The longest path between 2 points is...

The shortest path between 2 points is the length of the straight line connecting the 2 points.

What is the longest path between 2 points?

Well if the two points can be a limitless distance away from each other or if any part of the path can be a limitless distance from either point or if the path can be retraced, then of course the path between the points will also be limitless. So let's eliminate those solutions and ask the question again.

1. The 2 points cannot be really far from each other. In fact let's say the two points can be separated by a maximum of 3 inches.
2. The path you take from one point to the other cannot take you really far away from either point. In fact let's say that no part of the path can be no farther than 3 inches from either point.
3. No part of the path can be used more than once. e.g. You can't retrace any part of the path.
4. Even though it is not a requirement, it makes it easier to visualize if the original 2 points and the entire path are on the same flat surface.

What is the longest path between 2 points under these conditions?

On an 8.5x11 inch piece of paper visualize 2 points 3 inches apart and imagine a very small traveler going from point A to point B.