Archimedes
Mathematician · c. 287-212 BC · Mathematics, stage 3: Meet the mathematicians
Measured curved figures by trapping them between straight-sided ones, nineteen centuries before calculus.
Overview
Archimedes worked in Syracuse and was killed there when the city fell to Rome. He computed areas and volumes of curved figures using the method of exhaustion, squeezing a shape between inscribed and circumscribed polygons until the two closed on a single value, which is the idea a limit later made precise. He proved that the volume of a sphere is two thirds that of the cylinder around it, a result he asked to have marked on his tomb, and bounded the ratio of circumference to diameter between 22/7 and 223/71. A palimpsest rediscovered in 1906 revealed The Method, in which he explains that he first found many of his results by imagining figures balanced on a lever and only then proved them rigorously. Start with Measurement of a Circle, which is a few pages long.
Where to start reading
Measurement of a Circle c. 3rd century BC
A short treatise bounding the ratio of a circle to its diameter by comparing inscribed and circumscribed polygons of ninety-six sides.
On the Sphere and Cylinder c. 3rd century BC
Proves the relations between the surface area and volume of a sphere and of the cylinder that contains it.
The Method of Mechanical Theorems c. 3rd century BC
Explains how he discovered results by treating geometric figures as weights on a balance before proving them. On Project Gutenberg under the title "Geometrical Solutions Derived from Mechanics".
Part of
Sources
- Archimedes MacTutor History of Mathematics
- Archimedes Wikipedia
