www.derekthompson.org/p/i-know-why-the-mathematicians-weep
1 correction found
Two thousand years ago, the Greek mathematician Archimedes calculated the area of curved objects and pinned down the value of pi by measuring the areas of dozens of tiny polygons that filled out a circle.
This misstates Archimedes’ method for approximating π. Archimedes bounded π using the perimeters of inscribed and circumscribed polygons, not by measuring polygon areas.
Full reasoning
Archimedes did important work on areas, but this sentence gets his π method wrong.
For his approximation of π, standard histories of mathematics describe Archimedes as comparing the perimeters of polygons drawn inside and outside a circle. By increasing the number of sides up to 96, he squeezed the circle’s circumference between those polygon perimeters and derived upper and lower bounds for π.
That is different from saying he "pinned down the value of pi by measuring the areas of dozens of tiny polygons that filled out a circle." The cited historical sources say his bound on π came from perimeters/circumference, not from summing polygon areas.
So the error is not that Archimedes studied area at all — he certainly did — but that the article attributes the wrong geometric method to his approximation of π.
2 sources
- Archimedes Num An - MacTutor History of Mathematics
The circumference of a circle is less than 3 1/7 its diameter but more than 3 10/71 times the diameter. He obtained these inequalities by considering the circle with radius unity and estimating the perimeters of inscribed and circumscribed regular polygons of 96 sides.
- NOVA | Infinite Secrets | Approximating Pi (non-Flash) | PBS
Archimedes determined the upper and lower range of pi by finding the perimeters of inscribed and circumscribed polygons. By doubling the number of sides ... Archimedes was able to bring the two perimeters ever closer in length to the circumference of the circle and thereby come up with his approximation.