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On the bees’ hexagonal honeycomb:
“Bees…by virtue of a certain geometrical forethought…know that the hexagon is greater than the square and the triangle and will hold more honey for the same expenditure of material.” -Pappus of Alexandria
It’s good to challenge the students to think and come up with reasons why a hexagonal honeycomb is optimal. Why not squares? Why not circles?
A good lesson when teaching apothem and area of hexagons would be to find the area and perimeter of a portion of a beehive. And then compare to the area and perimeter of a theoretical beehive that’s squarish or circular, and discuss all the wasted space in such beehives.
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