Bee Geometry

This exercise is a part of Educator Guide: Geometric Hives and Renewable Energy Sources / View Guide
A photo of several bees sitting on top of a honey comb structure.
The nests of honeybees (one shown) consist of mostly hexagonal cells made from wax, but pairs of five-and seven-sided cells help fit together hexagons of different sizes.Todd Huffman/Wikimedia Commons (CC BY 2.0)

Directions for teachers:
To engage students before reading the article, have them answer the “Before Reading” questions as a warmup in class or for homework. Then, ask students to read the online Science News article “How geometry solves architectural problems for bees and wasps” and have them answer the “During Reading” questions. As an optional extension for curricular ties to convergent evolution and literary devices, have students discuss the “After Reading” questions. A version of the article, “How geometry solves architectural problems for bees and wasps,” appears in the August 12 print issue of Science News. Another version of the same article written at a lower reading level byScience News Explores is also available, “Bees and wasps devised the same clever math trick to build their nests.”

Directions for students:
Read the online Science News article “How geometry solves architectural problems for bees and wasps” and answer the following questions as directed by your teacher.

Before Reading
1. Using straight lines, sketch the shapes and partitioning that come to mind when you imagine a “honeycomb.” What do you think the purpose is of these partitions for insects?

Answers will vary. A honeycomb comprises numerous identical smaller shapes (hexagons, if you want to be specific). From above they appear to be organized in a tile-like pattern. A honeycomb’s hexagons provide storage spaces for bees, wasps and other similar nest-building species.

2. Imagine you are installing a new tile floor in your kitchen. When the tiles arrive, you realize they are the same shape but are two different sizes. Why will having two differently sized tiles make the tiling process harder than if the tiles were all the same size? Add to your sketch from the first question to create an example of the tiling problem described.

Answers will vary. Differently sized tiles will have sides of unequal lengths. Therefore, mismatched tiles will not come together in a continuous pattern the way they would have if the tiles were identical.

During Reading

1. As bee and wasp colonies grow, what problem must they address regarding their nests? Why do bees and wasp colonies face this problem?

As colonies grow, bees and wasps must increase the size of the hexagons cells making up their nests. When the colony reaches the point where it focuses more on raising reproductive-focused individuals rather than workers, the colony often needs larger cells.    

2. Why do bees and wasps use occasional five-sided and seven-sided cells in their nest-building?

Five-sided and seven-sided cells can bridge the gap between hexagon cells for workers in the colony and the larger bees or wasps that take part in reproduction.

3. From what material do honeybees construct their hexagonal cells? From what material do wasps construct their cells?

Honeybees construct their cells from wax. Wasps construct theirs from paper.

4. How many species of bees and wasps did Michael Smith and his team study?

Michael Smith and his team studied five species of honeybee, four species of Vespula wasp and one species of paper wasp.

5. What two types of data did scientists extract from nest images using image analysis tools? (Answer if you can: Are these measurements considered dependent variables or independent variables in the study? Why do they fit in that category.)

Researchers extracted data about the length of cell walls and the number of neighboring cells. These measurements are dependent variables because they change in response to an independent variable, such as the type or shape of cell.

6. One unique aspect of this study was the inclusion of measurements for “irregular” cells. Why had previous studies ignored irregular cells?

Irregular cells were difficult to measure by image analysis and so had to be measured by hand. They also appeared misshapen, so potentially construction errors.

7. Researchers discovered that bees put down alternating pairs of five-sided and seven-sided cells at the transition between larger and smaller cells. How many open sides are present in a shape-duo consisting of one five-sided shape and one seven-sided shape? How many open sides are present in a shape-duo of two six-sided shapes?

A five-seven pairing has 10 open sides. A six-six pairing also has 10 open sides.

After Reading
1. Bees and wasps are not close relatives in an evolutionary sense. (They diverged about 179 million years ago!) Despite their differences, they both use the same geometry trick to solve the nest-building problem. When unrelated species both come up with the same solution for solving similar problems, scientists call it “convergent evolution.” Consider what it means to “converge,” then explain why this term accurately describes the phenomenon in this story. Come up with another example of convergent evolution and explain how your example depicts dissimilar species solving similar problems in similar ways.  

To “converge” means to come together. So convergent evolution accurately describes the phenomenon in which two unrelated species come together somehow, such as forming similar solutions to problems. Bees and wasps converged on the same geometry solution to the nest-building problem. Answers will vary regarding other examples of convergent evolution. Responses may be more specific, such as wings on bats vs. insects. Or examples may be general, such as noting thorns appear on many diverse plant species as a means of predator defense.

 2. An analogy is a literary device that explains an unfamiliar concept by saying it is similar to some other concept that is more familiar. This story uses an analogy of tiling a floor. Explain how this analogy helps the reader understand a problem bees encounter when nest-building.

The analogy to tiling a floor helps a reader understand the beehive-building problem by providing a similar problem in geometry. Here, differently-sized shapes must fit together in an organized way.

3. Analogies are powerful tools. However, if not careful, they can give rise to misconceptions. The reason: While analogous concepts are similar, they still have differences. However, taking note of the analogous concepts’ differences can help address this potential problem. Identify one difference between the analogous concepts — tiling a floor and building a beehive — that could confuse a reader.

Answers will vary regarding differences between these ideas. But students may point to the process of tiling, which occurs in one session, with all materials at hand from the beginning. In contrast, hive-building is a long-term, continuous process of growth. And bees must make adjustments during the growth process to accommodate the changing needs of their colony.