Archimedes, of Syracuse

Biographical Information

Occupation, Sphere of Activity

Archimedes of Syracuse (c287-212 BC) was a mathematician and inventor. His father was Pheidias, an astronomer, of which we know nothing. While he is famous now, as he was then, largely because of his inventions, it is reported that he despised invention as being less "pure" than geometry, and he never wrote about his creations. Little is known about his life, though he is described by some as having been a relative - by others as a close friend - of Hiero (or Hieron) II, King of Syracuse, who employed him as a tutor to his son. He almost certainly spent a part of his life studying in Alexandria - where he is thought to have played an important role in the development of Euclidian mathematics. It is probably here that he met Conon of Samos, who he remained in correspondence with as a personal as well as professional friend.

Among the inventions he is credited with is the Screw of Archimedes, an early type of pump he is thought to have created when in Alexandria, which is still used in traditional agriculture in some areas of the world. He is also - almost certainly apocryphally - said to have installed an arrangement of mirrors on the city defences of Syracuse which set fire to attacking Roman ships. He is believed to have invented the compound pulley as a way of demonstrating the possibility of moving very large masses - he bragged that, moved to a position outside the Earth, he could move the entire planet without difficulty. More famously (though also less probably), he is said to have thought of a way of proving King Hiero II had been cheated when supplied with a new crown, by comparing the mass and volume of a block of pure gold of equal mass with the crown. By showing the crown had a larger volume than the equally massive block of gold, so the story goes, he proved that a metal with a lower density had been added to the gold. While the story is improbable, it may relate to one of his real achievements, the elucidation of Archimedes' Law, which explains the change in weight due to buoyancy experienced by objects submerged in water.

He wrote a number of books, ten of which have survived largely intact. These deal mostly with geometrical problems - particularly centres of gravity of solids, studies of spheres and conical sections, spirals and other mathematical matters. Among his propositions, particularly interestingly, are an approximation of 'pi' - which he reached after circumscribing and inscribing a circle with two 96-sided polygons, an explanation of the law of levers, a foundation for theoretical mechanics, a means of accurately approximating square roots of large numbers, a precursor to Newton and Leibniz's calculus and a proposed system of numbering for large figures which went high enough - 8x10^16 in modern notation - to count to a higher number than the number of grains of sand that would fill the universe - or so Archimedes believed.

Archimedes' work the Sandreckoner, in which he introduces his number system, is of historical interest, because it contains an early reference to Aristarchus' heliocentric system and uses results of Phidias (his father) and Eudoxus to determine the size of the universe. It is dedicated to Gelo (Gelon), King Hiero's son. In his book, the Method, Archimedes explains his scientific methods to the reader, and is a unique document, detailing how one of the greatest minds of the classical world worked. In On the Sphere and the Cylinder, which he considered to be his most important work, Archimedes proves that a sphere's surface area is two thirds that of the circumscribing cylinder (including bases) and a sphere's volume is two thirds that of a circumscribing cylinder.

Relationships

Archimedes was the son of astronomer Pheidias. He had a close relationship with astronomer and mathematician Conon of Samos.

Other Significant Information

Notable publications:

On Plane Equilibria or Centres of Gravity of Planes

On the Sphere and the Cylinder

On Spirals

On Floating Bodies

The Sandreckoner

Method

On Conoids and Spheroids

A Collection of Lemmas

The Quadrature of Parabola

The Measurement of the Circle

Honours, Qualifications and Appointments

None known

Notes

List of sources for the biographical information:

Encyclopaedia Britannica vol II, ( London (England), William Benton, 1976)

Gillispie, Charles C, Dictionary of scientific biography, vol II, (New York , Scribner's, 1970)

University of St Andrews, Archimedes of Syracuse, (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Archimedes.html, University of St Andrews, January 1999)