That move along the unit circle to the diagonal, and then I move back to the origin in a straight line.
然后沿单位圆的圆弧走到对角线处，接着这直线回到原点。
Instead of just somewhere,maybe I will have the origin,and I am trying to make it go around the origin in a circle at a certain angular velocity.
特别地，取原点,让物体以一定的角速度，围绕原点旋转。
I want to major in biology because I have long wondered about the origin of life.
我想要主修生物学，因为我一直在思考生命的起源。
What I do find interesting is the origin of the universe, the shape of space-time and the nature of black holes.
我真正感兴趣的是宇宙的起源、时空的形状和黑洞的性质。
Hopefully, you can see that if I take a normal vector to the sphere it is actually pointing radially out away from the origin.
我希望大家能够了解，如果我将法向量平移至球面，那么它将以原点为心向外放射。
When I draft business letters, when I want to further understand foreign cultures deeply, when I explore the origin of English, I will hold these treasures delightfully.
每当草拟商务信函时，每当想了解异国文化时，每当要了解英语的起源时，我都会捧起这些心爱的宝贝们。
The other option, which is the one I will choose, is to change the coordinate so that this point become the origin.
另一种选择，也就是我要选的那种，是转换坐标系，让这个点变成原点。
I submit to you that there are ways of defining an origin other than geography.
除了地理国家，还有其他方式可以界定起源。
I actually had a little bit to do with the origin of the notion of the signifying monkey; I'll come back to that later.
事实上我跟“意指的猴子“这个概念,有一点渊源，这个等会儿再讲。
Well, , see, that is a vector field that is equal to the vector from the origin to the point where I am, so it is pointing radially away from the origin.
也就是，这个向量场等价于,从原点指向给定位置的向量，所以它是以原点为心向外辐射的。
So, and similarly, if I take any other loop that avoids the origin, I can find, actually, a surface bounded by it that does not pass through the origin.
类似的，对于任何不经过原点的环路，都能找到一个以之为界的曲面，该曲面不经过原点。
If I move along this closed curve, I start at the origin.
沿这条闭曲线，从原点出发。
The picture, if I really wanted to draw a picture, would be everywhere it is a field that points towards the origin. And if I am further away then it gets smaller.
那么在我画的这幅图中,充满了方向指向原点的向量场,离原点越远，它就越小。
Can I find a surface that's bounded by this loop and that does not pass through the origin?
能找到一个以该环路为界，且不经过原点的曲面吗？
So, for example, let's say that I have a region that's the entire space with the origin removed.
比如说,有一个去掉原点的全空间。
Let's say that I gave you a sphere of radius a centered at the origin, or maybe just half of that sphere or some portion of it.
已知以原点为心，以a为半径的球面，也可以说是半球面或是球面的一部分。
r No matter which direction I go from the origin, r=a if I fixed it,r goes from zero to r equals a.
,无论从原点沿着哪个方向走，只要固定方向，r就是从0开始到。
Let's say that I want to go along this path from the origin, first along the X-axis to and then vertically to.
我想从原点开始沿着这条路径，首先沿x轴到，再垂直到。
I asked about the origin of his sorcery, but got little of importance, except that he had learned it from his father.
我问他的法术从何而来，但他的回答不过是敷衍，我只能知道他是从父亲那儿学到了这一手。
I've sort of done what I wanted, I kind of I think I have an answer now, which is 500 steps, it should be 4.5 units away from the origin.
某种意义上我完成了我想要的操作，我觉得我现在获得了答案，这个答案就是500步，它应该是离初始点4，5个单位。
After careful thought, I concluded four things that constitute the origin of fear.
经过思考我认为有四样东西是恐惧，害怕的根源。
Nowadays, though I seldom visit doctors, when I do, I ask for concoctions of traditional Chinese medicine that is vegan in origin.
如今，虽然我很少去看医生，但只要我去，我就会要求吃中药，而那就是传统意义上的素食主义。
Nowadays, though I seldom visit doctors, when I do, I ask for concoctions of traditional Chinese medicine that is vegan in origin.
如今，虽然我很少去看医生，但只要我去，我就会要求吃中药，而那就是传统意义上的素食主义。
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