We now know that π is in fact an irrational number, whose value can never be known with complete accuracy. His method for estimating π was taken to the extreme by Ludoph van Ceulen in the 16th Century, who used a polygon with an extraordinary 4,611,686,018,427,387,904 sides to arrive at a value of π correct to 35 digits. Interestingly, Archimedes seemed quite aware that a range was all that could be established and that the actual value might never be known. His estimate was between 3 1⁄ 7 (approximately 3.1429) and 3 10⁄ 71 (approximately 3.1408), which compares well with its actual value of approximately 3.1416.

By this so-called “ method of exhaustion” (or simply “ Archimedes’ Method”), he effectively homed in on a value for one of the most important numbers in all of mathematics, π. He first enclosed the circle in a triangle, then in a square, pentagon, hexagon, etc, etc, each time approximating the area of the circle more closely. For example, to estimate the area of a circle, he constructed a larger polygon outside the circle and a smaller one inside it. Method of ExhaustionĪpproximation of the area of circle by Archimedes’ method of exhaustionĪrchimedes produced formulas to calculate the areas of regular shapes, using a revolutionary method of capturing new shapes by using shapes he already understood. Today, Archimedes is widely considered to have been one of the greatest mathematicians of antiquity, if not of all time, in the august company of mathematicians such as Newton and Gauss. Little is known for sure of his life, and many of the stories and anecdotes about him were written long after his death by the historians of ancient Rome.Īlso an engineer, inventor and astronomer, Archimedes was best known throughout most of history for his military innovations like his siege engines and mirrors to harness and focus the power of the sun, as well as levers, pulleys and pumps (including the famous screw pump known as Archimedes’ Screw, which is still used today in some parts of the world for irrigation).īut his true love was pure mathematics, and the discovery in 1906 of previously unknown works, referred to as the “Archimedes Palimpsest”, has provided new insights into how he obtained his mathematical results.

ARCHIMEDES OF SYRACUSE – Eureka & The Principle Biography – Who was ArchimedesĪnother Greek mathematician who studied at Alexandria in the 3rd Century BCE was Archimedes, although he was born, died and lived most of his life in Syracuse, Sicily (a Hellenic Greek colony in Magna Graecia).

Archimedes of syracuse