It is well known that a circle is exactly circumscribed by six circles of the same diameter and that each circle exactly circumscribes a hexagon whose edge equals the radius of the circle. Why? How can the circumference which is the product of the circle diameter and an irrational number, i.e. PI, accommodate an integral number of circles? I suspect there's an easy explanation but I don't see it. Note that if you draw a circle on the circumference of the center one and then draw additional circles where the arc cuts its circumference you obtain the six pointed "flower" (shown faintly in red). Note also that although the equilateral triangles that make up the hexagons are close packed and the hexagons are close packed like a beehive off diagonal, three circles each share on triangle that's outside. Each circle looks like a six pointed star. If by any chance someone solves this mystery I hope they'll post a comment.
