That a triangle can be divided into 16 similar triangles is not so mysterious (to geometers),Mysterious pattern of "Sweet 16" in circle-squaring right triangle
that can be divided into 16 similar triangles, where 16 = 1 + 3 + 5 + 7
but how does 16 (instead of other increments) relate to this squared circle geometry
Bubble eQ16 shows a meaningful relationship with further emphasis on sqrt(2).
An intriguing geometric clue (re: 16 / 2 = 8 ) ...
A circle and its square connect at 8 symmetric points ... only
Rod