Question 5

By Krista Floer

Anything special about the path if he starts at the centroid?

I found that if Barney starts at the centroid, then the path formed is the same path as the path when Barney starts at a trisection point.

Path starting at Centroid |
Path starting at Trisection Point |

We can see that the paths would be the same if we think about some properties of the centroid. The centroid is the balance point of the triangle. In the picture on the right, each part of Barney's path is divided exactly in half by g. All segments offset each other, so we can say it is balanced. So logically, the path starting from the centroid has to be the same as the path starting from the trisection point.