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
it again after tirelessly building their home to fill in the spaces. Bees work together to create their hive and by only having to create hexagons they work together and follow the same pattern.
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
correct. He created the Hexagonal Honeycomb Conjecture, and stated that “regular hexagons provide the least-perimeter way to enclose infinitely many unit areas in the plane, hexagons are isoperimetric and are easy to replicate.” (maa.org) The reason behind why bees build their honeycombs using hexagons is amazing, they can minimize their use of honey and yet create a compact and sturdy structure. Charles Darwin described honeycombs as “a masterpiece of engineering which is absolutely perfect in economizing labor and wax.” (npr.org)
Bees are even more complex and creative than just their hives, the forager bee has the responsibility to go and discover a source of flowers with a good amount of nectar. From there it will return to its hive and inform the others of the place it found the flowers. Forager bees describe the location of the flower source by using a complicated process. First, it comes into the center of the hive and allows the other bees to try the small amount of nectar it collected from the flowers to see if its quality is enough to make the trip. Then this fascinating creature uses a dance known as the waggle to direct the other bees to the location. The forager shakes its body and by doing so it gives the other bees the necessary information to successfully reach the nectar. The bee uses vector calculus to optimally position itself in the three-dimensional world to the angle in which the food is located. Bees have a powerful sense of navigation with an almost inbuilt compass relative to the sun’s position. If the bee dances in a straight line towards the upper part of the hive, it indicates that the food is in the direction of the sun. The bee dancing towards the right indicates that the flower’s source is exactly 90 degrees. Bees have a good sense of location in the three-dimensional world by calculating the exact position of the traveling sun. Forager bees give directions every four minutes when the angle of the sun changes exactly by one degree to the west. This millisecond calculation has allowed bees to never lose their way. These intelligent bees even inform the others the distance from the flowers. The duration of dance and number of vibrations allow the forager bee to transmit this exact distance to the others. This one bee uses complex mathematics to communicate with the others and never makes any mistakes. To illustrate the intricate process and thinking required by foraging animals like bees and other, the Marginal Value Theorem was created.
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
food.
Whether it is in how they build their habitats, find the exact position of their food, or know when it is an optimal time to move to the next location bees are using complex math calculations. The reasoning behind the hexagonal hives, the use of waggle dance that uses vector calculus and physics, and the Marginal Value Theorem to know when it is time to move to another location in search of food is fascinating. It demonstrates the complexity and hard work a bee does to make sure that itself and its fellow bees are well-taken care of. Bees are very intelligent and are always alert knowing their next plan of action. Although they may look and sound scary on the outside their advanced thinking, behavior, and mathematical reasoning are like or even superior to that of humans.