Archimedes on Calculus

When I taught 8th grade science, we spent a considerable amount of time on Archimedes (machines, etc) and eventually Newton and the discovery of the calculus.

This news makes my heart swell as we continue to realize that we 20-21st century westerners weren’t the first to achieve such grand inventions as calculus or even a notion of grasping at the infinite…

Two of the texts hiding in the prayer book have not appeared in any other copy of Archimedes’s work, so no one but Heiberg had studied them until now. One of them, titled The Method, has special historical significance. It could be considered the earliest known work on calculus.

Archimedes wrote The Method almost two thousand years before Isaac Newton and Gottfried Wilhelm von Leibniz developed calculus in the 1700s. Reviel Netz, an historian of mathematics at Stanford University who transcribed the text, says that the examination of Archimedes’ work has revealed “a new twist on the entire trajectory of Western mathematics.”

In The Method, Archimedes was working out a way to compute the areas and volumes of objects with curved surfaces, which was also one of the problems that motivated Newton and Leibniz. Ancient mathematicians had long struggled to “square the circle” by calculating its exact area. That problem turned out to be impossible using only a straightedge and compass, the only tools the ancient Greeks allowed themselves. Nevertheless, Archimedes worked out ways of computing the areas of many other curved regions.

I hope my former 8th graders will here the name Archimedes again sometime in their life or career and think back to our class and how we were also grasping at infinity.

Math Trek: A Prayer for Archimedes, Science News Online, Oct. 6, 2007

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