61. Chapter 16: Archimedes The most illustrious mathematician of this later age was also the mechanical wizard of antiquity, archimedes of syracuse. Among http://www.anselm.edu/homepage/dbanach/arch.htm

Selections from Julia E. Diggins, String, Straightedge, and Shadow Viking Press, New York , 1965. (Illustrations by Corydon Bell) 16. A ROYAL ROAD, AFTER ALL During the 4th century B.C., Greek geometry burst its bonds and went on to the tremendous discoveries of the "age of giants." And Greek culture, too, burst from the mainland of Hellas and spread to most of the eastern Mediterranean. Both developments were connected with the romantic figure of Alexander the Great. After Plato's time, teachers and alumni from the Academy had gone on to found schools of their own. In particular, Plato's most famous associate, the great philosopher Aristotle, had set up the Lyceum in Athens, and started the systematic classification of human knowledge. And Aristotle's most renowned pupil was the warrior king Alexander of Macedon, who tried to conquer the world. In thirteen years, Alexander extended his rule over Greece proper, and Ionia, Phoenicia, Egypt, and the vast Persian domains as far as India. Then he died, and his empire broke up. But throughout those far-flung lands, he had founded Greek cities and planted the seeds of Greek civilization-the Greek language, Greek art, and, of course, Greek mathematics. Mathematicians traveled with his armies. And there is even a

62. Greek Scientists Archimedes, One of the most original thinkers of Antiquity was archimedes of syracuse (287212 BC). Because our approach to physics http://www.livius.org/gi-gr/greeks/scientists.html

home index ancient Greece portrait gallery Greek scientists Authors Historians Philosophers Politicians Scientists We know almost nothing about Thales of Miletus . Later generations told many anecdotes about this wise man, but it is difficult to verify the reliability of these stories. What seems certain is that he predicted the solar eclipse of 28 May 585, which was remembered because the Lydian king Alyattes and the Median king Cyaxares were fighting a battle on that day. Another reliable bit of information is that he did some geometrical research, which enabled him to measure the pyramids. However, his most important contribution to physics and philosophy is his attempt to give non-religious, rational explanations for physical phenomena. Behind the phenomena was not a catalogue of deities, but one single, original principle. Although his hypothesis that this principle was water is rather unfortunate, his idea to look for deeper causes was the true beginning of philosophy and science. One of the solutions to the problem postulated by Parmenides , was the hypothesis of Democritus of Abdera that matter was made up from atoms. There was no real evidence for this idea (which was not completely new), but is explained why change was possible. The atoms were always moving and clustering in various, temporary combinations. Therefore, things seemed to change, but 'not being' never changed into 'being'. (It was assumed that 'not being' was a vacuum, which means that it is in fact not a 'not being' because a vacuum exists in at least four dimensions.) The consequence of this idea is that we are allowed to use our senses, although Democritus warns us to be careful.

63. Archimedes Palimpsest Christie s Images, Ltd., 1998, It is nonetheless priceless, because it contains a compendium of mathematical treatises by archimedes of syracuse. http://www.thewalters.org/archimedes/palimpsest1.html

The Archimedes Palimpsest now in the care of the Walters Art Gallery is a manuscript... a rather small and unprepossessing manuscript. It has been damaged by mold, fire, and abuse. Christie's Images, Ltd., 1998 Christie's Images, Ltd., 1998 It is nonetheless priceless, because it contains a compendium of mathematical treatises by Archimedes of Syracuse. Most importantly, it includes the only copy of the treatise Method of Mechanical Theorems , in which Archimedes explained how he drew upon mechanical means to elucidate his mathematical theorems. It is also the only source in the original Greek for the treatise On Floating Bodies , in which Archimedes explores the physics of flotation and explains the formal proof for the principle of specific gravity.

64. Archimedes Archimedes AKA archimedes of syracuse Type Human Male Current Occupation Retired Former Occupations Military Advisor to the Greek King, Inventor http://www.thefixsite.com/travelers/archimedes.html

Archimedes AKA: Archimedes of Syracuse Type: Human Male Current Occupation: Retired Former Occupations: Military Advisor to the Greek King, Inventor, Mathematician Marital Status: Single Strength: Below Average Endurance: Superior Intelligence: Legendary Cunning: Average Education: Legendary Bravery: Above Average Speed: Average Charm: Above Average Preferred Weapons: his amazing intelligence Height: Weight: 140 lbs. Background: Archimedes was a famous Greek inventor that held the Romans at bay for months during the Battle of Syracuse with his amazing inventions. He discovered many things, including some of the basic theorums of geometry and mathematics. Career Highlights: Archimedes built many inventions, but his greatest was a time machine made from wood. Career Mishaps: The old inventor traveled to the far future of the 11th century to find futuristic warriors to help fight at the battle of Syracuse, but he failed to take into account the effect it would have on future history (see issue #9). Most redeeming quality: He's brilliant.

65. Archimedes Archimedes From the a href=http//www.wikipedia.org/wiki/Archimedes target=_blank wikipedia /a p archimedes of syracuse (circa 287212 BC), was a Greek http://www.abacci.com/books/authorDetails.asp?authorID=799

66. Armadillo City Search Engine - Address Search, Phone, Name, Job, Dallas Internet .. http//www.suathletics.com/ 6. Archimedes archimedes of syracuse. Born .. Archimedes was a native of Syracuse, Sicily. http http://www.texaspanhandleplains.com/search/index.php?REQ=Syracuse

67. Re: Archimedes And Diop of Sicily writes What is so amazing is that they (the miners) pump the water entirely by means of Egyptian screws that archimedes of syracuse invented during http://www.theafrican.com/Magazine/Athena/15.htm

Date: Thu, 23 May 1996 13:38:03 -0400 To: Athena Discuss Subject: Re: Archimedes and Diop FISHERGM@jmu.edu wrote: Contents Previous Next

68. Archimedes Of Syracuse : Updated 05-27-04 Gears EDS Curriculum Compressed Air History The Science of Pressure An investigation that was resolved over centuries. archimedes of syracuse Approximately 287212 BCE Archimedes http://www.nethorde.com/syracuse/archimedes-of-syracuse.html

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69. ARCHIMEDES POLYGON METHOD FOR CALCULATING THE VALUE OF Pi archimedes of syracuse (Born 287 BC 212 BC) Give me but one firm spot on which to stand, and I will move the earth. . archimedes of syracuse (ca. http://lhs.lexingtonma.org/Teachers/Trainor/pi/pi.htm

ARCHIMEDES' POLYGON METHOD FOR CALCULATING THE VALUE OF Pi "If a person does not keep pace with their companions, perhaps it is because he hears a different drummer" Henry David Thoreau ARCHIMEDES OF SYRACUSE (Born 287 B.C. - 212 B.C.) "Give me but one firm spot on which to stand, and I will move the earth." Archimedes of Syracuse (ca. 287-212 B.C.) was an ingenious mathematician, physicist, engineer and inventor. He was the first to develop a method for calculating Pi to a useful degree of accuracy. Pi is equal to the circumference (C) of a given circle divided by the diameter (D) of the circle (Pi = C/D). The diameter is a straight line and consequently easy to measure, but the circumference is a curved line therefore, it's measure could only be poorly estimated. Archimedes solved the curved line measuring problem by first constructing an inscribed regular polygon within the a given circle and adding up the measure of the sides (the perimeter). He clearly understood the perimeter's (P) measure would be less than the circle's circumference. Therefore, he constructed a second regular polygon circumscribed on the outside of the circle. This polygon's perimeter measure would be greater than the circle's circumference. He then substituted the average of the two polygon's perimeters as the circle's circumference "C". His equation was Pi = (polygon's perimeter didvided by polygon's diameter) or =P/D. He measured the diameter "D" of his constructed circle. Using a 96 sided regular polygon, his calculations for Pi using the formula, Pi = C/D produced the following results:

70. Information Headquarters: Archimedes Archimedes. archimedes of syracuse (circa 287 BC 212 BC), was a Greek mathematician, astronomer, physicist and engineer. Discoveries http://www.informationheadquarters.com/Physics/Archimedes.shtml

PharmacyHeadquarters SearchHeadquarters - Need a Payday Loan Talk politics at WashingtonTalk Archimedes How to Physics History Companies ... History of Computing This content from Wikipedia is licensed under the GNU Free Documentation License Links HOME Help build the worlds largest free encyclopedia

71. Mathcards.com - Mathematician Trading Cards archimedes of syracuse. The images and biographical content for the Math Cards on this site are used with permission from the http://www.mathcards.com/index.jsp?id=5

72. :: Ez2Find :: Archimedes URL http//tqjunior.thinkquest.org/4116/History/archimedes.htm?tqskip=1; archimedes of syracuse Site Info - Translate - Open New Window Kids/Teens http://ez2find.com/cgi-bin/directory/meta/search.pl/Kids_and_Teens/School_Time/M

Guide : Archimedes Global Metasearch Any Language English Afrikaans Arabic Bahasa Melayu Belarusian Bulgarian Catala Chinese Simplified Chinese Traditional Cymraeg Czech Dansk Deutsch Eesti Espanol Euskara Faroese Francais Frysk Galego Greek Hebrew Hrvatski Indonesia Islenska Italiano Japanese Korean Latvian Lietuviu Lingua Latina Magyar Netherlands Norsk Polska Portugues Romana Russian Shqip Slovensko Slovensky Srpski Suomi Svenska Thai Turkce Ukrainian Vietnamese Mode All Words Any Word Phrase Results Timeout Depth Adult Filter Add to Favorites Other Search Web News Newsgroups Images Guides Archimedes ez2Find Home Directory Kids and Teens School Time ... Mathematicians : Archimedes Web Sites Archimedes [Site Info] [Translate] [Open New Window] [ Kids/Teens/Mature Teens ] - Provides a detailed biography, including a look at the times in which he lived, the importance of his discoveries, his life, and his death. Also includes a timeline. URL: http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html Archimedes [Site Info] [Translate] [Open New Window] [ Kids/Teens ] - Student-written profile introduces the thinker and his contributions to the world of math. URL: http://tqjunior.thinkquest.org/4116/History/archimedes.htm?tqskip=1

73. Archimedes Screw Diadorus Sicilus. men easily irrigate the whole of it by means of a certain instrument conceived by archimedes of syracuse, and which it gets it`s name http://www.wcnet.org/~dgburget/Archimedes/Ascrew2.htm

Archimedes screw The Archimedes screw was used to raise water up. It was used by turning the beam in the center. Many men have marvelled at the speed it lifts water.These are some quotes from them. Diadorus Sicilus "...men easily irrigate the whole of it by means of a certain instrument conceived by Archimedes of Syracuse, and which it gets it`s name because it has the form of a spiral or screw." Diadorus Sicilus " Most remarkadle of all, they draw off streams of water by the so-called Egyptian screws, which Archimedes of Syracuse invented when he went by ship to Egypt." Athenaeus of Naucratis " The bilge-water,even when it became very deep could easily be pumped out by one man with the aid of a screw, an invention of Archimedes." Home

74. Archimedes Essay Direct Essays.com - Over 101,000 Essays, Term Papers And Book R We would know more about his life if his biography, written by his friend Hercleide, had not been lost (archimedes of syracuse. groups). The informat. http://www.directessays.com/viewpaper/86628.html

Click HERE for Instant Access! • Acceptable Use Policy • Technical Support • Customer Service ... • Paper Counter Welcome to DirectEssays.com to over high quality This is a short summary of this paper! Already a member? Go here to log in and view the entire paper! Archimedes Approximate Word count = 1428 Approximate Pages = 6 (250 words per page double spaced) Want to view this paper along with other term papers, essays, and book reports? Instant access , single user memberships can be purchased online with a credit card or online check! Membership Plans Credit Card Check Phone 30 day membership (recurring billing) 30 day membership (non-recurring billing) 90 day membership (recurring billing) 180 day membership (non-recurring billing) Once you have registered for an Account, No refunds can be issued. Please make sure you look over the site before you purchase an account!!! JOIN BY CREDIT CARD JOIN BY ONLINE CHECK JOIN BY PHONE All papers are for research and reference purposes only!

75. Siege Of Syracuse Describes the role of archimedes and other key figures in the siege of syracuse during the Second Punic War, as well as accounts by Polybius, Livy, and Plutarch. http://www.mcs.drexel.edu/~crorres/Archimedes/Siege/Summary.html

I N T R O D U C T I O N Back to . . . Archimedes Home Page This section . . . Introduction Polybius Livy Plutarch Dio Cassius Hiero II BC Hannibal(?) (247-183? BC Hieronymos BC Marcellus (268-208 BC Archimedes (287?-212 BC ) planning the defenses of Syracuse A t the beginning of the third century BC , the Mediterranean basin was controlled by the Carthaginians in the west and the Greeks in the east. The Romans controlled only a small area around Rome, but were poised to march. They locked horns with Carthage in the First Punic War (264-241 BC ), during which they greatly expanded their territory, although they did not capture the city of Carthage itself. The Greek city of Syracuse, where Archimedes lived, initially supported Carthage. But early in the war Rome forced a treaty of alliance from Syracuse's king, Hiero II , that called for Syracuse to pay tribute and provide grain to the Romans. T he Romans and Carthaginians renewed their antagonisms in 218 BC , the beginning of the Second Punic War. Under Hannibal, Carthage gained the first round of victories, culminating in Hannibal's crossing of the Alps into Italy (218 BC ) and his defeat of the Romans at Cannae (216 BC ). Hannibal's successes in Italy helped convince many Syracusans that they were allied with the wrong side.

76. Archimedes Home Page sources, and illustrations of all aspects of archimedes life, including the siege of syracuse, the death of archimedes, archimedes tomb, archimedes screw http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html

I N F I N I T E S E C R E T S NOVA , the PBS television science series, examines Archimedes' ideas of the infinite found in an ancient manuscript. Check your local NOVA listings (USA). Detail of a painting by Jusepe de Ribera (Spanish 1591-1652) in the Museo del Prado (Madrid, Spain) 125 x 81 cm Enlargements: 352 x 480 pixels, 30K 1457 x 1985 pixels, 269K Spanish postage stamp: March 24, 1963 Scott Catalogue Number 1159 378 x 430 pixels, 56K 757 x 861 pixels, 208K This site is a collection of Archimedean miscellanea under continual development with the following contents . . . Timeline Siege of Syracuse Archimedes' Claw New! Death of Archimedes Tomb of Archimedes Burning Mirrors The Golden Crown Archimedes Screw Stomachion The Cattle Problem Archimedean Solids Spheres and Planetaria The Lever Royal Family of Syracuse Coins of Syracuse Books on Archimedes Archimedes Crater Stamps of Archimedes Pictures of Archimedes New! Quick facts about Archimedes . . . Born About 287 BC in Syracuse , Sicily. At the time Syracuse was an independent Greek city-state with a 500-year history.

77. Coins Of Arethusa . archimedes Home Page. This section . . . Below are illustrations of ancient Syracusan coins featuring the image of Arethusa, the patron nymph of syracuse. http://www.mcs.drexel.edu/~crorres/Archimedes/Coins/Arethusa.html

C O I N S . O F . A R E T H U S A Back to . . . Archimedes Home Page This section . . . Coins of Arethusa "Oh save me! Oh guide me! And bid the deep hide me, for he grasps me now by the hair!" S HELLEY Below are illustrations of ancient Syracusan coins featuring the image of Arethusa , the patron nymph of Syracuse. Arethusa was a naiad (a water nymph) who frolicked in the vicinity of Olympia and who was desired and pursued by the river-god Alpheios . She appealed for assistance from Artemis , goddess of the moon and the hunt and the protector of women (the Roman Diana). Aretemis transformed her into an underground stream emerging as a freshwater spring on the Sicilian island of Ortygia, the future site of Syracuse. Undaunted, Alpheios diverted his river's flow underground to follow Arethusa, and both of their waters now mingle eternally in the Fountain of Arethusa in Ortygia. Arethusa is sometimes identified with Artemis, and also with Persephone , the Spring goddess. Her image on coins is usually accompanied by dolphins, which were common in the sea around Ortygia in classical times. The coins of Arethusa are arguably the most beautiful minted by the ancient Greeks. Their rapid artistic development from the archaic types at the beginning of the fifth century B.C. to the masterpieces of

78. Archimedes And Syracuse archimedes AND syracuse. archimedes helped syracuse defend itself from being invaded by opposing countries and empires for many years. http://www.ga.k12.pa.us/academics/MS/8th/romanhis/Forum/1999/nickw/syracuse.htm

ARCHIMEDES AND SYRACUSE Along with his contributions listed above, Archimedes also helped the people of his home, Syracuse. Syracuse is where Archimedes was born, where he lived for most of his life, and where he was killed. Archimedes helped Syracuse defend itself from being invaded by opposing countries and empires for many years. He did this with many war tactics that he invented, such as burning mirrors (shown above). In this tactic, huge mirrors were positioned in a way that light from the sun reflected off of them and concentrated a powerful beam of sunlight that was redirected at enemy ships. This act would set the ships on fire. The Syracusians won many victories this way, without a battle. Also, many other victories were won with Archimedes's war tactics. Syracuse was a Greek city-state. It was known as the center of Greek culture. Archimedes lived in Syracuse for most of his life. It was also the home of other great Greek cultural figures such as Arschylus, Pindar, and Theocritus, who all live before Archimedes's time. Syracuse, the great city-state, defeated Athens in 414 B.C. However in 212 B.C., Syracuse suffered a great loss, which included the death of one of the greatest minds ever in the world. HOME

79. Welkom Op Deze Website ! ARCHIMEDES VAN SYRACUSE http://members.tripod.lycos.nl/Archimedes/

80. Archimedes archimedes was born 287 BC in syracuse, Sicily. archimedes was buried syracuse, where he was born, were he grew up, where he worked, and where he died. http://www.crystalinks.com/archimedes.html

Archimedes Archimedes was born 287 BC in Syracuse, Sicily. Archimedes was a famous mathematician whose theorems and philosophies became world known. He gained a reputation in his own time which few other mathematicians of this period achieved. He is considered by most historians of mathematics as one of the greatest mathematicians of all time. He discovered pi. Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch. He was best known for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder, for his formulation of a hydrostatic principle Archimedes' principle and for inventing the Archimedes screw (a device for raising water). Archimedes Principal states: an object immersed in a fluid experiences a buoyant force that is equal in magnitude to the force of gravity on the displaced fluid. He also invented things such as the hydraulic screw - for raising water from a lower to a higher level, catapult, the lever, the compound pulley and the burning mirror. In mechanics Archimedes discovered fundamental theorems concerning the centre of gravity of plane figures and solids.

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