Then next week we'll do more complicated problems that involve motion in higher dimensions, how to go to two dimensions or three dimensions.
下周我们将会处理更复杂的问题,包括更高维数的物体运动,如何处理二维以及三维运动
If you live in two dimensions or more, you've got to use vectors to describe most things.
如果你要考虑二维或二维以上的问题,大多数情况下需要用矢量来描述
So here's the example I'm going to start with.
做二维几何的程序,关于平面上的点。
In fact, I'm going to use only two dimensions for most of the time because the difference between one dimension and two is very great.
实际上,大多数时候我只考虑二维的情况,因为一维和二维的差别很大
Between two and three and four and so on is not very different.
但二维,三维和四维,以及其它维数间的差别就不那么大了
So, when you go to two dimensions, you need a pair of numbers.
因此在二维空间里,你需要一对数字来描述
I picked for it two dimensions as the standard way to explain it.
我选取二维的情形作为标准模型来讨论
But this is the way to do it in two dimensions.
但这也是在二维空间里的方法
But, you know, in 2D, the options are not just left and right or north and south, but infinity of possible directions in which I could go those 5 km.
但在二维空间中,不仅可以向左向右或者向南向北,我在走那5公里的时候可以有无数个方向
That's the problem in two dimensions.
那是二维中的问题
We're going to do two.
接下来我们讲二维运动
We'll stop at two.
我们先考虑二维
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