Why Do Bees Prefer The Perfectly Shaped Hexagons?

Calculus has many different applications in human life, especially as technology is advancing into the world of machine learning and artificial intelligence. Although humans know how to apply mathematical theorems, research shows that even bees apply calculus to improve their lives. Bees are very advanced in the application of math compared to other animals. It was always questioned as to why the bee uses hexagons to produce their honeycombs. Many mathematicians wondered why any random shape would not work, but there are many specific reasons as to why bees prefer the perfectly shaped hexagons. Hexagons are a perfect shape to fill with honey because there are no spaces between the array of shapes, the bees do not want to have to go through
A Mathematician, named Alan Lightman stated, “there are only three geometrical figures with equal sides that can fit together on a flat surface without leaving gaps: equilateral triangles, squares, and hexagons.” (npr.org) Roman Mathematician, Marcus Terentius Varro who was fascinated with bees hypothesized that “a structure built from hexagons is probably a wee bit more compact than a structure built from squares or triangles. A hexagonal honeycomb would have the smallest total perimeter.” (npr.org) Bees also have the same characteristic as humans wanting to save their energy and still attain good results. They want a compact structure, knowing that it requires less wax to create the honeycomb. A bee consumes eight ounces of honey to produce a single ounce of wax, which is why using hexagon are the best structure and most profitable for them. Professor Thomas Hales, during his time at the University of Michigan, proved why Varro’s hypothesis was
It is used to most accurately represent the thinking that bees and others use when searching for food. The theorem focuses on the following factors “What is the optimal “giving up time” (when an organism should leave a patch that it is exploiting) and when should the animal say enough is enough and move on to find the next patch?” (animalbehavioronline.com) Food is easy to collect in the beginning but becomes harder with the factor of time, bees and other species need to figure out the best time to stop exploiting the resource and when to travel elsewhere. The Marginal Value Theorem states that the optimal foraging time is found when the instantaneous rate of accumulation is equal to the average rate of accumulation. This model best represents the thinking process that bees and other foragers use when collecting