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
2 8 7 B C
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2 1 2 B C
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ArchimedesArchimedesgrew up in the
Greek city-state of
Syracuse onthe island of
Sicily.
His father was
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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
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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. . .
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gen us n ma swell known,
Archimedes wasalso anastronomer and
madecontributions toscience as well.
Archimedes built amachine that
helped him to
continuation. . .
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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.
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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.
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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
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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
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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)
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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
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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”.
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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
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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.
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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.)
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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
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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)
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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).
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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).
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Taking the two resultstogether, Archimedesgave the result that3 10/71 < π < 3 1/7
This was a remarkablyaccurate result for its
time.
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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.
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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
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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
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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
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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
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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
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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.
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Archimedes was athis home totallyabsorbed in his
work.
His last recordedwords of are these,
"Noli turbanecirculos meos!"
This means, "Do not
disturb my circles!"
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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
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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
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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.
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THANK YOU !
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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: