As part of sudoroom Art Murmur in August 2012, I decided to bring circle packing to the masses.
Here's how I structured the game, and how you could build from it.
Equipment:
- The game pieces consisted of 3 sizes of circles at 2.5cm 5cm and 8cm radii.
- I was experimenting with the right point attribution for each. As shown the point values are 1, 3, and 8 respectively.
- The maps were drawn by Anca Mosoiu of TechLiminal, and included the standard square, the African continent, and a silhouette of a meditating Buddha (pictured).
Rules:
- Participants compete head-to-head,
- and are given 30-seconds,
- to lay down non-overlapping circles,
- within the drawn boundary.
- The competitor with the most points on the board at the end of the time wins.
Results:
- I tried to make the optimal strategy counter-intuitive which was to use the smallest pieces only. The ratio of points as I mentioned is: 1, 3, 8. If you calculate the ratio of area for each circle and normalize to the smallest circle you have ratios: 1, 4, 10.24.
- If we divide these ratios. we receive 1, .75, .78125 which approximate the decreasing return that I wanted to achieve.
- Children were competitive with adults. One child whose age meant that he could not spell his own name, showed fantastic geometric reasoning and opted for the mostly 1's strategy. Yet surprisingly only one competitor realized that all-1's not only gave the best points per area, but were also the easiest to pack.
Next steps:
Create a new set of circles in which whose points per area ratios are increasing rather than decreasing, and give contestants more time 1 minute perhaps? What would you change?
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