I am going to decompose my surface into very small flat pieces.
我这就要将曲面分解成小平面了。
Concretely what this means is I cut my surface into little pieces.
它的具体含义是，把曲面分割成一个个小块。
ROAD TEXTURE: The only surface I haven't touched yet was the road.
道路纹理：我还没有改变过的表面就剩下道路了。
I need a flat surface to write on.
我需要一个平面在上面写字。
I can then move that instance around the surface of the movie frame by frame.
然后我可以围绕动画框架的表面逐帧移动实例。
Now, above that I will have a parallelogram on my surface.
现在在上方的曲面上，有一个平行四边形。
And actually, I will choose another surface, S2, that maybe looks like that.
实际上，我将选择另一个曲面s2，它看起来应该是这样的。
Well, I claim this curve actually bounds another surface that is orientable.
我断言这条曲线，界定了另一个可定向的曲面。
I take one picture, surface, breathe, and repeat.
我拍下一张图片，就浮出水面、呼吸，如此反复。
Zen Master said: "I am sorry, you only see the surface of the outcome."
禅师说：“我很遗憾，你只看到表面的胜负。”
Let's say that I gave you this curve bounding this surface.
给你这个曲面和这个曲线作为它的边。
I mean when I say up, of course it is still perpendicular to the surface.
当我说向上时，它当然仍是垂直曲面的。
I make my home in water but have to come to the surface to breathe.
我把家安在水中，但不得不游到水面进行呼吸。
So, then I can choose my favorite surface bounded by C.
那么我可以选择一个被C界定的曲面。
Then I want to make my index finger point towardS the surface.
然后让食指指向那个曲面。
And, here's something I think is rumbling beneath the surface of this debate.
而且，我认为有些响声传到了，这次讨论的表面以下。
F I have my surface and I have my vector field f.
有一个曲面，还有一个向量场。
I have a parametric equation for my surface.
有曲面的参数方程。
I want to leave the surface alone.
我不想涉及表面。
I felt it. The surface was hot so I didn't open it.
我摸了下，表面好烫，我打不开。
But I didn't say: "that's not a table; that's a work surface."
但是我没有争辩说：‘那不是桌子；那是工作台面。’
Stokes I can choose my favorite surface whose boundary is this circle.
定理说，What，Stokes’，theorem，says，is，that,可以选择最喜欢的曲面，只要边界是这个圆就可以了。
"I think we've only scratched the surface of emotion in the brain," he says.
“我认为对于大脑中的情绪，我们只是了解了一些皮毛而已。”勒杜说。
I grabbed an empty box and moved everything from my desk surface to the box.
我拿来了一个空箱子，然后把桌面上的所有东西放了进去。
我知道它会再度出现的。
But I see on the surface of your face, I almost know nothing at all of you, suddenly feel what thing?
除了我表面上看到的你的样子，我对你几乎一无所知，突然间觉得这能算回事儿吗？
Above the unit disk means I don't care about this infinite surface.
在单位圆上方意味着，我不关心无穷远处。
This is how I want to describe the surface on which I will be integrating.
这个图像表达式是用来描述积分区域的。
I could see the surface of the moon if I were to go to the moon some day.
要是有一天我上了月球，我就能看看月球的表面是什么样子。
I screamed in pain as the knife cut the surface layer of my skin.
我的皮肤被割开了，我痛苦的嘶叫着。
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