Читать книгу The Little Book of Mathematical Principles, Theories & Things - Robert Solomon - Страница 30

This concerns formulae for the volume and surface area of a sphere.

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Archimedes is often described as the archetype of the absent-minded professor. Yet, he achieved more in mathematics, science, and technology than anyone else in the ancient world.

The diagram shows a sphere inside a cylinder. From this diagram Archimedes found two things:

1. The surface area of the sphere is the same as that of the cylinder (without the ends).

2. The volume of the sphere is two-thirds that of the cylinder.

The formulae 4πr² for the surface area, and ⁴/₃ πr³ for the volume followed. Archimedes was so proud of these results that the diagram was engraved on his tombstone.

Archimedes is famous for mathematics, scientific discoveries concerning centers of gravity and floating bodies, and such inventions as the Archimedes screw. He is also famous for leaping out of his bath and running around shouting “Eureka!”.

While the Roman army besieged Syracuse, where Archimedes was living, he invented terrifying war machines to drive them back. Despite this, they finally took the city. While he was busy tracing a geometrical figure on the sand, a soldier summoned him to attend the Roman governor. “Don’t disturb my circles!” he protested. These were his last words.

Sphere inside cylinder.