History

This section gives a brief history of the study of dense sphere packings. Further details appear at [43] and [20]. The early history of sphere packings is concerned with the face-centered cubic (FCC) packing, a familiar pyramid arrangement of congruent balls used to stack cannonballs at war memorials and oranges at fruit stands (Figure 1.1).

Sanskrit sources

The study of the mathematical properties of the FCC packing can be traced to a Sanskrit work (the Āryabhaṭīya of Āryabhaṭa) composed around 499 CE. The following passage gives the formula for the number of balls in a pyramid pile with triangular base as a function of the number of balls along an edge of the pyramid [40].

In modern notation, the passage gives two formulas for the number of balls in a pyramid with n balls along an edge (Figure 1.2):

Harriot and Kepler

The modern mathematical study of spheres and their close packings can be traced to Harriot. His work – unpublished, unedited, and largely undated – shows a preoccupation with sphere packings. He seems to have first taken an interest in packings at the prompting of Sir Walter Raleigh.