Is a pyramid with Kepler's packing of spheres the densest way to store spheres on the ground, remaining stably stacked under gravity? One wonders if there is a way to make the sides of the pyramid more steep, while keeping the pile nominally stable.
The base layer could be secured in 3 possible ways which will probably affect the answer. The balls could be fixed to the ground, unmovable. The balls could be confined by a rigid fence, but will move around frictionlessly within the fence. The balls could be confined by a flexible band of constant perimeter.
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