For players!!!! This comment is one big spoiler. Please, don't read it before playing.
---SPOILER---
* - dot is straight below another dot, so yes, we can connect it with just one line
* - dots on ground can be unconnected at all, just use two of them from left and right ends
* - we need three lines to connect dots and make an stable triangle, next dots can be connected to the same triangle to one of his sides, saves one line with every next dot
So here is my algorithm to solve all levels.
1 - Find dots vertically aligned. And connect them with one line. If there exists more vertically aligned dots, connect them too with one additional line (lines amount = dots amount - 1).
2 - Connect two dots on the ground, one from left side and one from right side. Ignore other dots between on the ground, left them unconnected.
3 - Use the line on the ground to build triangles with all other dots. If dots are connected vertically (first step), connect only highest dot.
4 - That's all. But because we have free lines and because of some bug with inertia calculation, connect top dots (or top of triangles) using rest of free lines.