Monday Morning Math: Hippocrates of Chios

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No, not that one!

Hippocrates of Chios was a Greek mathematician who followed Pythagoras and lived around 470-410 BCE. He was a contemporary of the more famous Hippocrates, the physician Hippocrates of Kos (c460-370 BCE). He is perhaps best known for his work on the classical geometry problems of squaring the circle and doubling the cube.

Astute readers will note that both of the geometry problems above are impossible to solve in general, but Hippocrates’ work led him to discover how to compute the areas of certain lunes, regions bounded by two circular arcs. (See this video for a pleasing application of Hippocrates’ discovery.)

The “Lune of Hippocrates”

The Greek philosopher Proclus credits Hippocrates with writing the first version of Elements of Geometry, much of which Euclid would later incorporate into his own Elements. In this text, Hippocrates introduced the use of letters to represent points, as well as naming objects using the points that defined them (e.g., “triangle ABC”). It is also believed that he had developed a method of “proof by exhaustion” (approximating circles by polygons with an increasing number of sides), later used by Eudoxus and Euclid. Unfortunately, Hippocrates’ text has been lost to history.

While respected as a mathematician, Hippocrates was viewed as “stupid and incompetent in the business of ordinary life” by Aristotle. He lost a large sum of money due to fraud, and had to teach geometry in Athens to make up for it.

Sources:

https://en.wikipedia.org/wiki/Lune_of_Hippocrates
https://mathshistory.st-andrews.ac.uk/Biographies/Hippocrates/

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