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Archimedes

Born: 298 BC in Syracuse, Sicily

Died: 212 BC in Syracuse, Sicily

Short Biography

Archimedes was a great mathematician of ancient times. His greatest contributions were in geometry. He also spent some time in Egypt, where he invented the machine now called Archimedes' screw, which was a mechanical water pump. Among his most famous works is Measurement of the Circle, where he determined the exact value of pi between the two fractions, 3 10/71 and 3 1/7. He got this information by inscribing and circumscribing a circle with a 96-sided regular polygon.

Archimedes made many contributions to geometry in his work on the areas of plane figures and on the areas of area and volumes of curved surfaces. His methods started the idea for calculus which was "invented" 2,000 years later by Sir Isaac Newton and Gottfried Wilhelm von Leibniz. Archimedes proved that the volume of an inscribed sphere is two-thirds the volume of a circumscribed cylinder. He requested that this formula/diagram be inscribed on his tomb.

His works (that survived) include:

• Measurement of a Circle
• On the Sphere and Cylinder
• On Spirals
• The Sand Reckoner

The Roman's highest numeral was a myriad (10,000). Archimedes was not content to use that as the biggest number, so he decided to conduct an experiment using large numbers. The question: How many grains of sand there are in the universe? He made up a system to measure the sand. While solving this problem, Archimedes discovered something called powers. The answer to Archimedes' question was one with 62 zeros after it (1 x 10⁶²)..

When numbers are multiplied by themselves, they are called powers.

Some powers of two are:

1 = 0 power=2⁰

2 = 1^st power=2¹

2 x 2 = 2^nd power (squared)=2²

2 x 2 x 2= 3^rd power (cubed)=2³

2 x 2 x 2 x 2= 4^th power=2⁴

There are short ways to write exponents. For example, a short way to write 81 is 3⁴.This is read as three to the fourth power.

• On Plane Equilibriums
• On Floating Bodies

This problem was after Archimedes had solved the problem of King Hiero's gold crown. He experimented with liquids. He discovered density and specific gravity.