mathematician and physics and the inventor of Grecian lived from 287 until 212 BC, and is generally considered the greatest mathematicians of antiquity, and has paved the methods of precision-engineered to measure curved lines and spaces and surfaces of the road in front of the account to talk, as he laid the foundations of mechanics and science of statics and Sconiat fluids.

Archimedes is universally acknowledged to be the greatest of ancient mathematicians. He studied at Euclid's school (probably after Euclid's death), but his work far surpassed the works of Euclid. 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 their "awesome" clarity. 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√3indicates that he'd partially anticipated the method of continued fractions. He found a method to trisect an arbitrary angle (using amarkablestraightedge — the construction is impossible using strictly Platonic rules). Although it doesn't survive in his writings, Pappus reports that he discovered theArchimedean solids. 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 hisPrinciple of the Lever, the other using a geometric series.

Archimedes' methods anticipated both the integral and differential calculus. He was similar to Newton in that he used his (non-rigorous) calculus todiscoverresults, but then devised rigorous geometric proofs for publication. His original achievements in physics include the principles of leverage, the first law of hydrostatics, and inventions like the compound pulley, the hydraulic screw, and war machines. His books includeFloating Bodies,Spirals,The Sand Reckoner,Measurement of the Circle, andSphere and Cylinder. He developed theStomachionpuzzle (and solved a difficult enumeration problem involving it). Archimedes proved that the volume of a sphere is two-thirds the volume of a circumscribing cylinder. He requested that a representation of such a sphere and cylinder be inscribed on his tomb.

That Archimedes shared the attitude of later mathematicians like Hardy and Brouwer is suggested by Plutarch's comment that Archimedes regarded applied mathematics "as ignoble and sordid ... and did not deign to [write about his mechanical inventions; instead] he placed his whole ambition in those speculations the beauty and subtlety of which are untainted by any admixture of the common needs of life."

Recently, modern technology has led to the discovery of new writings by Archimedes, hitherto hidden on a palimpsest, including a note that implies an understanding of the distinction between countable and uncountable infinities (a distinction which wasn't resolved until Georg Cantor, who lived 2300 years after the time of Archimedes). Although Archimedes was certainly one of the greatest geniuses ever, many listmakers would rank him lower than I have: He was simplytoofar ahead of his time to have great historical significance.

Archimedes discovered formulae for the volume and surface area of a sphere, and may even have been first to notice and prove the simple relationship between a circle's circumference and area. For these reasons,πis often calledArchimedes' constant. His approximation223/71 < π < 22/7was the best of his day, though Apollonius soon surpassed it.

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