Archimedes

Archimedes was an ancient Greek mathematician, engineer, and inventor whose work shaped geometry, mechanics, and hydrostatics.

Archimedes' principle: A principle stating that a body immersed in fluid experiences an upward force equal to the weight of fluid it displaces. This hydrostatic result is the discovery most directly attached to Archimedes' name.
Law of the lever: A rule that balances a lever when opposing forces have equal moments about its fulcrum. Archimedes demonstrated how distance from the fulcrum changes the force needed for balance.
The Sand Reckoner: A surviving treatise by Archimedes that develops a system for expressing enormous numbers. It reveals his interest in calculation and the scale of the universe.
Archimedes' cattle problem: A number-theory puzzle attributed to Archimedes involving the sizes of the Sun god's cattle herds. The puzzle displays mathematical sophistication beyond his better-known geometry.
Lever: A rigid bar that pivots around a fulcrum to transmit or multiply force. Archimedes analyzed how lever arms determine mechanical advantage.
Buoyancy: The upward force a fluid exerts on an immersed or floating body. It is the physical force quantified by Archimedes' principle.
On the Sphere and Cylinder: A treatise by Archimedes proving geometric results about spheres and their circumscribed cylinders. Archimedes regarded its sphere-and-cylinder result as a major achievement.
Archimedes' claw: A legendary siege device said to have lifted or overturned Roman ships attacking Syracuse. The story reflects ancient accounts of his defensive engineering, though details remain uncertain.
Center of mass: The position representing the weighted average location of a body's mass. His work on centers of gravity helped establish mathematical statics.
Archimedes' screw: A helical device that raises water as it rotates inside a tube or trough. This machine exemplifies the practical engineering associated with Archimedes.

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