Symmetry

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Team Pick - Symmetry

Growing up in Washington, I have often glimpsed a handful of butterflies floating through my backyard. I remember specifically the excitement that fluttered in my heart when I glimpsed what six-year-old me identified as a Monarch butterfly (Danaus plexippus). Looking back on that early spring afternoon, I know it was much more likely the Monarch’s lookalike, Viceroy (Limenitis archippus), which lives in Washington, unlike the Monarch. It wasn’t until three years ago when I began working as an outdoor education summer camp counselor that I learned that six-year-olds and adults alike often confuse the Monarch¹ and Viceroy². I couldn’t help but wonder if there was an easy way to help people discern the two species. Where do they differ and can we use concepts of symmetry to spot the differences?

While on the surface symmetry may seem like an elementary concept, if we take the time to look closer, it becomes easy to see why its applications to everything from engineering to chemistry are powerful. Upon examining two species of butterfly, we challenge the popular belief that butterfly wings are perfectly symmetrical and alike across species. We will define symmetry as perfectly alike parts facing each other or across an axis. By comparing the bilateral symmetry and the number of points of symmetry of the two species when they are reflected, I can seek to understand where they differ. Both of the following images are of real butterflies.

Bilateral symmetry is being divisible into two identical halves. In the graphic I created above, we can see the butterflies pass the bilateral symmetry test when reflected across the y-axis in the third row of the graphic. A point of symmetry is a part that has a matching part at the same distance from the central point³. For the butterflies, that means there are more points at which symmetry can be found. In this case, the number of points increases with the level of detail. In the bottom portion of the wing, there is more detail on the Viceroy whereas the Monarch’s pattern is more simple. There are a total of eight sections on the Monarch whereas the Viceroy has 12. This means there are more points of symmetry on the Viceroy.

A limitation of using symmetry when attempting to make an identification in the wild is that it is not possible to compare these species side by side in the wild as they do not both frequent our region. In conclusion, looking at the size and level of complexity of the patterning, otherwise known as points of symmerty, can help a person of any age identify local fauna correctly.

References

¹All About Monarch Butterfly Migration - An Incredible Journey | The Monarch Joint Venture. (n.d.). The Monarch Joint Venture. Retrieved February 22, 2022, from https://monarchjointventure.org/monarch-biology/monarch-migration

²Viceroy | Washington Department of Fish & Wildlife. (n.d.). Washington Department of Fish & Wildlife. Retrieved February 22, 2022, from https://wdfw.wa.gov/species-habitats/species/limenitis-archippus-lahontani

³Point Symmetry Definition (Illustrated Mathematics Dictionary). (n.d.). Math Is Fun. Retrieved April 5, 2022, from https://www.mathsisfun.com/definitions/point-symmetry.html