Archimedes

Lore & Background

Archimedes is credited with solving the 'wreath problem' for King Hiero II. According to Vitruvius, while stepping into a bath, Archimedes noticed the water level rose and realized this could determine the crown's volume, leading him to run naked through the streets crying 'Eureka!' Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. He is also said to have built a planetarium device that demonstrated the movements of the known celestial bodies, and may have been a precursor to the Antikythera mechanism. He is considered one of the leading scientists in classical antiquity and one of the greatest mathematicians of all time.

His surviving work shows he anticipated modern calculus by applying infinitesimals and the method of exhaustion to prove many geometrical theorems, including the area of a circle, the surface area and volume of a sphere, the area of an ellipse, and the area under a parabola. He derived an approximation of pi, defined the Archimedean spiral, and devised a system using exponentiation for large numbers. He was among the first to apply mathematics to physics, proving the law of the lever, using the concept of center of gravity, and enunciating the law of buoyancy known as Archimedes' principle.

In astronomy, he measured the apparent diameter of the Sun and the size of the universe. He designed innovative machines such as his screw pump, compound pulleys, and defensive war machines for Syracuse. He died during the siege of Syracuse, killed by a Roman soldier despite orders not to harm him. Cicero later visited his tomb, which was marked by a sphere and a cylinder representing his most valued mathematical discovery.

Common Misconceptions (Editorial)

• A common misconception is that Archimedes invented the principle of buoyancy (Archimedes’ principle) solely from the "Eureka!" bath story. While that anecdote from Vitruvius is famous, a different ancient account in the Carmen de Ponderibus describes him using a balance immersed in water to solve the golden wreath problem.
• Some assume Archimedes was a pure mathematician with no practical engineering role. In fact, the facts record that he designed the massive ship Syracusia, oversaw war machines during the Siege of Syracuse, and claimed he could move any large weight using pulleys or a windlass.
• It is often thought that Archimedes visited Alexandria and studied there. However, the facts state it is unknown whether he ever visited Alexandria, though his works addressed to scholars like Dositheus and Eratosthenes suggest collegial relations.

Why It Matters (Editorial)

Archimedes endures as a symbol of the fusion of abstract mathematics with tangible invention, from his rigorous proofs anticipating calculus to his legendary war machines. His legacy reminds us that the most profound scientific insights—like the law of the lever or the principle of buoyancy—can arise from everyday observations, and that a single mind can shape both theoretical knowledge and practical engineering for millennia.

Notable Quotes (Wikiquote)

"Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, philosopher, scientist and engineer." — Archimedes "I have found it! or I have got it!, commonly quoted as Eureka!" — Archimedes "Give me the place to stand, and I shall move the earth." — Archimedes "Give me a place to stand and with a lever I will move the whole world." — Archimedes