Archimedes life and history

archimedes his life and history

1. 3 rd 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: [email protected]

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 o n 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 (10 8 ). Archimedes called the numbers up to 10 8  "first numbers" and called 10 8  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, 10 8 ·10 8 =10 16 . 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 10 8 -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 10 63  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.”

27. 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.

28. 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.

29. 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.

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

31. 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)

32. 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.

33. 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.

34. legacy

35. 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).

36. Fields medal carrying a portrait of Archimedes

37. Any queries ?

38. Thank you