Measurement Sample

What is the largest number identical spheres that can be packed into a fixed space?

The densest known packing of spheres found is 0.7405. It remains an open question as to whether this really is the densest packing. No proof of this result has been accepted.

Extensions

Kissing Numbers

In two-dimensions, the sphere packing problem involves packing circles. This problem can be modeled with coins or plastic disks and is solvable by high school students.

An analogous problem asks how many circles can you pack around another circle. The answer is called the "kissing number" ("kiss" as in the billiard's sense). The kissing number for circles is 6. What is it for spheres? The kissing number for four-dimensional spheres is an unsolved problem. It is known to be either 24 or 25.