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# A Piece of Pi: Historical Perspectives from NLM

*By Kenneth M. Koyle and Jeffrey S. Reznick*

Today is Pi Day, the internationally-recognized event when communities of various disciplines come together to celebrate the importance and significance of the Greek letter π, the symbol used in mathematics to represent a constant—the ratio of the circumference of a circle to its diameter—which is approximately 3.14159.

Early mathematicians noted that the circumference of a circle is a little more than three times its width, and as far back as the 3rd century BCE the Greek scholar Archimedes developed a way to calculate this constant number using a 96-sided polygon to approximate a circle. Using this method, he determined that the ratio was slightly less than 22/7, which was incredibly accurate for the time. Archimedes’ calculations paved the way for generations of subsequent scholars to refine the ratio over the next two millennia.

One of the most prominent mathematicians of the medieval period, Johannes Sacro Bosco, made use of this ratio in the 13th century when he wrote the definitive text on spherical astronomy, a text that influenced such luminaries as Copernicus and Galileo. The National Library of Medicine holds a 14th-century German translation of this manuscript, replete with diagrams showing the properties of spheres and the orbits of celestial bodies.

Since Archimedes’ developed his constant, generations have been fascinated by it. This fascination continues today, quite literally, with Pi Day. It’s hard to say why this particular number has so thoroughly captured the human imagination, achieving almost mystical status among mathematicians. There are many other constants—Pythagoras and Euclid both predated Archimedes and developed their own formulae with geometrical constants—but something about Pi is special. Maybe it’s because it is an irrational number with an infinite series of randomly distributed digits, making it an unusual challenge to calculate and memorize an ever-increasing string of numbers. According to a 1764 dictionary of arts and sciences, which we hold in the History of Medicine collections, this challenge “has put some of the most celebrated men in all ages upon endeavouring to approximate it.” The first person to calculate 35 digits of Pi, Ludolph van Ceulen, was so proud of the feat that he had the number engraved on his tombstone when he died in 1610.

Although he was not the first to use the symbol π (the Greek letter p) to represent the perimeter of a circle, the renowned Swiss mathematician Leonhard Euler was responsible for making it the standard symbol for Archimedes’ Constant. Like many intellectuals of his time, Euler did not limit his pursuits to one branch of science. In addition to his important work in mathematical theory, Euler applied those theories to the development of complex, multi-lens microscopes and telescopes, as we can see in several of his books in our collections.

So, with these historical insights on Pi as demonstrated through the historical collections of the NLM, we proudly join in the Pi Day Celebration here at NIH (despite its postponement due to our local inclement weather). And we’ll go a step further, both in spirit of the weather to recall the magic of snowflakes, and in the spirit of humor expressed by Mental Floss, Kitchn.com, and other popular social media outlets, to encourage you to celebrate Pi Day—and the history of Pi—by baking a pie! What better activity while you’re snowed in? You can find lots of recipes in the many cookbooks available via NLM Digital Collections. Our pick is the appropriately-titled *Science in the Kitchen*, 1898, by Ella Ervilla Kellogg, the noted writer, early dietitian, and member of the Michigan Women’s Hall of Fame. Kellogg helpfully reminds us that “pie and cake are not necessarily utterly unwholesome” if prepared simply and eaten in moderation. It’s good advice to keep in mind if you choose to appreciate a rich but healthful pie—alongside the rich history of Pi—on Pi Day!

*Interested to see up-close the historical texts described in this blog post? Come for a visit! Our reading room is open from 8:30 to 5pm (EST) Monday through Friday except for Federal holidays.*