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 = 1st power=21
2 x 2 = 2nd power (squared)=22
2 x 2 x 2= 3rd power (cubed)=23
2 x 2 x 2 x 2= 4th 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.
