You need to get new friends, Pierce.

交新朋友了 皮尔斯。

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

船位置距参照线交400米。

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

我姥姥，我教授——们人交是谁呢？

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

因为月球轨道与太阳平面交有，称为交。

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

它是边际成本和需求曲线交。

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

因此，实际上，每交又添加了条边。

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

学生：使交相等，方程式相等并求解。

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

现在考虑一下月球交对这场潮汐拉锯战影响。

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

计算图中交数量有棘手。

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

没有其他选择交可以保证在五分钟内到所有机器蚂蚁。

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

然而，太阳和月亮从来没有比它们在交处更对齐。

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

当我这样做时，相关交实际上位于三角形外部。

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

但关键是将其视为一新图，其中这些交是顶。

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

例如，看看这简单图表，其中有三条线和交。

Every intersection point corresponds  with some quadruplet of points.

每交都对应于一些四组。

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

因此，这里顶总数不是 N，而是 N 加 N 选择四交。

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

分析表明，月球交周期峰值与红树林树冠覆盖时间一致。

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.

船位置是参照线A和B交处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交，我们会找到该是否位于每相应三角形内。

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数量，因为每交都来自不同和弦。