Arc Hi Me Des 2

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A r c h i m e

d e s o f S i c i l y

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ArchimedesArchimedesgrew up in the

Greek city-state of

Syracuse onthe island of

Sicily.

His father was



EARLY LIFE

Archimedes is known to bea relative of Hiero II, whowas the king of Syracuseduring Archimedes' life.

Hiero and Archimedeswere very close friends.However, nothing else is

known about any other



Archimedes had a good

education as a boy, for theGreeks loved knowledge andsent their sons to schools to

become knowledgeableGreek citizens. Some of thesubjects that he studied asa boy were poetry, politics,astronomy, mathematics,

music, art, and military

continuation. . .



gen us n ma swell known,

Archimedes wasalso anastronomer and

madecontributions toscience as well.

Archimedes built amachine that

helped him to

continuation. . .



THE ARCHIMEDEAN SCREW

One such story recounts how aperplexed King Hiero was unableto empty rainwater from the hull

of one of his ships. The Kingcalled upon Archimedes for

assistance. Archimedes' solution

was to create a machineconsisting of a hollow tube

containing a spiral that could be

turned by a handle at one end.



This invention of Archimedeswas also used for irrigation.

The screw was like a handpump that was used to spraywater directly from the Nile

onto the fields.



THE PUZZLE OF THE KING’SCROWN

King Hiero had commissioned anew royal crown for which he

provided solid gold to the

goldsmith. When the crownarrived, King Hiero was suspiciousthat the goldsmith only used some

of the gold, kept the rest forhimself and added silver to make

the crown the correct weight.

Archimedes was asked todetermine whether or not the



Archimedes was perplexedbut found inspiration whiletaking a bath. He noticed

that the full bath

overflowed when helowered himself into it,

and suddenly realized thathe could measure the

crown's volume by theamount of water it

displaced. He knew thatsince he could measure

the crown's volume, all he



Archimedes was soexuberant about his

discovery that he ran

down the streets of

Syracuse naked shouting,

"Eureka!" which meant

"I've found it!" in Greek.

NOW, this discovery isknown as the Principle of

Buoyancy (often called

Archimedes’ Principle)



It was his inventions of mechanical

contrivances and war machines – such aslevers, catapults, pulleys, movable poles

for dropping heavy weights on enemyships and cranes with hooks to raise and

smash enemy ships – that made himfamous. It’s even claimed that he used

giant magnifying glasses to set the

enemy vessels on fire.

Archimedes and the Defense of

Syracuse



After using a compound pulley to move avery heavy ship, Archimedes is reported

to have said, “Give me a place to stand onand I will move the earth”.



Altogether ten treatises of Archimedeshave survived, three devoted to planegeometry –

• Measurement of a Circle• Quadrature of the Parabola and Onspirals• Two to Three-dimensional geometry –On the Sphere and Cylinder and OnConoids and Spheroids• One on arithmetic – The Sand

Reckoner •

TEN TREATISES OFARCHIMEDES



A CONTRIBUTION TO MATHEMATICS

One of the easiest to visualisecontribution of Archimedes was the

method he used to find anapproximation for π using

circumscribed and inscribed regularpolygons of a circle. This appears as

Proposition 3 of Measurement of aCircle. What follows is a simplifiedversion of what Archimedes did.



Archimedes started with a circle of unit radius:

(What the unit usedwas is not important.

It could be 1 inch, or 1centimetre, or 1anything. Theimportant thing is

that all lengths will bemeasured using thesame unit.)



He then inscribed a regular hexagon inside the circle:

By comparingthe

circumference of the circle with

the perimeter of the hexagon, he

concluded that π > 3



Next, he inscribed a regular dodecagoninside the circle:

Again bycomparing the

circumference of the circle with

the perimeter of the dodecagon,

he concludedthat π > 3 1/10

(or moreprecisely

3.10597)



He then doubled the number of sidesof the regular polygon to 24, then 48,

then 96; each time obtaining betterand better approximations for π.

Using this method, he concluded that π > 3 10/71 (or 3.140845 as a

rounded decimal).



Archimedes then repeated the wholeprocess, but this time usingcircumscribed regular polygons:

By following a similar method, comparing the

circumference of the circle with the perimeters of regular

polygons with 6, 12, 24, 48 and eventually 96 sides, he

concluded that π < 3 1/7 (or 3.142857 as a rounded

decimal).



Taking the two resultstogether, Archimedesgave the result that3 10/71 < π < 3 1/7

This was a remarkablyaccurate result for its

time.



ARCHIMEDES’ CLAW

Archimedes' claw was invented to defend the

city of Syracuse. Known as the 'ship-shaker', it

is shaped like a crane arm, from which a largemetal hook was balanced. When the claw was

dropped on an attacking ship, it would lift the

ship by swinging the arm upwards and then sink

the ship.



DEATH RAY

There have beeM manydoubts about Archimedesweapon of the death Ray.

However in 2005 theDeath Ray was provedand tested by a

University class (MIT).Using over one hundred

mirrors,they made adummy profile of shipwith 5 inch thick wood

which ignited after

focusing all the mirrors toa s ecific oint on the



THE ARCHIMEDEANSOLIDS

TruncatedTetrahedron

The first is a figureof eight bases,being contained byfour triangles and

four hexagons.

Cuboctahedron After this comethree figures of

fourteen bases, thefirst contained byeight triangles andsix squares,

Truncated the second by six



Truncated Cubeand the third by eighttriangles and six octagons.

Rhombicuboctahedron

After these come twofigures of twenty-sixbases, the first containedby eight triangles andeighteen squares,

Truncated

Cuboctahedron

the second by twelve

squares, eight hexagonsand six octagons.

Icosidodecahed

ron

After these come three

figures of thirty-two



Truncated Icosahedronthe second bytwelve pentagonsand twentyhexagons,

TruncatedDodecahedron

and the third bytwenty trianglesand twelvedecagons.

Snub Cube After these comesone figure of thirty-eight bases,

being contained by

http://www.ics.uci.edu/~eppstein/junkyard/bucky.html






Rhombicosidodecahedron After this come twofigures of sixty-twobases, the firstcontained by twentytriangles, thirty squares

and twelve pentagons,

TruncatedIcosidodecahedr

on

the second by thirtysquares, twenty

hexagons and twelvedecagons.

Snub

Dodecahedron

After these there comes

lastly a figure of ninety-two bases, which is



DEATH OFARCHIMEDES

God created few men to have genius,Archimedes was one of those men. He

made many discoveries and figuredout many of the scientific principlesthat scientists now consider to be

some of the basic principles of mathand science. However, even famous

men can have insignificant endings.In 212 the Romans had gained controlof Syracuse after a long siege.



Archimedes was athis home totallyabsorbed in his

work.

His last recordedwords of are these,

"Noli turbanecirculos meos!"

This means, "Do not

disturb my circles!"



Archimedes wasworking on amathematical

problem and was so

absorbed in it that hebecame annoyed with

a certain Romansoldier who stepped

onto the cicles thathe was drawing. ThisRoman soldier had

come to bringArchimedes before



When Archimedes said this to thesoldier, the soldier became so

angry that he drew his sword and

killed Archimedes. When thesoldier's general heard what hehad done, the soldier was

executed. This was how the great

genius Archimedes met his end. Yet his work lives on today, and

we are the benefactors of hislabors in the fields of

mathematics, science, and





THE TOMB OFARCHIMEDES

carried a sculptureillustrating his favorite

mathematical proof,

consisting of a sphereand a cylinder of the

same height anddiameter. Archimedes

had proved that thevolume and surfacearea of the sphere aretwo thirds that of thecylinder including its

bases.



THANK YOU !



http://www.hyperhistory.net/apwh/bios/b2archimedes_p1ab.htm

http://www.archimedespalimpsest.org/archimedes_bio1.html

http://www.docstoc.com/docs/526491/Archimedes-Contributions-to-Math

http://en.wikipedia.org/wiki/Archimedes

http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html

http://web01.shu.edu/projects/reals/history/archimed.html

REFERENCES:



http://www.docstoc.com/docs/526491/Archimedes-Contributions-to-Mathematics







http://www.docstoc.com/docs/526491/Archimedes-Contributions-to-Mathematics



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Arc Hi Me Des 2