... starts with a small circle in the center of the large circle.
The above picture shows a program I wrote to actually draw the circles out. But you can see that this method does not yield maximum number of blue circles. There are still spaces around the red circle.
The method i used is to draw blue circle "rings" starting from the center outwards. i.e move out in the blue arrow direction for one circle diameter, then go around in the red arrow direction, then repeat next ring in the blue arrow direction.
Anyone can share a smarter method? Thank you all. I need only to calculate the number, but if there is a systematic way to draw will be better.