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Archimedes

c. 287 - 212 BCE

Archimedes

Archimedes was a Greek, living in Magna Graecia. He is considered one of the greatest mathematicians and engineers of the ancient world, and the source for many fascinating stories and anecdotes.

  • Nationality
  • Greek (of Syracuse, Sicily - Magna Graecia)

  • Subject
  • Physics, Mathematics

  • Fields
  • Engineering, Geometry, Astronomy, Inventions, Mechanical Engineering

  • Distinctions
  • Immortalisation by Cicero, and other writers of antiquity

    The world's first steamship with a screw propeller was named SS Archimedes, commemorating the invention of the Archimedes Screw, a water pump based on a spiral mechanism.

  • Publications
  • Archimedes Palimpsest, a long-lost parchment, which was read by x-ray techniques in the early 2000s, revealing many of his mathematical techniques.

    The Sand Reckoner

    The Method of Mechanical Theorems

    Cattle Problem

    On the Equilibrium of Planes, in which he expounds on the workings of levers: ('Give me a place to stand, and I will move the Earth').

    On the Measurement of a Circle

    On Spirals

    On the Sphere and the Cylinder

    On Conoids and Spheroids

    On Floating Bodies

    The Quadrature of the Parabola

    Ostomachion, a dissection puzzle, found also in Archimedes Palimpsest

  • Laws
  • Archimedes principle of buoyancy

  • Theories
  • Density

    Definition of π

    Volumes and surface areas of solids

    Infinitesimals, method of exhaustion, limits, and the area under a parabola

    System of exponentiation for expressing large numbers

    Mathematical descriptions of hydrostatics, statics, and lever

  • Equations
  • Archimedes Principle: A buoyant force is equal to the weight of the fluid it displaces.

    The volume and surface areas of a sphere are two-thirds of those of a cylinder with the same diamerer.

    $r = a + bθ$, where $r$ and $θ$ are polar coordinates, and $a$ and $b$ (real) numbers. Archimedes describes a mechanical curve in his 28 propositions in his work On Spirals, describing the Archimedean Spiral as a locus of points moving away, and rotating at constant angular velocity, from a fixed point over time.

  • Experiments/Discoveries
  • Hydrostatic Balance, to measure density. Subject of the famous Eureka moment.

    Archimedes screw: a handcranked water pump

    'Death ray' and 'Claw of Archimedes'

    Circle measurement by exhaustion method, providing a value for pi π

    Lever and block-and-tackle: Archimedes designed tools for lifting, as well as improvements to the catapult.

Much detail about Archimedes and his work has been lost. However, the Romans later immortalised him, and his legend was reawakened by the rediscovery of his writings (in parchment documents called palimpsests) at the start of the European Renaissance, 1400s. A final palimpsest was discovered in 1906, in Constantinople, and read by x-ray techniques in the early 2000s, revealing that his mathematical techniques were very advanced, and were fore-runners of calculus.

Archimedes Palimpsest
Archimedes Palimpsest: his pages were cut in two and rebound into a liturgical text

Given the threat from the Romans during the 2nd Punic War, Archimedes invented many weapons of war, to defend the city of Syracuse, in modern Sicily. These included a 'death ray', focusing light from many mirrors to sink wooden ships before they could reach the shore, and an overhead claw to lift and sink ships. But he also invented more peaceful devices, such as the Archimedes' Screw, a spiral which could lift water efficiently, which became a standard device, like Archimedes' lever, in engineering.

Archimedes Palimpsest
The examination of Archimedes' Palimpsest, using x-ray and multi-spectral analysis, revealed his great insights previously obscured by medieval liturgical overwriting

The term 'eureka' (Greek for 'I have found it') derives from a legend about Archimedes. He had been set the task of determining whether the gold used to make a crown for the king had been mixed with baser metals. While bathing, he realised that the volume of water displaced would provide the volume, thereby allowing the density to be measured, hence proving that the crown had an average density lower than gold. It is not recorded what happened to the corrupt goldsmith, but a lively account of the story is given in Andrew Bone's comic novel Vitruvian Boy.

Archimedes tomb
Cicero discovering the tomb of Archimedes, by Benjamin West, 1805. The tomb was surmounted by a statue of a sphere and a cylinder.

Archimedes was killed by a Roman soldier during the invasion of Syracuse (Sicily, then part of Magna Graecia), despite orders that he be unharmed. An anecdote recounts how he was working on a mathematical problem at the time, and had drawn circles in the sand. According to Valerius Maximus, a 1st century writer, Archimedes' last words were: "obsecro, istum disturbare" (I beg you, do not disturb this). Stuff of legend.

Archimedes' tomb was uncovered by Cicero in 75BCE. It had a sculpture of a sphere and a cylinder, Archimedes mathematical proof that the volume and surface area of a sphere equal two-thirds those of a cylinder.

Ostomachion
Ostomachion puzzle: a type of geometrical jigsaw illustrated by Archimedes





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