You need to get new friends, Pierce.

你得交点新朋友了 皮尔斯。

My meemaw, my professor — who's in the middle of that Venn diagram?

我的姥姥，我的教授——你们两个人的交点是谁呢？

16.your position distance 400 metres from intersection of reference line.

你船的位置距参照线交点400米。

Because there are two points where the moon’s orbit crosses the sun’s plane, called nodes.

因轨道与太阳平面的交点有两点，称交点。

So, in effect,   each intersection point adds two more edges.

因此，实际上，每个交点又添加了两条边。

Set the intersection points equal, the equations equal to each other and solve.

学生：使交点相等，方程式相等并解。

It's where marginal--it's where the marginal cost and the demand curve intersects.

它是边际成本和线的交点。

So now consider the influence of lunar nodes  on this tidal tug of war.

现在考虑一下交点对这场潮汐拉锯战的影响。

No other choice of two intersection points is guaranteed to get all the robo-ants within five minutes.

没有其他选择的两个交点可以保证在五分钟内得到所有的机器蚂蚁。

However, the Sun and Moon are never more  aligned than they are at a node.

然而，太阳和亮从来没有比它们在交点处更对齐。

When I do that the relevant intersection  point actually sits outside of the triangle.

当我这样做时，相关的交点实际上位于三角形的外部。

But the key is to treat this as a new graph  where those intersection points are them vertices.

但关键是将其视一个新图，其中这些交点是顶点。

For example, look at this simple diagram where  we have three lines and two intersection points.

例如，看看这个简单的图表，其中有三条线和两个交点。

Counting the number of intersection points in  the diagram is a little bit trickier.

计算图中交点的数量有点棘手。

So the total number of vertices here  would not be N but N plus N choose four total intersection points.

因此，这里的顶点总数不是 N，而是 N 加 N 选择四个交点。

Every intersection point corresponds  with some quadruplet of points.

每个交点都对应于一些四组点。

The analysis showed that  the peaks of the lunar nodal cycle coincided with the cover of the mangrove canopy.

分析表明，交点周期的峰值与红树林树冠的覆盖时间一致。

17.your position distance 500 metres from intersection of reference line A and reference line B and distance 700 metres to port side of reference line C.

你船的位置是参照线A和B交点处500米，在距参照线C左侧700米。

Now that we have a set of intersection  points on separate planes, we find whether the point is inside each corresponding triangle.

现在我们有了一组位于不同平面上的交点，我们会找到该点是否位于每个相应的三角形内。

One idea might be that it should be the number of pairs  of chords since every intersection point comes from two different chords.

一种想法可能是它应该是和弦对的数量，因每个交点都来自两个不同的和弦。