And the prototypical area that we look at is the unit square, resting on I hat and J hat.

我们看到的原型区域是单位正方形 位于I帽和J帽上。

And they do: square the speed, and you end up with units of meters squared per second

四分之一的速度，你会得到 单位是平方米每平方秒。

So what a space-filling curve does is it aims to take up all the area it can within one unit square.

所以空间填充曲线的作用是在一个单位正方形内尽可能占据所有区域。

So even though this transformation smushes things about it seems to leave areas unchanged, at least in the case of that one unit square.

所以即使这个变换把周围的东西都打碎了但它似乎没有改变面积 至少在一个单位正方形的情况下是这样。

Actually, though, if you know how much the area of that one single unit square changes, it can tell you how the area of any possible region in space changes for starters.

实际上 如果你知道一个单位正方形的面积变化了多少 它就可以告诉你空间中任何可能区域的面积是如何变化的。