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Consortium for Mathematics and its Applications

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September 20, 2022
Written on . Posted in Fun with Math.

Math in Pictures: Have a Seat but Not Too Close

Birds sitting on wires often seem to be very regularly spaced.

What are they thinking?  Probably not much given their bird-size brains, or perhaps a lot more than we realize. When birds congregate on wires, there is often some shifting of place as more and more birds arrive. Students who might be interested in birds (or in the mathematics of bird behavior) could investigate the way they arrange themselves on wires in a variety of ways.

birds on a wire

For example, working with photos the students take themselves or with photos found online, they could measure the spacings between birds and study the statistics of the distribution of spacings. How regular are they? How do they change in relation to the number of birds present? Do the properties of the distributions vary by species?

To get at these and other questions, the students might need to consider the role perspective plays in the photograph and any distortion introduced by the lens of the camera. For example, a wide-angle lens could make birds at the edges of the photo appear further apart than those near the center.

Students who enjoy coding could create a simple agent-based simulation where birds land on a line and then adjust themselves according to how near their right and left neighbors are. What simple rules might generate computer simulation results that match the distributions seen in nature?

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The Consortium for Mathematics and Its Applications is an award-winning non-profit organization whose mission is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world.