Among Archimedes writings, the following five treatises are of particular interest:

On the Sphere and Cylinder (two volumes) - this contains his discovery that the volume of a sphere is two-thirds that of the cylinder in which it is inscribed, and that the surface area of a sphere is four times that of its greatest circle.

On the Measurement of the Circle - a short work which contains his approximation for the value of Pi. Archimedes showed that Pi lies between 223/71 and 22/7. The latter value was used throughout the Middle Ages and it is still used today when a rough calculation is required. This work also contains accurate approximations of the square roots of various numbers.

On Floating Bodies (two volumes) - this is the first known work in hydrostatics (the study of liquids at rest), a branch of science of which Archimedes is considered the founder. This is the work that leads to the Archimedes Principle, which states that a body partially or completely immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

The Method of Mechanical Theorems - this describes the process of discovery in mathematics. In it, Archimedes describes some of the 'mechanical' techniques he used to arrive at the values he proved mathematically in On the Sphere and Cylinder.

The Sand Reckoner - this is a small work, written for the layman. It deals with the inadequacies of the Greek numerical notation system, by showing how to express a very large number - the number of grains of sand that it would take to fill the universe. In doing this, he, in effect established a place-value system, with a base of 100,000,000. In this work, he also describes the theory put forward by the Greek astronomer Aristarchos of Samos, that the Sun is at the centre of the Universe, but dismisses it as 'impossible'.

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See also:    'Eureka' - the story of Archimedes and the Golden Crown    |    Who was Galileo?