Archimedes was one of the greatest mathematicians and inventors of his

time. He was born in Syracuse, Sicily around the year 287BC. Archimedes

was educated in Alexandria, Egypt, but spent most of his life in Sicily. When

in Sicily, he stayed in or near Syracuse and did nothing but experiment and

research.

Archimedes made many contributions to mathematics. One of the

more important discoveries Archimedes made was he found a way to

measure the areas and volumes of objects that are irregularly shaped.

Archimedes used a way of discovery, based on weighing infinitely thin slices

of objects, to find the volumes and areas figures emerging from conic

sections. He formulated ways to measure the area of a curved surface and

he found a way to determine the area and volume of objects like cylinders

and paraboloids that are solid and bounded by curved surfaces. He also

proved that "the volume of a sphere is two-thirds the volume of a

circumscribed cylinder". Archimedes took so much pride in this discovery

that he requested that a representation of this formula be inscribed on his

tomb. He is also known for his approximation of pi (p). His method for

finding the approximation was by "circumscribing and inscribing a circle

with regular polygons having ninety-six sides". Archimedes stated that the

value of p was between 31/7 and 310/71. Some of his other theorems concern

the centers of gravity of solids and plane figures. Remarkably, some of

Archimedes's methods anticipated many discoveries of modern science, such

as integral calculus. This is unusual because integral calculus wasn't

"invented" until two thousand years after Archimedes lived.

Among all the contributions Archimedes has made, he is most

recognized for what is now called Archimedes' Principle. Archimedes'

Principle is his theory on the weight of an object immersed in a liquid. This

theory states that "any object floating upon or submerged in a fluid is

buoyed upward by a force equal to the weight of the displaced fluid". If the

object is heavier than the surrounding fluid, it will sink. The opposite would

happen if the object were lighter. The buoyant force is brought about by the

fluid's weight. An immersed object that is lighter than the liquid will tend to

float because there is more pressure on the bottom of the object because as

the fluid gets deeper, the pressure increases. If the object and liquid weigh

the same, then the object will stay motionless because it will be in

equilibrium. Another use of Archimedes' Principle is to find out the density

and volume of an object with an extremely irregular shape. First, the object

would be weighed in the air, then in water. The volume of the water

displaced is found by getting the difference of the weights. Since the

volume of displaced water is equal to the volume of the object, the density

can be found. To find the density, divide the weight by the volume.

Archimedes wasn't only a mathematician, but also an inventor. One of

his most notable inventions is the screw pump. Archimedes invented this

machine during his stay in Egypt. The Archimedes' screw, as it is sometimes

called, is designed to lift water from a stream and pump it to fields in a

higher area. The Archimedes' screw was also used by the Romans to build

expansive aqueduct systems, some of which are still being used. The screw

pump is a cylinder containing a wide thread screw and to use it, you would

put it on an incline with one end in the stream. As you turned the screw, the

water was raised higher. During the Roman conquest of Sicily, he helped

prepare a defense against the Romans. Archimedes made several inventions

at this time. They included the catapult, the compound pulley, and a mirror

system to focus the sun's light onto enemy ships to ignite them. Archimedes'

theories led to the later inventions of the hydrometer and the lever.

Despite his extraordinary efforts, Syracuse was taken over by the

Romans and Archimedes was killed. He died in the year 212BC. and was

believed to have been killed by a soldier who interrupted Archimedes while

calculating something in the sand. It is said that he offended the soldier by

remarking, "Do not disturb my diagrams.". Archimedes wrote several works

on mathematics. The surviving ones are Sphere and Cylinder, Measurement

of the Circle, Spirals, The Sand Reckoner, Quadrature of the Parabola, Plane,

Equilibriums, Conoids and Spheroids, and Floating Bodies.