Archimedes father of maths

1. ARCHIMEDES
Father of MATHEMATICS
BY : KESHAV JINDAL
CLASS AND SEC : 9TH E

2. BIOGRAPHY
 Archimedes, (born c. 287 B.C., Syracuse, Sicily [Italy]—died 212/211 B.C.,
Syracuse), the most famous mathematician and inventor in ancient Greece.
 Archimedes probably spent some time in Egypt early in his career, but he
resided for most of his life in Syracuse, the principal Greek city-state in
Sicily, where he was on intimate terms with its king, Hieron .
 Archimedes published his works in the form of correspondence with the
principal mathematicians of his time, including the Alexandrian
scholars Conon of Samos and Eratosthenes of Cyrene.
 He played an important role in the defense of Syracuse against the siege
laid by the Romans in 213 BCE by constructing war machines so effective
that they long delayed the capture of the city.
 When Syracuse eventually fell to the Roman general Marcus Claudius
Marcellus in the autumn of 212 or spring of 211 BCE, Archimedes was killed
in the sack of the city.

3.  Archimedes, the greatest mathematician of antiquity, made
his greatest contributions in geometry. His methods
anticipated the integral calculus 2,000 years before Newton
and Leibniz. He was the son of the astronomer Phidias and
was close to King Hieron and his son Gelon, for whom he
served for many years.
 In the 3rd Century BC, Archimedes: invented the sciences of
mechanics and hydrostatics. discovered the laws of levers and
pulleys, which allow us to move heavy objects using small
forces. invented one of the most fundamental concepts
of physics – the center of gravity.

4. Inventions of Archimedes
in physics

5. Archimedes principle
 Archimedes’ principle, physical law of buoyancy, discovered by the
ancient Greek mathematician and inventor Archimedes, stating that
any body completely or partially submerged in a fluid (gas or liquid)
at rest is acted upon by an upward, or buoyant, force, the magnitude
of which is equal to the weight of the fluid displaced by the body. The
volume of displaced fluid is equivalent to the volume of an object
fully immersed in a fluid or to that fraction of the volume below the
surface for an object partially submerged in a liquid. The weight of
the displaced portion of the fluid is equivalent to the magnitude of the
buoyant force. The buoyant force on a body floating in a liquid or gas
is also equivalent in magnitude to the weight of the floating object
and is opposite in direction; the object neither rises nor sinks. For
example, a ship that is launched sinks into the ocean until the weight
of the water it displaces is just equal to its own weight. As the ship is
loaded, it sinks deeper, displacing more water, and so the magnitude
of the buoyant force continuously matches the weight of the ship and
its cargo.

6. ARCHIMEDES SCREW
• A large part of Archimedes' work in engineering probably arose from fulfilling the
needs of his home city of Syracuse. The Greek writer Athenaeus of
Naucratis described how King Hiero II commissioned Archimedes to design a
huge ship, the Syracusia, which could be used for luxury travel, carrying supplies,
and as a naval warship. The Syracusia is said to have been the largest ship built
in classical antiquity. According to Athenaeus, it was capable of carrying 600
people and included garden decorations, a gymnasium and a temple dedicated to
the goddess Aphrodite among its facilities. Since a ship of this size would leak a
considerable amount of water through the hull, the Archimedes' screw was
purportedly developed in order to remove the bilge water. Archimedes' machine
was a device with a revolving screw-shaped blade inside a cylinder. It was turned
by hand, and could also be used to transfer water from a low-lying body of water
into irrigation canals. The Archimedes' screw is still in use today for pumping
liquids and granulated solids such as coal and grain. The Archimedes' screw
described in Roman times by Vitruvius may have been an improvement on a
screw pump that was used to irrigate the Hanging Gardens of Babylon. The
world's first seagoing steamship with a screw propeller was the SS Archimedes,
which was launched in 1839 and named in honor of Archimedes and his work on
the screw.

7. Invention of Archimedes
in mathematics

8. Measurement of 3d shapes
• There are nine extant treatises by Archimedes in Greek. The principal results
in On the Sphere and Cylinder (in two books) are that the surface area of
any sphere of radius r is four times that of its greatest circle (in modern
notation, S = 4πr2) and that the volume of a sphere is two-thirds that of the
cylinder in which it is inscribed (leading immediately to the formula for the
volume, V = 4/3πr3). Archimedes was proud enough of the latter discovery to
leave instructions for his tomb to be marked with a sphere inscribed in a
cylinder. Marcus Tullius Cicero (106–43 BCE) found the tomb, overgrown with
vegetation, a century and a half after Archimedes’ death.
• Measurement of the Circle is a fragment of a longer work in which π (pi),
the ratio of the circumference to the diameter of a circle, is shown to lie
between the limits of 3 10/71 and 3 1/7. Archimedes’ approach to determining
π, which consists of inscribing and circumscribing regular polygons with a large
number of sides, was followed by everyone until the development of infinite
series expansions in India during the 15th century and in Europe during the
17th century. That work also contains accurate approximations (expressed as
ratios of integers) to the square roots of 3 and several large numbers.