7 problems

$4n+2$ conjecture. Every periodic trajectory on a triangle tiling has period $4n+2$ for some positive integer $n$.

No-dense-trajectories conjecture. Trajectories on triangle tilings never exhibit dense behavior.

Tree conjecture. Every periodic trajectory on a triangle tiling encloses a tree.

Altitude-subtiling conjecture. Any such tiling contains the altitude; equivalently, it is a subtiling of the 2-tiling defined by the altitude.

The d-matrix identity conjecture. If ${\bf d}$ is $m$ times the identity matrix, then the tiling is quadratic.

Let $ABC$ be a triangle that is $N$-tiled, meaning it is tiled by $N$ congruent triangles. Let the tile have angles $\alpha$ and $\beta$ satisfying … and suppose that $\alpha$ is n…

The problem asks for the positive integers $N$ for which some triangle can be cut into $N$ congruent triangles. Soifer's Problem 6.7 conjecture. The solution should be that $N$ mus…