The fastest and most severe method would be to cut the whole plant down just above ground level.

最快、最严厉的方法是将整个植物砍倒在平以上。

Green, for example, here is the ground plane, I think.

例如，绿色，我认为这里是平。

Then a period of glaciation Locked up lots of Earth's water, which dramatically lowered sea levels.

然后一段冰川期锁住上的大量水分，这极大降低海平。

Before the eyes of the stunned, thrilled audience, photographs came to life and moved across a flat screen.

在那些既感吃惊又兴奋的观众前，图片栩栩如生在平屏幕上移过。

Now Sophie could see exactly where on the plane the marble had rolled because it had left a black line on the board.

现在索菲可以准确看到弹子在平上动的位置，因为它在棋盘上留下一条黑线。

Well, Dan's thought was to refract that light through a glass rod, so that it was relatively evenly spread across an entire plane.

丹的想法是通过玻璃棒折射光线，使其相对均匀分布在整个平上。

The reason triangles are used, and not squares, or polygons, or some other more complex shape is simplicity: three points in space unambiguously define a plane.

使用三角形而不是正方形或其他更复杂的形状的原因是简单性：空间中的三个点唯一一个平。

If we look at the milky way, we can  clearly make out a galactic plane in which the solar system orbits the center every 230 million  years.

如果我们观察银河系，可以清楚看到一个银河平，在这个平上，太阳系每2.3亿年绕中心旋转一周。

You can really see what happens with sea level rise and storm because apart from these planted mangroves and some donated telephone poles keeping the sea back, it's pretty much ruined.

你可以清楚看到海平上升和风暴带来的破坏， 除这些种植的红树林和一些捐赠的电话线杆在阻挡海水外，这片区域几乎已被完全毁坏。

Nevertheless, it's good to peek our heads outside of flatland now and then to, you know, see what it means to apply these ideas in more than just those two dimensions.

尽管如此 我们还是可以时不时跳出平 看看在二维空间之外应用这些思想意味着什么。

If industrial pollutants are capable of heating global temperatures to the point that glaciers begin to melt, it is urgent for us to know precisely how high sea levels will rise as a result.

如果工业污染物能够将全温度加热到冰川开始融化的程度，那么我们迫切需要准确知道海平将因此上升多高。

But part of our goal here is to find a more efficient algorithm that only requires computing the function on as few points as possible; only having limited view of the colors of the plane, so to speak.

但我们的目标之一是找到一个更高效的算法， 只需要在尽可能少的点上计算函数值；换句话说， 只是有限观察平的颜色。