Geometry.Net - Scientists: Archimedes Of Syracuse

Story Of Archimedes Taking Bath
archimedes of syracuse (circa 287 212 BC) Following is an excerptfrom Vitruvius, The Ten Books of Architecture. In the case of
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Extractions: Vitruvius, The Ten Books of Architecture In the case of Archimedes, although he made many wonderful discoveries of diverse kinds, yet of them all, the following, which I shall relate, seems to have been the result of a boundless ingenuity. Hiero, after gaining the royal power in Syracuse, resolved, as a consequence of his successful exploits, to place in a certain temple a golden crown which he had vowed to the immortal gods. He contracted for its making at a fixed price, and weighed out a precise amount of gold to the contractor. At the appointed time the latter delivered to the king's satisfaction an exquisitely finished piece of handiwork, and it appeared that in weight the crown corresponded precisely to what the gold had weighed. But afterwards a charge was made that gold had been abstracted and an equivalent weight of silver had been added in the manufacture of the crown. Hiero, thinking it an outrage that he had been tricked, and yet not knowing how to detect the theft, requested Archimedes to consider the matter. The latter, while the case was still on his mind, happened to go to the bath, and on getting into a tub observed that the more his body sank into it the more water ran out over the tub. As this pointed out the way to explain the case in question, without a moment's delay, and transported with joy, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking; for as he ran he shouted repeatedly in Greek
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Archimedes Of Syracuse (ca. 287-ca. 212 BC) -- From Eric Weisstein's World Of Sc
production archimedes of syracuse is probably the most famous of all
http://www.astro.virginia.edu/~eww6n/bios/Archimedes.html

Extractions: Greek mathematician who flourished in Sicily. He is generally considered to be the greatest mathematician of ancient times. Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch. Archimedes performed numerous geometric proofs using the rigid geometric formalism outlined by Euclid , excelling especially at computing areas and volumes using the method of exhaustion He was especially proud of his discovery for finding the volume of a sphere showing that it is two thirds the volume of the smallest cylinder that can contain it. At his request, the figure of a sphere and cylinder was engraved on his tombstone. In fact, it is often said that Archimedes would have invented calculus if the Greeks had only possessed a more tractable mathematical notation. By inscribing and circumscribing polygons on a circle for instance, he was able to constrain the value of pi ) between 3 10/71 and 3+1/7.
Archimedes Of Syracuse: Introduction
archimedes of syracuse. Introduction the greatest of Greek mathematicians.In the third century BCE, Rome was involved in a series
http://cerebro.cs.xu.edu/math/math147/02f/archimedes/archintro.html

Extractions: In the third century BCE, Rome was involved in a series of military conflicts (the Punic Wars) with the Greek city-state of Carthage , situated across the Mediterranean Sea on the African coast . Caught in the middle of these conflicts was Syracuse, another city-state on the coast of Sicily, which was claimed by both sides. Initially allied with Carthage against Rome at the outset of the First Punic War in 263 BCE, Syracuse soon switched allegiance. The King of Syracuse, Hiero II , managed to keep war at bay by honoring this treaty with Rome, but the situation became precarious in the later years of the century as the Carthaginian general Hannibal was gaining the upper hand in Spain and Italy against poorly managed Roman armies. Archimedes (287 - 212 BCE), son of Phidias, an astronomer, was thought to have been a kinsman of Hiero. In his youth, Archimedes ventured to Alexandria in Egypt to avail himself of the best education to be found in the Greek world. There he would have been able to study the texts at the great Library of Alexandria, where Euclid had worked, and he made friendships with other philosopher-mathematicians, most notably Conon of Samos with whom he corresponded for many years. Archimedes eventually returned to Syracuse, where he earned fame as an "engineering consultant" to the king, inventing many clever devices for the military defense of the city: catapults, grappling hooks, and improvements to the architecture of the city walls.
Archimedes Of Syracuse: Quadrature Of The Parabola
archimedes of syracuse. Source The Works of Archimedes, Sir Thomas L. Heath,ed., Dover, 1953, pp. 233235, 248-252. Quadrature of the Parabola.
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Extractions: When I heard that Conon, who was my friend in his lifetime, was dead, but that you were acquainted with Conon and withal versed in geometry, while I grieved for the loss not only of a friend but of an admirable mathematician, I set myself the task of communicating to you, as I had intended to send to Conon, a certain geometrical theorem which had not been investigated before but has now been investigated by me, and which I first discovered by means of mechanics and then exhibited by means of geometry. Now some of the earlier geometers tried to prove it possible to find a rectilineal area equal to a given circle and a given segment of a circle; and after that they endeavoured to square the area bounded by the section of the whole cone and a straight line, assuming lemmas not easily conceded, so that it was recognized by most people that the problem was not solved. But I am not aware that any one of my predecessors has attempted to square the segment bounded by a straight line and a section of a right-angled cone [a parabola], of which problem I have now discovered the solution. For it is here shown that every segment bounded by a straight line and a section of a right-angled cone [a parabola] is four-thirds of the triangle which has the same base and equal height with the segment
Archimedes Of Syracuse
archimedes of syracuse 287 BC 212 BC archimedes of syracuse was born in the year287 BC and died in 212 BC, both in Syracuse, Sicily, now part of Italy.
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Extractions: Archimedes of Syracuse was born in the year 287 B.C and died in 212 B.C, both in Syracuse, Sicily, now part of Italy. Archimedes lived in Syracuse, on the island of Sicily in Italy, all of his life, except when studying with Euclid in Alexandria, Egypt. Archimedes had an astronomer for a dad. His name was Phidias. All we know about Phidias was what Archimedes wrote about him in THE SANDRECKONER. One of Archimedes' good friends, Heracleides, wrote a biography on Archimedes, yet this very valuable information was lost over the years. Another good friend of Archimedies was Conon, a mathematician whom Archimedes studied with. He lived a healthy life, but died at 75. There are three theories on how Archimedes died. It was during the Second Punic War, after the Romans captured Syracuse. Archimedes did many things in math, but was also an inventor. He is famous in geometry and calculus. It is said Archimedes found integral calculus 2000 years before Newton and Leibniz. Archimedes also first calculated pi and the volume of a sphere. He also did other work with volume. As an inventor, he made war engines, and he invented a pump that is still used in many parts of the world.
Toukokuun 2000 Fyysikko
Archimedes archimedes of syracuse Archimedes (ENCYCLOPÆDIA BRITANNICA) Syracuse(ENCYCLOPÆDIA BRITANNICA) Archimedes screw ARCHIMEDES Archimedes
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Extractions: Arkhimedes syntyi Syrakuusassa Sisilian itärannikolla vuonna 287 eKr. Arkhimedes oli Syrakusan kuninkaan Hieron II:n sukulainen. Arkhimedes on tunnettu sekä matemaatikkona että fyysikkona. Edellä kerrotuista poiketen hänen fysiikan saavutuksensa olivat hyvin käytännönläheisiä. Sentähden häntä voidaan pitää keksijänä ja insinöörinä. Fysiikassa Arkhimedes tunnetaan parhaiten Arkhimedeen laista , joka kertoo, että kappale menettää nesteeseen upotettaessa painostaan syrjäyttämänsä nestemäärän painon verran. Kerrotaan , että hän sai ajatuksen kylvyssä, kun hänen piti selvittää oliko kultaseppä varastanut kultaa ja korvannut sen muulla metallilla kuninkaan kruunussa. Punnitsemalla kruunun ilmassa ja vedessä hän sai painojen erotuksesta laskettua kruunun tilavuuden ja edelleen sen tiheyden. Koska kulta on hyvin painava metalli, oli helppo todeta petos. Toinen tärkeä työ oli vivun tasapainolaki . Tämä on statiikan tärkeimpiä kulmakiviä. Sentähden häntä pidetään statiikan eli tasapaino-opin perustajana. Tasapaino-oppiin liittyi hänen keksimänsä talja.
Archimedes Of Syracuse (ca. 287-ca. 212 BC) -- From Eric Weisstein's World Of Sc
archimedes of syracuse (ca. 287ca. 212 BC), Greek mathematician whoflourished in Sicily. He is generally considered to be the greatest
http://www.edu365.com/aulanet/comsoc/Lab_quimica/quimics/Archimedes.htm

Extractions: Greek mathematician who flourished in Sicily. He is generally considered to be the greatest mathematician of ancient times. Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch. Archimedes performed numerous geometric proofs using the rigid geometric formalism outlined by Euclid , excelling especially at computing areas and volumes using the method of exhaustion He was especially proud of his discovery for finding the volume of a sphere showing that it is two thirds the volume of the smallest cylinder that can contain it. At his request, the figure of a sphere and cylinder was engraved on his tombstone. In fact, it is often said that Archimedes would have invented calculus if the Greeks had only possessed a more tractable mathematical notation. By
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Archimedes Biography
archimedes of syracuse. Background archimedes of syracuse (pronounced arka-meed-eez)is considered one of the greatest mathematicians in history.
http://math.about.com/library/blbioarchimedes.htm

Extractions: Background: A rchimedes of Syracuse (pronounced ar-ka-meed-eez) is considered one of the greatest mathematicians in history. In fact, he is believed to be one of the three greatest mathematicians along with Isaac Newton and Carl Gauss. His greatest contributions to mathematics were in the area of Geometry. Archimedes was also an accomplished engineer and an inventor. He was believed to have been obsessed with Geometry though.
Biographies.html
archimedes of syracuse. Archimedes was killed in Syracuse when the Romans capturedit in 212 BC The commander, Marcellus, gave orders not to harm Archimedes.
http://archive.ncsa.uiuc.edu/Edu/RSE/RSEorange/biosub.html

Extractions: The following list are biographies that have been submitted by students participating in the Mathematics project. The mathematicians are ones who have studied , have used in their work or were chosen by students for personal reasons. If you wish to add to this list submit your biography on the History page. Muhammed was born in 780 A.D. and died in 850 A.D. He was an Arabic mathematician who introduced the Hindu decimal system and the use of zero into Arabic mathematics. He also extended the work of Diophantis on algebraic equations in a book, the title which included the word al-jabr (transposition) from which the modern word algebra is derived. I chose this mathematician because he sounded interesting, and important to the world of mathematics. Jennifer, 1996 Although no one knows for sure, people speculate that Archimedes was born sometime around 287 B.C. As a boy he probably attended school in Alexandria, which was the center of Greek learning. After school Archimedes went to live in Syracuse, Sicily, which was then a Greek colony. Here he did much work for the king, Hiero. Archimedes made many discoveries in Math and Physics. One of his mathematical advances was with pi. Archimedes found a way to determine a more exact value of pi. He showed the value of pi was somewhere between 3 1/7 and 3 10/71. This discovery made it possible to solve many problems relating to the area of a circle and the volume of cylinders. Another invention was that of a new type of numeration system. Archimedes' new system worked much better with large numbers than the Roman and Greek systems.
The Life Of Archimedes - The Spiral Of Archimedes
1 OConnor, JJ and Robertson, EF archimedes of syracuse. 3 OConnorand Robertson, archimedes of syracuse. 4 ibid. 5 Boswell, Foster.
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Extractions: The Life of Archimedes The Life of Archimedes The Screw of Archimedes Other Sources of Information Archimedes was a man of great mathematical and mechanical wisdom. It is through him that much of what we consider today to be mathematical integration came to be. However, the aspect of his work which we shall here endeavor to examine, is the water-screw. Before discussing this practical invention which has stood the test of time, it seems necessary to first examine the life of the man who was Archimedes. Archimedes was a Syracusan, born in that Sicilian city during the year 287 B.C. Very little is known of his parentage, except that his father was a man named Phidias, and was an astronomer by trade. Image 1 He studied mathematics in Alexandria, Egypt with the successors of the great Euclid. There was also a belief, by Linceo Mirabello, that Archimedes was a pupil of Platos during his youth in Syracuse. Given the span of sixty years between Platos death and Archimedes birth, this seems highly unlikely. Archimedes fascination with mathematics was immense. He worked with it in everything that he undertook, and throughout his life, he made several very important discoveries that have had significant effects on todays world of mathematics: he applied an early form of mathematical integration known as the
Title
archimedes of syracuse Ca. 287 BCE to 212 BCE archimedes of syracuse is generallyconsidered to be the greatest mathematician of ancient times.
http://www.math.uvic.ca/courses/math415/Math415Web/greece/gmen/architext.html

Extractions: Archimedes of Syracuse is generally considered to be the greatest mathematician of ancient times. Archimedes was a native of Syracuse, a Greek colony in Sicily, and after his early education in Alexandria, returned there to spend the rest of his life. He was friends with many prominent mathematicians in Alexandria including Eratosthenes , the great librarian. Unlike many early thinkers, Archimedes was legendary even in his own day. He was extremely rigorous and was only satisfied in publishing the most polished proofs. He did extensive work in pure mathematics and was an extraordinary engineer. Although Archimedes preferred pure mathematics, the Roman siege of Syracuse motivated him to put his efforts towards engineering projects such as the great war engines mentioned by Plutarch. Archimedes reportedly invented huge cranes and levers that were used by him to pick up Roman war ships from the ocean and crush them against the rocks. Archimedes' ingenuity allowed Syracuse to resist the Roman siege for three years. He was killed when the Romans finally invaded the city. At the time, he was reportedly working at his sand table when an angry Roman soldier ran him through. The Roman general Marcellus, aware and in awe of his adversary's mental prowess, was so upset at this event that he had the soldier killed and gave Archimedes an honourable burial.
Archimedes
archimedes of syracuse. 287 BC 212 BC. Archimdeds of Syracuse.Archimedes was born in 287 BC in Syracuse, Sicily. His
http://www.seaford.k12.ny.us/Sites/Seaford_Web_Site/Middle/math/MS_Math_WebPages

Extractions: Home Page Manor Elementary Harbor Elementary Middle School ... School Calendar Archimedes of Syracuse 287 BC - 212 BC Archimdeds of Syracuse Archimedes was born in 287 BC in Syracuse, Sicily. His father Phidias was an astronomer possibly related to King Hiero II of Syracuse. As a youth, Archimedes spent some time in Egypt studying. Then upon returning home his name and reputation began to grow. Archimedes' mechanical skill combined with his theoretical knowledge enabled him to construct many ingenious devices. He began to pursue the invention of machines that were to be used to defend Syracuse. Some of these inventions were the catapult, the compound pulley and a burning mirror. His most famous invention is called the Archimedes' screw which is still used in some parts of the world today. Archimedes most major contributions were in geometry. The most famous of all his discoveries was Measurement of the Circle, in which he placed the value of between 3 + 10/71 and 3 + 1/7. Another discovery, that he states casually in one of his writings, an approximation of the square root of 3 in the form of:
Archimedes
and circumscription of regular polygons on a circle, he was able to constrainthe value of between 3 10 / 71 and 3 1 / 7 . à®, archimedes of syracuse.
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Extractions: He is considered the greatest mathematician of ancient times. He performed numerous geometric proofs using the rigorous geometry of Euclid. His Method of Exhaustion allowed him to compute areas and volumes of geometric figures. He discovered that the volume of a sphere is the volume of the smallest cylinder that can contain it. At his request, the figure of a sphere and cylinder was engraved on his tombstone. By a series of inscription and circumscription of regular polygons on a circle, he was able to constrain the value of between 3 and 3 Archimedes was also a great engineer. He formulated Archimedes' Principle of Buoyancy and the Law of the Lever. The Principle of Buoyancy states that the force exerted on an immersed object (i.e. the buoyancy force) is equal to the weight of the liquid displaced. There is a story regarding Archimedes' discovery of this principle: upon discovering the principle while taking a bath, he jumped out of his bath and ran naked through the streets shouting "Eureka!" (i.e. I have found it!). During the Roman siege of Syracuse, he is said to have single-handedly defended the city by constructing lenses to focus the sun's light on Roman ships and huge cranes to turn them upside down. Some of his works are Floating Bodies, On Balances and Levers, On Plane Equilibriums, The Sand Reckoner, Quadrature of the parabola, On Conoids and Spheroids, Measurement of a Circle, On Spirals
Archamedes
Connor, JJO' and Robertson, E F. archimedes of syracuse. Archimedes. OnlinePosting. Weisstein Eric W. archimedes of syracuse (ca. 287ca.
http://www.lams.losalamos.k12.nm.us/technology/Sciquests/Archamedes.htm

Extractions: Archimedes was a scientist and philosopher in ancient Greece. He was one of the first scientists to understand mater and density. Students should understand why Archimedes was important to society. Use the provided web sites to answer the questions about Archimedes. After all of the questions have been answered, there is a project so students can see if they understand the importance of Archimedes. http://www.shu.edu/projects/reals/history/archimed.html http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Archimedes.html http://scienceworld.wolfram.com/biography/Archimedes.html Explain the events that led up to Archimedes death. Explain how an Archimedes' screw works. Explain what was an Archimedes' claw was used for and its advantages. What event allowed the Romans to take over Syracuse despite Archimedes inventions? Explain how Archimedes proved that the blacksmith hadn't used only gold in the king's crown. Explain what long term effects Archimedes had on society?
LookSmart - Archimedes Of Syracuse
Archimedes MacTutor History of Mathematics Discusses in detail the life, accomplishments,and death of ancient Greek philosopher archimedes of syracuse.
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Archimedes
from Thales of Miletus and Pythagoras of Samos in the 6th century BC to Pappus ofAlexandria in the 4th century AD, archimedes of syracuse (287 212 BC) is
http://www-maths.mcs.st-andrews.ac.uk/~gmp/gmpANA.html

Extractions: In the very long line of Greek mathematicians from Thales of Miletus and Pythagoras of Samos in the 6th century BC to Pappus of Alexandria in the 4th century AD, Archimedes of Syracuse (287 - 212 BC) is the undisputed leading figure. His pre-eminence is the more remarkable when we consider that this dazzling millenium of mathematics contains so many illustrious names, including Anaxagoras, Zeno, Hippocrates, Theodorus, Eudoxus, Euclid, Eratosthenes, Apollonius, Hipparchus, Heron, Menelaus, Ptolemy and Diophantus. (See the St Andrews archive History of Mathematics for information about these mathematicians.) Although his main claim to fame is as a mathematician, Archimedes is also known for his many discoveries and inventions in physics and engineering, which include the following. His invention of the water-screw, still in use in Egypt, for irrigation, draining marshy land and pumping out water from the bilges of ships. His discovery of the hydrostatic principle that a body immersed in a fluid is subject to an upthrust equal to the weight of fluid displaced by the body. This discovery is said to have inspired his famous cry "Eureka" ("I have found it"). Before discussing the work covered in his book Measurement of the Circle , we mention briefly a few of the other significant contributions which Archimedes made to mathematics.
Bigchalk: HomeworkCentral: Archimedes (Biographies)
ARCHIMEDES; Archimedes timeline; archimedes of syracuse. ARCHIMEDES'INVENTIONS World Book Online Article on ARCHIMEDEAN SCREW; World Book
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Archimedes
Software Handleiding Zoeken archimedes of syracuse (287 BC 212BC). Archimedes greatest contributions were in geometry. His methods
http://www.fys.kuleuven.ac.be/pradem/fysici/Archimedes.html

Extractions: Pradem Leuven Demo's Applets Laboproeven ... Zoeken Archimedes of Syracuse (287 BC - 212 BC) Archimedes greatest contributions were in geometry. His methods anticipated the integral calculus 2000 years before Newton and Leibniz. Find out more at: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Archimedes.html Pradem Leuven

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