- Pack N congruent discs into a shape. Maximize disc area.
- Cover a shape with N overlapping congruent discs. Minimize disc area. Previously, constellations.
- Divide a shape into N regions of equal area, minimizing perimeter.
- 3D and higher dimensions.
On a curved manifold, a circle or disc is defined by a center and distance function.
Inspirations: "Partitions of Minimal Length on Manifolds" (Beniamin Bogosel and Edouard Oudet), "The minimal perimeter for N confined deformable bubbles of equal area" (S.J. Cox and E. Flikkema)
The perimeter-minimizing equal-area partition of the surface of a sphere for a given N would be nice as a physical model, though it would take some thought to 3D print because 3D printers typically don't do colors. Surface of a cube or box is easier: just glue pre-printed paper illustrating the partitions onto the faces.
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