Off-road with the bead box

Today AV received a new lesson on cross multiplication.  It involved an improvised checkerboard and a box of beads.  The lesson itself was unremarkable.  What happened afterward was so remarkable.

I called JV over for a lesson and AV was fooling around with the beads instead of putting them away.  I sat to give him the hint:  “Clean your stuff up.  I have important lessons to give.”  JV by now was enticed by the beads.  He began to build a bead triangle.  AV was building a circle with the 10 bars.  I at least had the presence to pause to watch before launching into a clean-up rant.

Here is what ensued.

Dashed prediction that the decagon would meet in the middle.
Why does it work more perfectly with 7?
Logic says this should work
"Yes!" It stayed up until a split second after the shutter closed.