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Mathematics

Archimedes had became a master at mathematics, especially geometry. He spent
most of his time working on solving new problems. Sometimes he became so involved
in his work that he forgot to eat.

Communicated with mathematicians

For years after he left Alexandria, Archimedes would often communicate with
mathematician friends who remained in Alexandria. He would send his fellow

mathematicians statements of his latest theorems, but he would not send the proofs
of those theorems. The reason was that some of the mathematicians would claim the
results as their own. Without being able to figure out the proof, they could not claim
credit.

Math discoveries

Some of the mathematical problems Archimedes solved concerned areas and
volumes of geometric figures. He had to devise a better number system and a new

way to determine the formulae for the areas and volumes of spheres, cylinders,
parabolas, and other plane and solid figures.

Circles and spheres

Archimedes showed that the surface of a sphere is four times that of a great circle,
that the volume of a sphere is two-thirds the volume of a circumscribed cylinder, and
that the surface of a sphere is two-thirds the surface of a circumscribed cylinder

including its bases.

Pi

In his measurements of circles, Archimedes showed that the exact value of pi (π)
1
10
was between the numbers 3 /71 and 3 /7. He found this by approximating a circle by
a regular polygon having 96 sides. This was the most accurate approximation of pi at
that time.

Integration

One of the methods he used to find the areas, volumes and surface areas of many

bodies was an early form of integration. This was considered his greatest
mathematical invention, leading to the field of Calculus.

To determine the area of sections bounded by geometric figures such as parabolas

and ellipses, Archimedes broke the sections into an infinite number of rectangles and
added the areas together.

(Greek Grandeur, Hebrew Heart) 36