Archimedes

Archimedes

  Archimedes is universally known to be the greatest of ancient mathematicians. He studied at Euclid's school, but his work far surpassed than the works of Euclid. For example, some of Euclid's more difficult theorems are easy analytic consequences of Archimedes' Lemma of Centroids. His achievements are particularly impressive given the lack of good mathematical notation in his day. His proofs are noted not only for brilliance but for unequaled clarity, with a modern biographer describing Archimedes' treatises as "without exception monuments of mathematical exposition . so impressive in their perfection as to create a feeling akin to awe in the mind of the reader." Archimedes made advances in number theory, algebra, and analysis, but is most renowned for his many theorems of plane and solid geometry. He was first to prove Heron's formula for the area of a triangle. His excellent approximation to √3 indicates that he'd partially anticipated the method of continued fractions. One of his most remarkable and famous geometric results was determining the area of a parabolic section, for which he offered two independent proofs, one using his Principle of the Lever, the other using a geometric series. Some of Archimedes' work survives only because Thabit ibn Qurra translated the otherwise-lost Book of Lemmas; it contains the angle-trisection method and several ingenious theorems about inscribed circles. Thabit shows how to construct a regular heptagon; it may not be clear whether this came from Archimedes, or was fashioned by Thabit by studying Archimedes' angle-trisection method. Other discoveries known only second-hand include theArchimedean semiregular solids reported by Pappus, and the Broken-Chord Theorem reported by Alberuni.

               Sources:
http://fabpedigree.com/james/mathmen.htm

http://www-groups.dcs.st-and.ac.uk/~history/BiogIndex.html

http://www.math.com/students/mathematicians.html