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ARCHIMEDES:The discoverer of pie

Archimedes (approximately 285---212 B.C.) was the most famous ancient Greek mathematician and inventor. He invented the Screw of Archimedes, a device to lift water, and played a major role in the defense of Syracuse against a Roman Siege, inventing many war machines that were so effective that they long delayed the final sacking of the city.

Archimedes' mathematical work exhibits great boldness and originality in thought, as well as extreme rigor. Among his mathematical accomplishments is the computation of pi, which is the ratio of the circumference of a circle to its diameter. His approach consisted of inscribing and circumscribing regular polygons with many sides in and around the circle, and computing the perimeter of these polygons. This provided him with an upper and a lower bound for pi.

If one knows that the area of the circle equals pi times the square of the radius of the circle then one can also compute pi from that relationship. (Of course one has to prove the equivalence of these two definitions of pi.) This approach to computing was used until the late 17th century when more powerful calculus based series expansions became available.

What is π?

Webster's Collegiate Dictionary defines π as "1: the 16th letter of the Greek alphabet... 2 a: the symbol pi denoting the ratio of the circumference of a circle to its diameter b: the ratio itself: a transcendental number having a value to eight decimal places of 3.14159265"

A number can be placed into several categories based on its properties. Is it prime or composite? Is it imaginary or real? Is it transcendental or algebraic? These questions help define a number's behavior in different situations. In order to understand where π fits in to the world of mathematics, one must understand several of its properties: π is irrational and π is transcendental.

The symbol for pi:

was introduced by the English mathematician William Jones in 1706, who wrote:\

3.14159=...

Archimedes (approximately 285---212 B.C.) was the most famous ancient Greek mathematician and inventor. He invented the Screw of Archimedes, a device to lift water, and played a major role in the defense of Syracuse against a Roman Siege, inventing many war machines that were so effective that they long delayed the final sacking of the city.

Archimedes' mathematical work exhibits great boldness and originality in thought, as well as extreme rigor. Among his mathematical accomplishments is the computation of pi, which is the ratio of the circumference of a circle to its diameter. His approach consisted of inscribing and circumscribing regular polygons with many sides in and around the circle, and computing the perimeter of these polygons. This provided him with an upper and a lower bound for pi.

If one knows that the area of the circle equals pi times the square of the radius of the circle then one can also compute pi from that relationship. (Of course one has to prove the equivalence of these two definitions of pi.) This approach to computing was used until the late 17th century when more powerful calculus based series expansions became available.

What is π?

Webster's Collegiate Dictionary defines π as "1: the 16th letter of the Greek alphabet... 2 a: the symbol pi denoting the ratio of the circumference of a circle to its diameter b: the ratio itself: a transcendental number having a value to eight decimal places of 3.14159265"

A number can be placed into several categories based on its properties. Is it prime or composite? Is it imaginary or real? Is it transcendental or algebraic? These questions help define a number's behavior in different situations. In order to understand where π fits in to the world of mathematics, one must understand several of its properties: π is irrational and π is transcendental.

The symbol for pi:

was introduced by the English mathematician William Jones in 1706, who wrote:\

3.14159=...

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