Archimedes: The Father of Mathematics

Summary

  • Birth: c. 287 BC in Syracuse, Sicily (colony of Magna Graecia)
  • Death: c. 212 BC in Syracuse, Sicily (during the Second Punic War)
  • Alias(es): Archimedes of Syracuse
  • Ethnicity: Greek
  • Residence(s): Syracuse, Sicily; Alexandria, Egypt (during school)
  • Language(s): Works were written in Doric Greek (Sicilian)
  • Religion(s): Judaic Christian
  • Father: Phidias/Pheidias (astronomer and mathematician)
  • Mother: Unknown
  • Spouse(s): Unknown
  • Children: Unknown
  • Relatives: King Herion II (unconfirmed), Gelon (unconfirmed)
  • Acquaintances: Conon, Dositheus, Eratosthenes, Heracleides
  • Class/Wealth Notes: Upper
  • Institutions/Degrees: The School of Alexandria
  • Profession(s): Mathematician, engineer, astronomer, physicist, inventor
  • Field(s) of Study: Hydrostatics, Mechanics, Geometry, Calculus, Defense
  • Famous Works: The Sand Reckoner, On the Equilibrium of Planes, On Floating Bodies, On the Measurement of a Circle, On Spirals, On the Sphere and the Cylinder, On Conoids and Spheroids, The Quadrature of the Parabola, Ostomachion, The Method of Mechanical Theorems, Book of Lemmas (Liber Assumptorum), Cattle Problem
  • Legacy: “Eureka!”; known as “The Father of Mathematics”; with Newton and Gauss he is commonly referred to as one of the three greatest mathematicians who ever lived; last words were “Do not disturb my circles”;
  • Cause of Death: Killed in Syracuse, Sicily during the Second Punic War despite orders from the Roman general Marcellus to leave him unharmed. The Greek historian Plutarch reported that Roman soldiers killed Archimedes to steal his scientific instruments. Another version states he was stabbed for ignoring a Roman soldier’s orders because he was too entranced in a geometrical diagram he drew in the sand.
  • Notable Historian(s): Isidore of Miletus, Eutocius, Plutarch, Polybius, Thābit ibn Qurra (Arabic translator), Gerard of Cremona (Latin translator)


Archimedes’ Principle & The First Law of Hydrostatics

Story: Archimedes was tasked to determine if the new crown made for King Herion II was made of solid gold. While taking a bath, he observed the level of water in the tub rise as he got in… leading to his “Eureka!” moment regarding density and displacement.

Science: A body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Therefore Archimedes could immerse the crown in water, measure the amount of water displaced, divide it by the weight of the crown, and arrive at the density of the crown.

Impact: Hydrostatics, or the study of the mechanical properties of liquids at rest, was born. Archimedes’ Principle regarding buyancy and density is used throughout science today. It’s used in the building of ships, other industrial manufacturing, and really any type of engineering. Without it, well, we might be “screwed” (see Archimedes’ other works below).


Other Works

  • Archimedes’ Screw – This consists of a long screw enclosed in a cylinder. With tilted so that its bottom tip is placed in the water, turning the screw pushes water up the screw and out the top. This was used to bilge water out of large ship he designed, the Syracusia.
  • Law of the Lever – Achimedes supplied the first real scientific explanation of how levers work in his work titled On The Equilibrium of Planes (although he certainly did not invent levers).
  • Method of Exhaustion and Pi – Archimedes used the “method of exhaustion” to determine approximate areas and volumes of circles. It involves drawing one polygon outside of a circle, and inscribing a similar polygon on the inside of the circle. Since the area of a polygon (at that time) could be worked out more easily than a circle, Archimedes would determine the areas of the polygons, continuously adding more sides to the polygons, computing the new areas, and estimate the area of the circle which falls between those of the inner and outer polygons. This helped him determine an approximation of pi which he set at somewhere between 3.1429 and 3.1408.
  • Spheres and Cylinders – Archimedes, through the use of several means, proved that a sphere had two-thirds the volume and surface area of a cylinder that circumscribes the sphere.
  • Engineering Feats – Archimedes engineered and built several machines, based on the physical properties and relationships he had proven, to help defend Syracuse from the Roman assault. These included giant pulleys and catapults that would lift ships out of the water and shake them up, destroying them (check out the “claw of Archimedes”). He also built a giant mirror that focused the sunlight onto a ship to burn it.


Adsideological Discussion

Archimedes’ life highlights when a needs translates to accomplishments. This is a characteristic of most inventions, because they need money to flourish and inventors need money to succeed and continue inventing. But Archimedes’ accomplishments were much more than this. It seems to me that he was driven by pure curiosity and intellect, a desire to test his mind against science and nature.

At some level, perhaps he spent too little time outside of his passion of mathematics and discovery. A passion is supposed to be a majority consumer of time and energy. However, no legacy really exists, outside of his scientific accomplishments, that tells us about Archimedes the man and Archimedes the neighbor. Perhaps this has something to do with the time frame in which he lived, but a story told is a story told. Regardless, Archimedes was a life changer and contributed an incredible balance of both an immediate impact and a long term impact on society.

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