archimedes his life and history

1. 3RD NATIONAL
CONFERENCE ON
MATHEMATICS
CONDUCTED BY : N.A.M.T

2. THE MAN WHO DARED
TO MOVE THE EARTH
PAPER PRESENTER:SANJEEV TUMMALA
SRI PRAKASH SYNERGY SCHOOL
PEDDAPURAM, A.P
E-MAIL: sanjeevt2010ind@gmail.com

3. “give me a place to stand
and I will move the earth”

4. ARCHIMEDES
THE MAN WHO DARED
TO MOVE THE EARTH

5. BIOGRAPHY
 Archimedes was born
around 287 B.C. in the
Greek city-state of
Syracuse on the island of
Sicily.
 He died around 212 B.C.
at the age of 75.
 He is a Greek
mathematician, engineer,
inventor, physicist, and
astronomer
 He was the son of
Phidias, an astronomer.

6. BIOGRAPHY
• According to Plutarch,
Archimedes came
from the same royal
family as the city’s
ruler, King Hieron II.
• Archimedes stayed in
Syracuse his whole
life, except for the
time when he went to
Alexandria.

7. BIOGRAPHY
• It was said that while he
was in Alexandria, he
studied with the pupils of
Euclid and became
friends with Conon of
Samos and with
Eratosthenes.
• Upon his return to
Syracuse from Egypt, he
devoted his life to the
study of mathematics.

8. BIOGRAPHY
• It seemed that it was
the devotion to Hieron
that induced
Archimedes to divert
his mathematical
studies to his
engineering skills.
• In fact, many of his
inventions were
created at Hieron’s
request.

9. BIOGRAPHY
• He also invented
various war machines
in defending his city
against the Romans.
• Because of these
machines, Roman
soldiers were in
abject terror and
refused to advance.

10. BIOGRAPHY
• When the defenders, had
feasted and drank their fill of
a religious festival, pro-
Roman sympathizers inside
the city directed the enemy to
a weak point in the walls.
Marcellus gave explicit orders
to his officers that the life and
household of Archimedes
should be spared; but before
they could locate the great
scientist, he had been slain
by a common soldier.

11. BIOGRAPHY
• Accounts of his death has
been told in various forms:
– Traditional Story
• He was absorbed in a
geometrical problem whose
diagram was drawn in the
sand. As the shadow of an
approaching Roman soldier
fell over his diagrams, the
agitated mathematician
called out, “Don’t disturb my
circles!” The soldier,
insulted at having orders
thus given to him, retaliated
by drawing his sword

12. Archimedes being killed by a roman soldier

13. DISCOVERIES and
INVENTIONS

14. MATHEMATICAL
CONTRIBUTION
OF ARCHIMEDES

15. MEASUREMENT OF A CIRCLE
• Archimedes was the first one to precisely
calculate the value of pi. He accomplished
this by finding the areas of 2 polygons: the
polygon that was inscribed inside the
circle, and the polygon in which a circle
was circumscribed.

16. MEASUREMENT OF A CIRCLE
• Archimedes didn’t calculate the exact
value of pi, but rather came up with a very
close approximation – he used 96-sided
polygons to come up with a value that fell
between 3.1408 and 3.14285

17. ON SPHERE AND CYLINDER
With cylinder circumscribing a sphere, he
showed that the surface area of a sphere
is four times that of a great circle. He also
finds the area of any segment of a sphere
and shows that the volume of a sphere is
2/3 the volume of a circumscribed
cylinder.

18. THE SAND RECKONER
• The Sand Reckoner (Psammites) is a work
by Archimedes in which he set out to determine an
upper bound for the number of grains of sand that fit
into the universe. In order to do this, he had to
estimate the size of the universe according to the
contemporary model, and invent a way to talk about
extremely large numbers. The work, also known in
Latin as Archimedis Syracusani Arenarius &
Dimensio Circuli, which is about 8 pages long in
translation, is addressed to the Syracusan king Gelon
II (son of Hiero II), and is probably the most accessible
work of Archimedes; in some sense, it is the
first research-expository paper.

19. • There are some people , king Gelon for instance
who think that the number of grains of sand is
infinite in multitude and Archimedes of course is
an exception, here they mean not only the sand
grains in Syracuse but in the entire universe.
• Even though he set out to count the grains of
sand in the universe, the Greek system of
counting was not easy to play with and hence he
had to devise a new system of counting.
THE SAND RECKONER

20. THE SAND RECKONER
• Greek mathematical notation was not
positional; it utilized many symbols and
was cumbersome to work with.

21. • First, Archimedes had to invent a system of naming large
numbers. The number system in use at that time could
express numbers up to a myriad (10,000), and by utilizing
the word "myriad" itself, one can immediately extend this
to naming all numbers up to a myriad myriads (108).
• Archimedes called the numbers up to 108 "first numbers"
and called 108 itself the "unit of the second numbers".
Multiples of this unit then became the second numbers,
up to this unit taken a myriad-myriad times, 108·108=1016.
• This became the "unit of the third numbers", whose
multiples were the third numbers, and so on. Archimedes
continued naming numbers in this way up to a myriad-
myriad times the unit of the 108-th numbers, i.e., .
• After having done this, Archimedes called the numbers he
had defined the "numbers of the first period", and called
the last one, , the "unit of the second period".
THE SAND RECKONER

22. THE SAND RECKONER
• The "M" is a myriad, and represents 10,000. The
Greek word is murious (uncountable, pl. murioi). The
Romans converted this to myriad.
• The Sand Reckoner is a remarkable work in which
Archimedes proposes a number system that uses
powers of a myriad (base 100,000,000) and is capable
of expressing numbers up to 8 x 1063 in modern
notation.
• He argues in this work that this number is large
enough to count the number of grains of sand which
could be fitted into the universe.

23. ARCHIMEDEAN SPIRAL
• This spiral was studied by Archimedes in
about 225 BC in a work On Spirals. It had
already been considered by his
friend Conon.
• Archimedes was able to work out the
lengths of various tangents to the spiral. It
can be used to trisect an angle and square
the circle.

24. OTHER
ACCOMPLISHMENTS

25. BOUYANCY
King Hieron II had given the goldsmith a
particular amount of gold to melt down and
make into a crown. When the crown was
made and returned to the king, the king
was suspicious that the goldsmith had
stolen some of the gold and replaced it
with an equal weight of silver.
The king turned to Archimedes for help…

26. BOUYANCY
Archimedes happened to go to
the bath, and on getting a tub
observed that the more water ran
out over the tub. As this pointed
out the way to explain the case in
question, he jumped out of the tub
and rushed home naked, crying
with a loud voice that he had
found what he was seeking; for
he, as he ran, shouted repeatedly
in Greek, ‘EUREKA, EUREKA,’
meaning “I have found it.”

28. THE LAW OF LEVER
• Archimedes did not invent the lever, however he
gave an explanation about the principle
• Earlier descriptions of the lever are found in
the Peripatetic school of the followers of Aristotle.
• According to Pappus of Alexandria, Archimedes'
work on levers caused him to remark: "Give me a
place to stand on, and I will move the Earth.“
• Plutarch describes how Archimedes
designed block-and-tackle pulley systems,
allowing sailors to use the principle of leverage to
lift objects that would otherwise have been too
heavy to move.

30. ARCHIMEDES SCREW
• A machine for raising water, allegedly
invented by Archimedes for removing
water from the hold of a large ship.
One form consists of a circular pipe
enclosing a helix and inclined at an
angle of about 45 degrees to the
horizontal with its lower end dipped in
the water; rotation of the device
causes the water to rise in the pipe.
Other forms consist of a helix
revolving in a fixed cylinder or a
helical tube wound around a shaft.

31. ARCHIMEDES SCREW
• Modern screw pumps, consisting of
helices rotating in open inclined troughs,
are effective for pumping sewage in
wastewater treatment plants. The open
troughs and the design of the screws
permit the passage of debris without
clogging.

32. • Modern Archimedes' screws which have replaced some of the
windmills used to drain the polders at Kinderdijk in the
Netherlands

33. DEATH RAY
•The death ray involves a
simple principle of setting
up fire by focusing of light
onto the desired object.
•Archimedes allegedly set
up an entire fleet of Roman
ships by using parabolic
reflectors
•Each mirror is capable of
generating heat of up to
6000K (surface temp of
sun)

34. GIANT CLAW
The Claw of Archimedes is a
weapon that he is said to have
designed in order to defend
the city of Syracuse. Also
known as "the ship shaker,"
the claw consisted of a crane-
like arm from which a large
metal grappling hook was
suspended. When the claw
was dropped onto an attacking
ship the arm would swing
upwards, lifting the ship out of
the water and possibly sinking
it.

35. CATAPULTS
• A catapult is a ballistic device
used to launch a projectile a
great distance without the aid
of explosive devices—
particularly various types of
ancient and medieval siege
engines. Although the catapult
has been used since ancient
times, it has proven to be one
of the most effective
mechanisms during warfare.
The word 'catapult' comes from
the Latin 'catapulta', which in
turn comes from the Greek
itself from , "downwards“ "to
toss, to hurl". Catapults were
invented by the ancient
Greeks.

36. LEGACY

37. •Galileo praised Archimedes many times, and referred to him as
a "superhuman". Leibniz said "He who understands Archimedes
and Apollonius will admire less the achievements of the
foremost men of later times."
•There is a crater on the Moon named Archimedes (29.7° N,
4.0° W) in his honour, as well as a lunar mountain range,
the Montes Archimedes (25.3° N, 4.6° W).[
•The Fields Medal for outstanding achievement in mathematics
carries a portrait of Archimedes, along with a carving illustrating
his proof on the sphere and the cylinder. The inscription around
the head of Archimedes is a quote attributed to him which reads
in Latin: "Transire suum pectus mundoque potiri" (Rise above
oneself and grasp the world).
•Archimedes has appeared on postage stamps issued by East
Germany (1973), Greece (1983), Italy (1983), Nicaragua (1971),
San Marino (1982), and Spain (1963).

38. Fields medal carrying a portrait of Archimedes