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 10^{62})..

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

Some powers of two are:

1 = 0 power=2^{0}

2 = 1^{st} power=2^{1}

2 x 2 = 2^{nd} power (squared)=2^{2}

2 x 2 x 2= 3^{rd} power (cubed)=2^{3}

2 x 2 x 2 x 2= 4^{th} power=2^{4}

There
are short ways to write exponents. For example, a short way to write
81 is 3^{4}.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*.