So what would the inscribed shape look like if the smaller circle had a radius of 1 unit instead of 2 (one sixth the size vs one third)? I suppose a hexagonal shape with arcs for sides?
Yes. Did you ever see the Spirograph toy? That worked the same way, but the holes for the pen were at different distances inside the smaller circle, and the circles had teeth like gears. There were different sizes of wheels so you could make a lot of different patterns.
So what would the inscribed shape look like if the smaller circle had a radius of 1 unit instead of 2 (one sixth the size vs one third)? I suppose a hexagonal shape with arcs for sides?
Yes. Did you ever see the Spirograph toy? That worked the same way, but the holes for the pen were at different distances inside the smaller circle, and the circles had teeth like gears. There were different sizes of wheels so you could make a lot of different patterns.
This animation was on my mind today because I was looking for a Spirograph for my daughter.