From Wikipedia, the free encyclopedia
Archimedes of Syracuse
(Greek: Ἀρχιμήδης) 
Archimedes Thoughtful by Fetti (1620)

Born 
c. 287 BC
Syracuse, Sicily
Magna Graecia 
Died 
c. 212 BC
Syracuse

Residence 
Syracuse, Sicily 
Ethnicity 
Greek 
Fields 
Mathematics, Physics, Engineering, Astronomy, Invention 
Known for 
Archimedes' Principle, Archimedes' screw, Hydrostatics, Levers, Infinitesimals 
.^ Archimedes (287212 BC). "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^ Archimedes Archimedes was a mathematician and inventor from ancient Greece best known for his discovery of the relation between the surface and volume of a sphere and ... Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ This gifted Greek mathematician and inventor once said, "Give me a place to stand and rest my lever on, and I can move the Earth." "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
.^ Although Newton should certainly be in the top 5 of any such list, if one thinks through this clearly, one has to conclude that Charles Darwin was mankind’s greatest scientist to date. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^ Archimedes of Syracuse Greek mathematician, scientist and inventor Archimedes regarded as one of the leading scientists and inventor of all time though there are very much a few details of his life mentioned. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ ARCHIMEDES  GREATEST SCIENTIST EVER? Math is the "queen of sciences," and Archimedes is widely regarded as one of the greatest mathematicians ever  perhaps the most influential of them all. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ He is known for his formulation of hydrostatic principle commonly known as "Archimedes Principle" and at the same time he is the first who recognize and used the power of lever. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
He is credited with designing innovative
machines, including siege engines and the
screw pump that bears his name.
.^ The physicist grabs a bucket and leaps towards the sink, fills the bucket with water and puts out the fire. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
^ The engineer starts to calculate how much water it takes to put out the fire. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
^ His invention of the waterscrew, still in use in Egypt, for irrigation, draining marshy land and pumping out water from the bilges of ships. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^{[1]}
.^ In conclusion, Archimedes is well deserved to be named as one of the greatest mathematicians. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ Also Archimedes is also considered one of the three greatest mathematicians ever, as with Newton and Gauss. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ It was authored by one of the greatest mechanical minds in history: the legendary Archimedes , who knew a thing or two about spheres right down to his dying words... 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^{[2]}^{[3]} .^ He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of Pi. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ The method of exhaustion gives us the formulae for calculating areas. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ For example, he gave the approximations of and square roots of some large numbers, insights on the solutions of cubic equations and arithmetic series. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^{[4]} .^ He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ So, there are a > > lot of things that we know about very large numbers. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^ So, there are a > > > lot of things that we know about very large numbers. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
.^ The soldier was enraged by this, and killed Archimedes with his sword. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a twoyearlong siege. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ According to Plutarch (45120 AD), Archimedes is said to have requested his friends and relations that, when he was dead, they would place over his tomb a sphere containing a cylinder, inscribing it with the ratio which the containing solid bears to the contained. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
^ This is also reflected by the fact that in Statements 1 and 5 of "Spheres and Cylinders" Archimedes dealt with the equation a 2 : x = x : b . Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ Archimedes gave instructions that his tombstone should have displayed on it a diagram consisting of a sphere with a circumscribing cylinder. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^ Archimedes had proved that the volume and surface area of the sphere are two thirds that of the cylinder including its bases. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Volume of the cylinder = ´ Volume of the sphere . Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity.
.^ A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Archimedes  we're back  Archimedes  The Open CAD After a lot of work, some news and no release, we're back on full speed (or almost) with Archimedes' new version. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ He is known for his formulation of hydrostatic principle commonly known as "Archimedes Principle" and at the same time he is the first who recognize and used the power of lever. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Archimedes  we're back  Archimedes  The Open CAD After a lot of work, some news and no release, we're back on full speed (or almost) with Archimedes' new version. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ ARCHIMEDES  GREATEST SCIENTIST EVER? Math is the "queen of sciences," and Archimedes is widely regarded as one of the greatest mathematicians ever  perhaps the most influential of them all. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^{[6]}
Biography
Archimedes was born
c.
.^ BC in the seaport city of Syracuse, Sicily, at that time a colony of Magna Graecia. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Archimedes (287  212 B.C.) was born at Syracuse of Sicily as a son of the astronomer Pheidias. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
.^ The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^{[7]} In
The Sand Reckoner, Archimedes gives his father's name as Phidias, an
astronomer about whom nothing is known.
.^ Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Archimedes proposed the following problem when he visited Hieron, the King of Syracuse: . Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ It is said that Archimedes was a relative of Hieron, the king of Syracuse. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^{[8]} .^ In 1906, J. L. Geiberg (1854  1928) found in Turkey a book containing a lot of Archimedes' works, including "The Methods", which was written by Archimedes to describe where his beautiful ideas came from. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ Many works were written by Archimedes, including "On the Sphere and Cylinder", "On the Measurement of a Circle", "On Conoids and Spheroids", "On Spirals", "The Sandreckoner", "On Quadrature of the parabola", "Book of Lemmas" and "The Methods". Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^{[9]} .^ It is unknown, for instance, whether he ever married or had children. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ When he was learning at Alexandria, he made friends with Conon, Eratosthenes and many others. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ He probably visited Egypt and studied at Alexandria at the school which Euclid had started there. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
.^ He referred to Conon of Samos as his friend, while two of his works (The Sand Reckoner and the Cattle Problem) have introductions addressed to Eratosthenes. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ During his youth Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^{[a]}
Archimedes died
c.
.^ BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a twoyearlong siege. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Galileo was eventually forced to recant his heliocentrism and spent the last years of his life under house arrest on orders of the Holy Inquisition. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^ A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ In the section 'Mathematical Achievements', the reader will be given a detailed discussion of Archimedes' books and achievements. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ The aim of this article is to discuss the mathematical achievements and methodologies of Archimedes, and each of these topics is given a separate section below. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
.^ A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Other thoughts of mine are the Roman soldier killed Archimedes most likely because he was pissed at him for building the siege engines that killed many of comrades. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
.^ The soldier was enraged by this, and killed Archimedes with his sword. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Other thoughts of mine are the Roman soldier killed Archimedes most likely because he was pissed at him for building the siege engines that killed many of comrades. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^ According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ The soldier was enraged by this, and killed Archimedes with his sword. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Plutarch also gives a lesserknown account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ The soldier was enraged by this, and killed Archimedes with his sword. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Romanian soldiers got into Archimedes' camp secretly and killed him. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
.^ General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ I’d say pretty much all scientifically educated people would consider Einstein, Newton & Darwin as the top 3 (though not necessarily in that order). Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^{[10]}
.^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^ His real importance in mathematics, however, lies in his discovery of formulae for the areas and volumes of spheres, cylinders, parabolas, and other plane and solid figures. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
A
sphere and
cylinder were placed on the tomb of Archimedes at his request.
.^ Other thoughts of mine are the Roman soldier killed Archimedes most likely because he was pissed at him for building the siege engines that killed many of comrades. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^ He was killed at the siege of Syracuse by a Roman soldier whose challenge he ignored while immersed in a mathematical problem. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
^ The next panel has the soldier going "Fuck your circles," and then he just goes nuts on Archimedes. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
.^ This quote is often given in Latin as "Noli turbare circulos meos", but there is no reliable evidence that Archimedes uttered these words and they do not appear in the account given by Plutarch. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Plutarch also gives a lesserknown account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^{[10]}
.^ The tomb of Archimedes carried a sculpture illustrating his favorite mathematical proof, consisting of a sphere and a cylinder of the same height and diameter. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Archimedes gave instructions that his tombstone should have displayed on it a diagram consisting of a sphere with a circumscribing cylinder. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ He made a lot of greatest contribution in science, mathematics, astronomy, mechanics and engineering for his discovery of the relation between the surface and the volume of a sphere and its circumscribing cylinder. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ Archimedes had proved that the volume and surface area of the sphere are two thirds that of the cylinder including its bases. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ He found the volume and surface area of a sphere. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ He made a lot of greatest contribution in science, mathematics, astronomy, mechanics and engineering for his discovery of the relation between the surface and the volume of a sphere and its circumscribing cylinder. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ In 75 BC, 137 years after his death, the Roman orator Cicero was serving as quaestor in Sicily. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ C H Edwards (see reference below) writes how Cicero, while serving as quaestor in Sicily, had Archimedes' tombstone restored, and adds "The Romans had so little interest in pure mathematics that this action by Cicero was probably the greatest single contribution of any Roman to the history of mathematics." Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ He had heard stories about the tomb of Archimedes, but none of the locals was able to give him the location. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ Eventually he found the tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
.^ Cicero had the tomb cleaned up, and was able to see the carving and read some of the verses that had been added as an inscription. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Euclid collected and rearranged all the known facts about geometry, up to his time, in stepbystep order and added some new propositions and proofs. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
^{[11]}
.^ A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Archimedes Stuff Archimedes Stuff on eBay Life & Death of Archimedes of Syracuse Archimedes Stuff on eBay Book on the Spotlight on Archimedes more... Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
^ Archimedes Stuff Archimedes Stuff on eBay Life & Death of Archimedes of Syracuse Archimedes Stuff on eBay Book on the Spotlight on Archimedes Archimedes' Discoveries . Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]
The account of the siege of Syracuse given by
Polybius in his
Universal History was written around seventy years after Archimedes' death, and was used subsequently as a source by Plutarch and
Livy. It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in order to defend the city.
^{[12]}
Discoveries and inventions
The Golden Crown
Archimedes may have used his principle of buoyancy to determine whether the golden crown was less
dense than solid gold.
.^ Although there was not much known about the value of the ratio between the circumference and diameter of a circle, and it was impossible to evaluate ratios using irrational numbers with the number system at that time, Archimedes was still able to point out the relationships between the volumes and areas of various geometric shapes. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
.^ The Sicilian King, Archimedes was told, Ordered a crown from a large lump of gold, And though the weight of the gold was completely correct, The goldsmith's eye made the King suspect That he'd made up the weight with some cheaper metal And stolen some gold, that his debts he might settle. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
^{[13]} .^ Bohr’s work helped solve the problems classical physics could not explain about the nuclear model of the atom. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^ Experts on the history of mathematics believe that Archimedes himself could not solve this problem either because in 1965, with the help of computers, the answer was found to be of 206500 digits ([ 2 ], page 97  98). Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ In "On the Sphere and Cylinder", "On Measurement of a Circle", "On Quadrature of the parabola", "On Conoids and Spheroids" and "On Spirals", Archimedes often use the method of exhaustion to solve the problems. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the
volume of the crown.
.^ He found the upthrust, produced on a body's base*, To be equal in weight to the water displaced, And soon volumes and weights would make it quite plain What various metals the crown could contain, And so he could easily show to his Royalty The absolute proof of the goldsmith's disloyalty. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
.^ He found the upthrust, produced on a body's base*, To be equal in weight to the water displaced, And soon volumes and weights would make it quite plain What various metals the crown could contain, And so he could easily show to his Royalty The absolute proof of the goldsmith's disloyalty. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
.^ It was discovered after Lord Rayleigh tried (1893) to measure the density of nitrogen gas accurately: he found that chemicallygenerated nitrogen gas was less dense than nitrogen separated from air, by a small but persistent amount. SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]
Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "
Eureka!" (
Greek: "εὕρηκα!," meaning "I have found it!")
^{[15]}
The story of the golden crown does not appear in the known works of Archimedes.
.^ In 1919, Goddard wrote a scientific article, "A Method of Reaching Extreme Altitudes," describing a highaltitude rocket; it was published in a Smithsonian report. Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]
^ THE NATURE OF LIGHT One of the main goals of physics is to develop plausible conceptual models, as they are called, in terms of which various physical phenomena can be described and explained.
^{[16]} .^ In popular tradition he is remembered for the construction of siegeengines against the Romans, the Archimedes' screw still used for raising water, and his cry of eureka ("I have found it') when he discovered the principle of the upthrust on a floating body. Math Jokes and Archimedes  Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]
^ Alexipharmacal "...The same may be extracted out ot other Alexipharmacal bodies, which Princes may use at meals, instead of ordinary Salt ..." "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.
^{[17]} Using this principle, it would have been possible to compare the density of the golden crown to that of solid gold by balancing the crown on a scale with a gold reference sample, then immersing the apparatus in water.
.^ Overtime was expensive, sure, but at a certain point that became less important than the fact that slower construction meant later and therefore more expensive outlays. SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]
^ We have discovered prime numbers that are far larger than 10^500, and those would be primes in the Incognitum. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^ In fact, if one assumed that the size of their charge was equal to that of a hydrogen ion in electrolysis (a proposition that was verified by experiment later) their mass was less than 1/1000 of the mass of a hydrogen atom.
This difference in buoyancy would cause the scale to tip accordingly.
Galileo considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself."
^{[18]}
The Archimedes Screw
.^ His problems arose largely from the fact that he was an eccentric who was unable to work with (and consequently to learn from) other people, and the increasing unreality of his ideas shows it.” . Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^ To remove this misperception, in his only work on arithmetic, "Arithmetic on Sand Grains", Archimedes proposed a new way to denote large numbers and calculated the number of sand grains in the world. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ Of course it is hard to compare ancient and more recent breakthroughs, but Archimedes’ work would have more total impact as he also laid the foundations of physics and mathematical engineering. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
.^ Archimedes proposed the following problem when he visited Hieron, the King of Syracuse: . Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ And that King Ptolomey built a tower in Pharos, where he set a glass, that he could see for six hundred miles, see by it the enemy ships, that invaded his country and plundered it ..." "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^ It is said that Archimedes was a relative of Hieron, the king of Syracuse. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
The
Syracusia is said to have been the largest ship built in classical antiquity.
^{[19]} According to Athenaeus, it was capable of carrying 600 people and included garden decorations, a
gymnasium and a temple dedicated to the goddess
Aphrodite among its facilities. Since a ship of this size would leak a considerable amount of water through the hull, the
Archimedes screw was purportedly developed in order to remove the bilge water.
.^ Archimedes invented the water screw, a device for raising water using an encased screw open at both ends. Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]
.^ Hot to use your “marketer’s eye” to spot the hidden value in websites—and turn them into cold, hard cash in your pocket...
^ It was first turned into reality in 1953 by Charles Townes (1915  ) and his students, using radiation of about l cm wavelength emitted and absorbed by ammonia molecules.
.^ Roman times and is still in use today.
^ The Archimedes screw is still in use today. Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]
^ Archimedes invented the water screw, a device for raising water using an encased screw open at both ends. Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]
.^ Roman times and is still in use today.
^ The Archimedes screw is still in use today. Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]
^ Brass , often used, and let it melt six or sever times, that it may be pure and cleansed. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^{[20]}^{[21]}^{[22]}
The Claw of Archimedes
.^ It is said that Archimedes was a relative of Hieron, the king of Syracuse. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
Also known as "the ship shaker," the claw consisted of a cranelike arm from which a large metal grappling hook was suspended.
.^ Draw it with a gentle fire, it will Distil out by drops after the water..." "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
.^ There was a misperception among some ancient Greeks that the number of sand grains in the world was infinite and the number could not be represented by a number. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^{[23]}^{[24]}
The Archimedes Heat Ray – myth or reality?
.^ Archimedes (287  212 B.C.) was born at Syracuse of Sicily as a son of the astronomer Pheidias. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ Heron lived during the first century AD and is sometimes called Hero. Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]
^ Levers were first described about 260 BC by the ancient Greek mathematician Archimedes (287212 BC). Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]
.^ We read that Archimedes at Syracuse with burning glasses defeated the forces of the Romans. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^{[25]} .^ GEIGER COUNTER The Geiger counter (sometimes called the GeigerMuller counter) is a device that detects ionizing radioactivity (including gamma rays and Xrays)  it counts the radioactive particle that pass through the device. Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]
^ Archimedes invented the water screw, a device for raising water using an encased screw open at both ends. Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]
This purported weapon has been the subject of ongoing debate about its credibility since the Renaissance.
René Descartes rejected it as false, while modern researchers have attempted to recreate the effect using only the means that would have been available to Archimedes.
^{[26]} It has been suggested that a large array of highly polished
bronze or
copper shields acting as mirrors could have been employed to focus sunlight onto a ship. This would have used the principle of the
parabolic reflector in a manner similar to a
solar furnace.
A test of the Archimedes heat ray was carried out in 1973 by the Greek scientist Ioannis Sakkas. The experiment took place at the
Skaramagas naval base outside
Athens. On this occasion 70 mirrors were used, each with a copper coating and a size of around five by three feet (1.5 by 1 m). The mirrors were pointed at a plywood
mockup of a Roman warship at a distance of around 160 feet (50 m). When the mirrors were focused accurately, the ship burst into flames within a few seconds. The plywood ship had a coating of
tar paint, which may have aided combustion.
^{[27]}
.^ The males are about one tenth the size of the females (which range in length from 5 to 30 cm). SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]
^ THE NATURE OF PHYSICS THE NATURE OF PHYSICS A. P. French Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA INTRODUCTION The world is full of experiences that cry out for explanations.
Flames broke out on a patch of the ship, but only after the sky had been cloudless and the ship had remained stationary for around ten minutes. It was concluded that the device was a feasible weapon under these conditions. The MIT group repeated the experiment for the television show
MythBusters, using a wooden fishing boat in
San Francisco as the target. Again some charring occurred, along with a small amount of flame. In order to catch fire, wood needs to reach its
flash point, which is around 300 degrees Celsius (570 °F).
^{[28]}
.^ The experiment can be done under such conditions that only one photon passes through the apparatus at a time.
^ I mention this not for the sake of the particular result, but because it points to another essential feature of physics  the dependence on direct observation or experiment.
It was also pointed out that since Syracuse faces the sea towards the east, the Roman fleet would have had to attack during the morning for optimal gathering of light by the mirrors.
.^ PM Phillyastro @iamfry: the point of this article is that if western civilization had not lost the knowledge that these books contain, we would be far ahead of where we are in technology right now. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^ PM greenprince Love the look of Ab urbe condita libri, by Livy..would made Ancient History, back in High School way easier! 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^ I think he's a blowhard too but you're going way too far out of your way. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^{[1]}
Other discoveries and inventions
.^ And he did – today we still feel his impact through a lever spanning 2200+ years of Archimedesinspired science. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^ The best example is perhaps the lever, the principle of which was recognized by Archimedes about 250 B.C.: "...unequal weights are in equilibrium only when they are inversely proportional to the arms from which they are suspended."
According to
Pappus of Alexandria, his work on levers caused him to remark: "Give me a place to stand on, and I will move the Earth." (
Greek:
δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω)
^{[29]} Plutarch describes how Archimedes designed
blockandtackle pulley systems, allowing sailors to use the principle of
leverage to lift objects that would otherwise have been too heavy to move.
^{[30]} .^ The first scientist to recognize and use the power of the lever was Archimedes . "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled.
^{[31]}
.^ Archimedes (287  212 B.C.) was born at Syracuse of Sicily as a son of the astronomer Pheidias. Mathematical Database  Math Funland  Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]
^ It was authored by one of the greatest mechanical minds in history: the legendary Archimedes , who knew a thing or two about spheres right down to his dying words... 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^ And Hermes the learned, said, t hat the sun and the moon are the life of all things living... "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
Cicero mentions similar mechanisms designed by
Thales of Miletus and
Eudoxus of Cnidus.
.^ For, say they, the Atoms that flew out of the Iron , and meet in the Loadstone in one figure, so that they easily embrace one the other..." "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^ Herodotus says, that Artabazus and Timoxenus did this, when one would declare anything to the other..." "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^ What A Commonsense Person Would Do: A person full of commonsense would say: (a) since physics has no infinities then let us only do Mathematics to the largest (smallest) numbers that physics needs to use. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
Marcellus' mechanism was demonstrated, according to Cicero, by
Gaius Sulpicius Gallus to
Lucius Furius Philus, who described it thus:
Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. — When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth, when the Sun was in line.^{[32]}^{[33]}
This is a description of a
planetarium or
orrery.
.^ It was authored by one of the greatest mechanical minds in history: the legendary Archimedes , who knew a thing or two about spheres right down to his dying words... 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^ PM Phillyastro @iamfry: the point of this article is that if western civilization had not lost the knowledge that these books contain, we would be far ahead of where we are in technology right now. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^ On SphereMaking , by Archimedes . 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
.^ Here's another modern classic that'll change the world. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
Constructing mechanisms of this kind would have required a sophisticated knowledge of
differential gearing. This was once thought to have been beyond the range of the technology available in ancient times, but the discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks.
^{[34]}^{[35]}
Mathematics
.^ Niels Bohr was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^ With the Turing test, meanwhile, he made a significant and characteristically provocative contribution to the debate regarding artificial intelligence: whether it will ever be possible to say that a machine is conscious and can think. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^ It was incredibly difficult to categorize them in a top 10 list as they all had astounding contributions to their respective fields, and I made numerous changes to the order as I compiled the list. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
Plutarch wrote: "He placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life."
^{[36]}
.^ Firstly; where is ARCHIMEDES? Archimedes was the first to introduce infinitesimals which is the foundation of calculus. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
Through proof by contradiction (
reductio ad absurdum), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the
method of exhaustion, and he employed it to approximate the value of
π (pi). He did this by drawing a larger
polygon outside a
circle and a smaller polygon inside the circle. As the number of sides of the polygon increases, it becomes a more accurate approximation of a circle. When the polygons had 96 sides each, he calculated the lengths of their sides and showed that the value of π lay between 3
^{1}⁄_{7} (approximately 3.1429) and 3
^{10}⁄_{71} (approximately 3.1408), consistent with its actual value of approximately 3.1416. He also proved that the
area of a circle was equal to π multiplied by the
square of the
radius of the circle.
.^ AM Inspector_Anys I missed the part where Plato was a physicist, or that a deityriddled epic isn't "religious" unless enough people at a given time think the deity/deities are "real". 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^ AM iamfry I missed the part where Plato was a physicist, or that a deityriddled epic isn't "religious" unless enough people at a given time think the deity/deities are "real". 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
This is the
Archimedean property of real numbers.
^{[37]}
In
Measurement of a Circle, Archimedes gives the value of the
square root of 3 as lying between
^{265}⁄_{153} (approximately 1.7320261) and
^{1351}⁄_{780} (approximately 1.7320512).
.^ I have flipped websites in the past for a very cool profit but using your system I was able to actually make more money in 2 flips than I made in 7 flips previously.
He introduced this result without offering any explanation of the method used to obtain it. This aspect of the work of Archimedes caused
John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results."
^{[38]}
As proven by Archimedes, the area of the
parabolic segment in the upper figure is equal to 4/3 that of the inscribed triangle in the lower figure.
If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller
secant lines, and so on. This proof uses a variation of the series
1/4 + 1/16 + 1/64 + 1/256 + · · · which sums to
^{1}⁄_{3}.
.^ He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: "There are some, King Gelo (Gelo II, son of
Hiero II), who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited." To solve the problem, Archimedes devised a system of counting based on the
myriad.
.^ You've seen my 6figure profits, and now you're about to own the exact system I used to fill my bank accounts.
^ Castilian, as now pronounced in most of Spain, does have the Þ sound, but like Italian generally uses a Roman letter tee for any theta in a Greek loan word. SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]
^ One wonders if we would be any better collectively if we all the had the equivalent brainpower and insight of the 10 cited in this topic. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^{[39]}
Writings
.^ Of course it is hard to compare ancient and more recent breakthroughs, but Archimedes’ work would have more total impact as he also laid the foundations of physics and mathematical engineering. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^ His two main works, written in Greek, are De natura animalium (On the Nature of Animals) and Varia historia (Miscellany). "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^{[40]} .^ Math made only a fleeting attempt to incorporate duality such as in the regularpolyhedra of a duality relationship of sides with angles with other properties. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^ There will be room for broad interdisciplinary thematic discussions by various authors as well as for detailed interpretations of individual, or groups of, documents and pieces of other evidence. SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]
^ Averroes composed 38 treatises on the various works of Aristotle , as well as original tracts on astronomy, physics, and medicine. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
Pappus of Alexandria mentions
On SphereMaking and another work on
polyhedra, while
Theon of Alexandria quotes a remark about
refraction from the
nowlost Catoptrica.
^{[b]} During his lifetime, Archimedes made his work known through correspondence with the mathematicians in
Alexandria. The writings of Archimedes were collected by the
Byzantine architect
Isidore of Miletus (
c. 530 AD), while commentaries on the works of Archimedes written by
Eutocius in the sixth century AD helped to bring his work a wider audience.
.^ Jerome, who knew Hebrew, usually translated the epithet directly into a corresponding Latin epithet  Dominus Exercituum. SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]
.^ From what I've read, Homer was considered something like the ghetto version of epic Greek works" Totally irrelevant if Homer was not the influential person during his time. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^{[41]} .^ And he did – today we still feel his impact through a lever spanning 2200+ years of Archimedesinspired science. Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
^ Over the years since then, we have extended the work of Galileo and Newton .... Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
^{[42]}
Surviving works
Archimedes is said to have remarked about the
lever:
Give me a place to stand on, and I will move the Earth.
 On the Equilibrium of Planes (two volumes)
 The first book is in fifteen propositions with seven postulates, while the second book is in ten propositions. In this work Archimedes explains the Law of the Lever, stating, "Magnitudes are in equilibrium at distances reciprocally proportional to their weights."
 Archimedes uses the principles derived to calculate the areas and centers of gravity of various geometric figures including triangles, parallelograms and parabolas.^{[43]}
 This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who was a student of Conon of Samos. In Proposition II, Archimedes shows that the value of π (pi) is greater than ^{223}⁄_{71} and less than ^{22}⁄_{7}. The latter figure was used as an approximation of π throughout the Middle Ages and is still used today when only a rough figure is required.
 This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation
 with real numbers a and b. .^ This gifted Greek mathematician and inventor once said, "Give me a place to stand and rest my lever on, and I can move the Earth."
 "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^ Apollonius of Perga Apollonius of Perga, a Greek mathematician of the 3d and early 2d centuries BC, was known as the Great Geometer. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
 On the Sphere and the Cylinder (two volumes)
 In this treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter. .^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.
 "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
.^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
.^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.
 This is a work in 32 propositions addressed to Dositheus. In this treatise Archimedes calculates the areas and volumes of sections of cones, spheres, and paraboloids.
 On Floating Bodies (two volumes)
 In the first part of this treatise, Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a center of gravity. This may have been an attempt at explaining the theory of contemporary Greek astronomers such as Eratosthenes that the Earth is round. The fluids described by Archimedes are not selfgravitating, since he assumes the existence of a point towards which all things fall in order to derive the spherical shape.
 In the second part, he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, similar to the way that icebergs float. Archimedes' principle of buoyancy is given in the work, stated as follows:
Any body wholly or partially immersed in a fluid experiences an upthrust equal to, but opposite in sense to, the weight of the fluid displaced.
 In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He achieves this by calculating the value of a geometric series that sums to infinity with the ratio ^{1}⁄_{4}.
 This is a dissection puzzle similar to a Tangram, and the treatise describing it was found in more complete form in the Archimedes Palimpsest. Archimedes calculates the areas of the 14 pieces which can be assembled to form a square. Research published by Dr. Reviel Netz of Stanford University in 2003 argued that Archimedes was attempting to determine how many ways the pieces could be assembled into the shape of a square. Dr. Netz calculates that the pieces can be made into a square 17,152 ways.^{[44]} The number of arrangements is 536 when solutions that are equivalent by rotation and reflection have been excluded.^{[45]} The puzzle represents an example of an early problem in combinatorics.
 The origin of the puzzle's name is unclear, and it has been suggested that it is taken from the Ancient Greek word for throat or gullet, stomachos (στόμαχος).^{[46]} Ausonius refers to the puzzle as Ostomachion, a Greek compound word formed from the roots of ὀστέον (osteon, bone) and μάχη (machē  fight). The puzzle is also known as the Loculus of Archimedes or Archimedes' Box.^{[47]}
 This work was discovered by Gotthold Ephraim Lessing in a Greek manuscript consisting of a poem of 44 lines, in the Herzog August Library in Wolfenbüttel, Germany in 1773. It is addressed to Eratosthenes and the mathematicians in Alexandria. Archimedes challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. .^ Here, Physics would say that there is no more physics beyond the numbers of the Planck Units.
 #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
.^ So, there are a > > lot of things that we know about very large numbers. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^ So, there are a > > > lot of things that we know about very large numbers. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^ So, there are a lot of things that we know about very large numbers. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^{[49]}
 In this treatise, Archimedes counts the number of grains of sand that will fit inside the universe. This book mentions the heliocentric theory of the .^ Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler’s laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.
 Top 10 Most Influential Scientists  Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]
.^ Sure, I admit that infinity exists, for example the infinitude of primes exists, but once I go beyond the number 10^500, I can no longer use Aristotlean Logic that mathematics is based upon and must use Physics logic which is nonlinear. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^ Can modern day mathematicians accept the idea that their subject ends at a large finite number of 10^500? #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^ The first scientist to recognize and use the power of the lever was Archimedes . "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
The introductory letter states that Archimedes' father was an astronomer named Phidias. The Sand Reckoner or Psammites is the only surviving work in which Archimedes discusses his views on astronomy.^{[50]}
 This treatise was thought lost until the discovery of the .^ But don't expect mathematicians to give up work on the existing > infinite structures.
 #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^ Specifically: To subtilize, as the humors of the body, or to break them into finer parts. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
^ Find messages by this author Archimedes Plutonium wrote: > If all numbers were finite numbers, then the set of all primes is not > infinite, because > every Finite number has a successor. #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
Archimedes may have considered this method lacking in formal rigor, so he also used the method of exhaustion to derive the results. .^ Alphabet Alphabet  The letters of a language arranged in the customary order; the series of letters or signs which form the elements of written language. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
Apocryphal works
Archimedes'
Book of Lemmas or
Liber Assumptorum is a treatise with fifteen propositions on the nature of circles. The earliest known copy of the text is in
Arabic.
.^ Find messages by this author On Jan 6, 12:33pm, Archimedes Plutonium  Hide quoted text   Show quoted text  . #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
^ Martin Gardner, author of The Colossal Book of Mathematics "The incomparable Clifford Pickover has written another rich science narrative that at once informs and entertains. Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
^ Find messages by this author On Jan 4, 11:27pm, Archimedes Plutonium  Hide quoted text   Show quoted text  . #266 mathematics ends at about 10^500 Re: powerset  sci.logic  Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]
The
Lemmas may be based on an earlier work by Archimedes that is now lost.
^{[51]}
It has also been claimed that
Heron's formula for calculating the area of a triangle from the length of its sides was known to Archimedes.
^{[c]} However, the first reliable reference to the formula is given by
Heron of Alexandria in the 1st century AD.
^{[52]}
Archimedes Palimpsest
The foremost document containing the work of Archimedes is the
Archimedes Palimpsest. In 1906, the Danish professor
Johan Ludvig Heiberg visited
Constantinople and examined a 174page goatskin parchment of prayers written in the 13th century AD. He discovered that it was a
palimpsest, a document with text that had been written over an erased older work. Palimpsests were created by scraping the ink from existing works and reusing them, which was a common practice in the Middle Ages as
vellum was expensive. The older works in the palimpsest were identified by scholars as 10th century AD copies of previously unknown treatises by Archimedes.
^{[53]} The parchment spent hundreds of years in a monastery library in Constantinople before being sold to a private collector in the 1920s. On October 29, 1998 it was sold at auction to an anonymous buyer for $2 million at
Christie's in
New York.
^{[54]} .^ Of the 90 or so plays Aeschylus wrote, only seven have survived in complete form, among them the 'Oresteia' trilogy, 'The Seven against Thebes' and 'Prometheus Bound'. "Natural Magick"  "Glossery/Index  A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]
It is the only known source of
The Method of Mechanical Theorems, referred to by Suidas and thought to have been lost forever.
Stomachion was also discovered in the palimpsest, with a more complete analysis of the puzzle than had been found in previous texts. The palimpsest is now stored at the
Walters Art Museum in
Baltimore,
Maryland, where it has been subjected to a range of modern tests including the use of
ultraviolet and
xray light to read the overwritten text.
^{[55]}
The treatises in the Archimedes Palimpsest are:
On the Equilibrium of Planes, On Spirals, Measurement of a Circle, On the Sphere and the Cylinder, On Floating Bodies, The Method of Mechanical Theorems and
Stomachion.
Legacy
The
Fields Medal for outstanding achievement in mathematics carries a portrait of Archimedes, along with his proof concerning 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).
^{[58]}
.^ Nicaragua Postage Stamp List . Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
^ Nicaragua postage stamps, 496497 . Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
^{[59]}
A movement for civic engagement targeting universal access to health care in the US state of
Oregon has been named the "Archimedes Movement," headed by former Oregon Governor
John Kitzhaber.
^{[61]}
See also
Notes and references
Notes
a. ^{^} In the preface to
On Spirals addressed to Dositheus of Pelusium, Archimedes says that "many years have elapsed since Conon's death."
Conon of Samos lived
c. 280–220 BC, suggesting that Archimedes may have been an older man when writing some of his works.
.^ Throughout, he includes fascinating, littleknown tidbits relating to the law or lawgiver, and he provides crossreferences to other laws or equations mentioned in the book. Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
^ It was authored by one of the greatest mechanical minds in history: the legendary Archimedes , who knew a thing or two about spheres right down to his dying words... 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
^ The only reason we know the books exist at all is that other books from the time reference them (including some Cliffs Notesstyle summaries) but that's it. 7 Books We Lost to History That Would Have Changed the World  Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]
Of the surviving works by Archimedes,
T. L. Heath offers the following suggestion as to the order in which they were written:
On the Equilibrium of Planes I,
The Quadrature of the Parabola,
On the Equilibrium of Planes II,
On the Sphere and the Cylinder I, II,
On Spirals,
On Conoids and Spheroids,
On Floating Bodies I, II,
On the Measurement of a Circle,
The Sand Reckoner.
.^ In this book, I discuss landmark laws of nature that were discovered over several centuries and whose ramifications have profoundly altered our everyday lives and understanding of the universe. Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
Arabic scholars also attribute to Archimedes the 'theorem on the broken
chord' … Archimedes is reported by the Arabs to have given several proofs of the theorem."
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 ^ "Archimedes' Weapon". Time Magazine. November 26, 1973. http://www.time.com/time/magazine/article/0,9171,908175,00.html?promoid=googlep. Retrieved 20070812.
 ^ Bonsor, Kevin. "How Wildfires Work". HowStuffWorks. http://science.howstuffworks.com/wildfire.htm. Retrieved 20070723.
 ^ Quoted by Pappus of Alexandria in Synagoge, Book VIII
 ^ Dougherty, F. C.; Macari, J.; Okamoto, C.. "Pulleys". Society of Women Engineers. http://www.swe.org/iac/lp/pulley_03.html. Retrieved 20070723.
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 ^ Cicero. "De re publica 1.xiv §21". thelatinlibrary.com. http://www.thelatinlibrary.com/cicero/repub1.shtml#21. Retrieved 20070723.
 ^ Cicero. "De re publica Complete etext in English from Gutenberg.org". Project Gutenberg. http://www.gutenberg.org/etext/14988. Retrieved 20070918.
 ^ Rorres, Chris. "Spheres and Planetaria". Courant Institute of Mathematical Sciences. http://www.math.nyu.edu/~crorres/Archimedes/Sphere/SphereIntro.html. Retrieved 20070723.
 ^ "Ancient Moon 'computer' revisited". BBC News. November 29, 2006. http://news.bbc.co.uk/1/hi/sci/tech/6191462.stm. Retrieved 20070723.
 ^ Plutarch. "Extract from Parallel Lives". fulltextarchive.com. http://fulltextarchive.com/pages/PlutarchsLives10.php#p35. Retrieved 20090810.
 ^ R.W. Kaye. "Archimedean ordered fields". web.mat.bham.ac.uk. http://web.mat.bham.ac.uk/R.W.Kaye/seqser/archfields. Retrieved 20091107.
 ^ Quoted in T. L. Heath, Works of Archimedes, Dover Publications, ISBN 0486420841.
 ^ Carroll, Bradley W. "The Sand Reckoner". Weber State University. http://physics.weber.edu/carroll/Archimedes/sand.htm. Retrieved 20070723.
 ^ Encyclopedia of ancient Greece By Nigel Guy Wilson Page 77 ISBN 0794502253 (2006)
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 ^ Rorres, Chris. "Stamps of Archimedes". Courant Institute of Mathematical Sciences. http://math.nyu.edu/~crorres/Archimedes/Stamps/stamps.html. Retrieved 20070825.
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Further reading
 Boyer, Carl Benjamin (1991). A History of Mathematics. New York: Wiley. ISBN 0471543977.
 Dijksterhuis, E.J. (1987). Archimedes. Princeton University Press, Princeton. ISBN 0691084211. Republished translation of the 1938 study of Archimedes and his works by an historian of science.
 Gow, Mary (2005). Archimedes: Mathematical Genius of the Ancient World. Enslow Publishers, Inc. ISBN 0766025020.
 Hasan, Heather (2005). Archimedes: The Father of Mathematics. Rosen Central. ISBN 9781404207745.
 Heath, T.L. (1897). Works of Archimedes. Dover Publications. ISBN 0486420841. Complete works of Archimedes in English.
 Netz, Reviel and Noel, William (2007). The Archimedes Codex. Orion Publishing Group. ISBN 0297645471.
 Pickover, Clifford A. (2008). .^ Pickover examines more than 40 great laws, providing brief and cogent introductions to the science behind the laws as well as engaging biographies of such scientists as Newton, Faraday, Ohm, Curie, and Planck.
 Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
^ Laws of Science and the Great Minds Behind Them 22 Centuries of Discovery Do We Discover or Invent Laws? Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
^ Archimedes to Hawking: Laws of Science and the Great Minds Behind Them Return to Cliff Pickover's main web page . Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
.^ Clifford A. Pickover , Oxford University Press ( Buy at Amazon.Com ) Book Praise . Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]
ISBN 9780195336115.
 Simms, Dennis L. (1995). Archimedes the Engineer. Continuum International Publishing Group Ltd. ISBN 0720122848.
 Stein, Sherman (1999). Archimedes: What Did He Do Besides Cry Eureka?. Mathematical Association of America. ISBN 0883857189.
The Works of Archimedes online
.
This audio file was created from a revision dated 20090331, and does not reflect subsequent edits to the article. (Audio help)