answer, and then we check it and we spit something out.
然后我们运行一个小循环,好了，我们现在来看看,如果x≥0或者x＜,我们看这儿,我们会输出一些内容,或者我们运行一个小循环来获取答案,然后我们检验一下，然后得到结果。
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You cannot answer that, even if I promised to move only along the x-axis, because I think...I don't want to pose this as a question, because I think the answer is fairly obvious to everybody.
即使我保证只在 x 轴上移动,你们仍然无法回答,因为我觉得...我不想将其作为一个问题,因为我认为答案是显而易见的
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