April 1, 2021

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This article was originally published as a chapter in the book “Design and Catastrophe: 51 Scientists Explore Evidence in Nature"

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Pappus of Alexandria (290–350 AD) was the last of the great Greek geometers. He is best known for his Synagoge, which is a voluminous collection of the most significant work done in ancient Greek mathematics. To him are attributed the following words that certainly frame the subject here exposed: “Bees … by a 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.”[1]

Tessellations, or tilings, are a collection of polygons that fill the plane with no overlaps or gaps. There are regular tessellations, those that use identical regular polygons to fill the plane, and semiregular tessellations that use two or more regular polygons, each with the same side length. There are only three regular polygons that can be used to tessellate the plane to form a regular tessellation: the equilateral triangle, the square, and the hexagon. This is possible because of the angle measures of these polygons. The angle around each vertex in a tessellation must be 360 degrees. Therefore, the interior angle degree of a regular polygon should divide into 360 evenly. The interior angles of the equilateral triangle, the square, and the hexagon are 60, 90, and 120, respectively, which fulfills the requirement. These are the only regular polygons with this property.

We share the planet with bees and appreciate these wonderful insects for their significant role in pollination and the production of honey and beeswax, among other things. However, when it comes to abstract thinking, bees are not known for formalizing theorems or writing manuals.

Clearly, bees have not studied the geometrical intricacies of tessellation theory or the principles of optimal construction design. Nevertheless, some of their behavior patterns when building a hive can be explained mathematically from the perspective of tessellation theory and optimal housing design. One such behavior that makes me think about God as the Creator and Universal Designer is the innate ability of bees to use the least expenditure of energy and materials.

Although the bees are surely unaware of the geometrical intricacies of tessellation theory, they were created with the ability to use the optimal design for their honeycombs. It can be mathematically demonstrated that of the three polygons, the hexagon has the smallest perimeter for a given area.[2] So, when bees are constructing hexagonal prism cells in the hive, they use less wax and do less work to enclose the same space than if tessellating space with prisms of square or triangular bases.[3] The honeycomb walls are made up of cells that are thirty-two hundredths centimeter thick, yet they can support 30 times their own weight.[4] The bees create hexagonal prisms in three rhombic sections, and the walls of the cell meet at exactly 120-degree angles.[5] What is truly remarkable is that bees work simultaneously on different sections of the honeycomb, which shows by their behavior a strong feeling of collectivity, communication, and unity of purpose throughout the hive.

I think God shows Himself in several ways in our universe, both in the animate and inanimate world. Particularly, through bees’ behavior when building their honeycombs, we can think of God as an artist who loves order and beauty, since honeycombs are highly ordered and aesthetic structures. Beyond that, we can also ponder God as the mastermind who not only created bees as wonderful insects but also created us as His masterpiece. As such, we are called to observe critically our surroundings and understand how things work and how things are in the natural world. This understanding should eventually lead us to the acceptance of God as our Creator and Universal Designer.

NOTES

[1] Cited in CB Boyer, U Merzbach. A history of mathematics. 3rd ed. Hoboken (NJ): Wiley; 2011, p. 142.

[2] F Morgan. The hexagonal honeycomb conjecture. Transactions of the American Mathematical Society 1999; 351(5):1753–1763.

[3] J Nickel. Mathematics: is God silent? Vallecito (CA): Ross House; 2001.

[4] LF Deborah. Hidden mysteries of the honeybee. Maitland (FL): Xulon; 2009. 5.

[5] AFI Bajunid, MY Abbas, AH Nawawi. Tessellating “honeycombs.” WIT Transactions on Ecology and the Environment 2016; 148(June):141–152. doi:10.2495/RAV110141.

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Luciano González is director of the Geoscience Research Institute branch office in the Interamerican Division and is a professor of mathematics, physics, and science and religion at Montemorelos University. He holds a PhD in Earth Science from Loma Linda University. His current research focuses on stable isotopes and heat flow in magmatic rocks of the American Cordillera. His educational outreach includes authoring the book Curso Introductorio de Álgebra Lineal; writing articles such as Divine Geometry in Nature, published in College and University Dialogue; and working on launching the video series Punto Geo, with the goal of diffusion through social media of geology, physics, cosmology, and other sciences from a creationist perspective. University Dialogue; and working on launching the video series PuntoGeo, with the goal of diffusion through social media of geology, physics, cosmology, and other sciences from a creationist perspective.