The Archimedes Principle
The principle of buoyancy — that an object submerged in fluid displaces fluid equal to its own volume, and experiences an upward force equal to the weight of that displaced fluid — is still taught in every physics course. Legend says Archimedes discovered it in his bath and ran through the streets shouting "Eureka!" (I have found it).
Calculating Pi
Archimedes computed π to between 3 10/71 and 3 1/7 by inscribing and circumscribing polygons around a circle — a method that laid the foundation for integral calculus. His bounds (3.1408… to 3.1428…) remained the most accurate in the Western world for centuries.
The Archimedes Screw
A helical screw inside a cylinder, turned by hand or by animal, lifts water from low to high elevation. Versions of the Archimedes screw are still used today in irrigation, wastewater treatment plants, and even some modern hydroelectric generators.
War Machines and the Claw
During the Roman siege of Syracuse (214–212 BCE), Archimedes designed defensive war machines including catapults, hot-beam reflectors (possibly parabolic mirrors to focus sunlight on ships), and the Claw of Archimedes — a crane-like device that grabbed Roman ships and capsized them. The Romans were so intimidated they feared attacking during daylight.
Mathematical Legacy
Archimedes computed the areas and volumes of parabolas, spheres, and cylinders. His Method — rediscovered in 1906 in the Archimedes Palimpsest — shows he used a proto-calculus approach to integrate shapes, anticipating Newton and Leibniz by nearly 2,000 years.
Frequently Asked Questions
What are Archimedes most famous inventions?
The Archimedes screw (water-lifting device), compound pulleys, war machines used in the siege of Syracuse, and parabolic mirrors. His mathematical discoveries include the principle of buoyancy and an approximation of pi.
Did Archimedes invent calculus?
Not formally, but he developed proto-calculus techniques — using infinitely thin slices to compute areas and volumes — that anticipated the work of Newton and Leibniz by almost 2,000 years.
What did Archimedes discover about pi?
Archimedes proved that pi lies between 3 10/71 (≈3.1408) and 3 1/7 (≈3.1428) by calculating the perimeters of inscribed and circumscribed 96-sided polygons around a circle.
