Benjamin Banneker is an important mathematician in history, not only for being a wide-ranging thinker who studied astronomy, clocks, nature, and mathematics (to name a few), but also for being an early important African American intellectual. Born in 1731 near Baltimore, Maryland, to a free African American woman and a former slave, Banneker grew up without a formal education. Nevertheless, he became known for helping to survey the original border of Washington, D.C., publishing almanacs, and building extremely accurate clocks.
Banneker became intrigued by one mathematical piece of nature: cicadasn particular, one species that first arrived when he was a teenager. His instinct at the time? Destroy them! (Teens will be teens.) But in 1766, the cicadas arrived again. Now in his thirties, Banneker chose to respect the buzzing-and-clicking creatures instead. They arrived again in 1783, always showing up in precisely 17-year increments. At this point, Banneker not only respected the cicadas, he was studying them. He correctly predicted that they would appear again in 1800, and ventured guesses as to why the insects waited that particular number of years to reemerge each time. In fact, there are several periodic cicadas in the U.S., and their life cycles are either 13 or 17 years.
So, why have the cicadas settled on 13 and 17? If you’re a math teacher reading this, consider posing that question to your students and see if they spot one key trait those two numbers have in common: they’re both prime. This is nature’s way of ensuring that a 13-year species and a 17-year species are almost never around at the same time—or during the time of any other periodically emerging species, for that matter.
Compare their appearances with two fictional cicadas that appear every 12 and 16 years, two numbers that are decidedly not prime:
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