You have a 4 m × 4 m garden bed. Tomato plants need 50 cm of space. How many can you fit in rows? In a hexagonal pack?
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Square grid
Each plant takes a 0.5 × 0.5 cell. 4 m / 0.5 = 8 per side. 8 × 8 = 64 plants.
Try it
Hexagonal pack
Rows offset by 0.25 m. Each row still has 8 plants but rows are 0.43 m apart. ~9 rows. About 72 plants — 12% more produce.
Bees and oranges pack hexagonally for the same reason: it's the densest possible arrangement of equal circles in a plane.