Fiddler on the Proof: Fiddler (06/14/2024)

fiddler_20240614.md

Fiddler on the Proof

Ravi Dayabhai 🔵 2024-06-14

Problem

You want to pack four rows of unit circles into a rectangle with a base of 8. You’re considering two strategies for packing:

Square packing. In this case, four rows of circles each are packed in an array of squares.

Hexagonal packing. In this case, the bottom row has four circles, and higher rows alternate between having three and four circles.

Solution

Hexagonal packing is more efficient.

Rationale

(See comment below.)

Correction: The opposite conclusion should be drawn since there is a simplification error in the above!