The Mathematics of a Beehive: Why Bees Are Natural Engineers

Hexagons: Why Bees Use This Shape?

Let’s start with why bees choose the hexagon shape for the cells of the hive. It has been mathematically proved that a hexagon is among the most efficient ways to tile any flat plane without gaps and with the least amount of material. This arrangement is also associated with superior strength and durability.

The following are some main reasons why this shape is preferred by the bees.

• Hexagons Leave No Gaps

Squares, equilateral triangles, and regular hexagons are the only shapes that can tile a flat surface without leaving considerable gaps. However, among these shapes, hexagons are the only ones that possess the largest area relative to their perimeter. This leads to the storage of most honey with the least wax and an even spread of forces across the walls of the beehive.

• They Minimize Wax Use

Bees have to consume about 6-8 pounds of raw honey to produce a single pound of wax, which makes it a resource and energy-intensive process. By using hexagon shapes, bees save up to 40% and 30% wax compared to using circular and square-shaped cells.

• High Strength to Weight Ratio

Hexagonal structures give hives a remarkable strength-to-weight ratio. These structures give the hives a stable load distribution, low weight, and high rigidity. This is what imparts these hives an exceptional weight-bearing capacity.

The Natural Engineering Prowess of Honeybees

The following are a few points that underscore the mathematical prowess of honeybees, which indicates why these are nature’s top engineers.

Warm Wax and Collective Behavior: Key Ingredients to Make a Hexagon

Bees do not directly make hexagons. Initially, they create cylindrical wax cells while the material is still pliable and warm. As thousands of bees work together inside the hive, more heat is produced, which further warms up and softens the wax.   

These cylinders press against each other from all sides. The combination of heat flow and surface tension allows the walls to settle down in the shape of hexagons. This way, bees utilize basic physics laws to create these amazing structures.   

The Honeycomb Conjecture: An Age-Old Mystery Finally Resolved

In 36 BC, Marcus Varro, a renowned Roman scholar, came up with the honeybee’s geometry theorem, also known as the honeycomb conjecture. He said that the bees use this shape because a hexagonal grid is the most efficient way to divide any surface into regions of equal area with minimum total perimeter.

This statement was proven in 1999 by a mathematician named Thomas C. Hales. He published a proof which showed that a hexagonal tiling can minimize the boundary length of any given area, which leads to the use of the least total wall material.

Turns out, honey bees realized this truth millions of years ahead of us humans.

 The Mathematical Precision of the Hives

It is also interesting to note that honey bees do not create perfectly vertical hexagonal cells. Instead, they tilt them upward about 13o which prevents the honey from spilling out.

The base of each cell is made of three rhombus panels that meet at angles of 109.47° and 70.53°, which is the same geometry that is seen in molecular structures and crystals. Bees instinctively use this geometry to maximize the strength of the hive without using a lot of material.

The Sun as a Blueprint

Bees use polarized light, sun positioning, and memory-based internal maps for navigation. This data helps them orient combs at very precise vertical angles. Bees also use this information to make key structural elements of the hives, which impart greater strength to them.

Maximum Heat Distribution in Hexagons

The uniform hexagonal shape spreads the heat evenly inside the hive. This temperature stability is essential for the growth and survival of the larvae. This shape minimizes heat loss in the winter and maintains the brood temperature at 34.5,which ensures the safety of both the hive and the colony.

Excellent Wight Bearing Capacity

Bees create hives using hexagons that possess exceptional load-bearing capacities. The structure of the hive can support up to 30x its weight. And not just that, a single hive can contain more than 44 pounds or about 20 kg of bee honey. This superior strength is the result of the intricate craftsmanship and engineering talent of the honey bees.

Visit Geohoney today to learn more about bees and to explore our premium quality, raw, and pure honey varieties that promise the best flavor and health benefits all in one.

FAQs

What is the geometric shape of a beehive?

The geometric shape of a beehive is a hexagon. This shape gives the hive greater strength, storage capacity, and weight-bearing capacity.

How do honey bees use math?

Honey bees can perform addition and subtraction using colors as symbols with minimal training. These creatures can also distinguish between odd and even numbers.

What is the honeycomb theory in math?

This theory states that a regular hexagonal grid gives you the most efficient way to divide a surface into regions that have an equal area and the least total perimeter.

Are honey bees mathematicians? 

Bees are nature’s mathematicians because they can create efficient geometric structures and understand complex concepts like addition, subtraction, and zero.