Essay, Research Paper: Archimedes

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.