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Archimedes of Syracuse (Greek: Template:Polytonic c. 287 BC – c. 212 BC) was an ancient Greek mathematician, physicist and engineer. Although little is known of his life, he is regarded as one of the leading scientists in classical antiquity. In addition to making discoveries in the fields of mathematics and geometry, he is credited with designing machines that were innovative. He laid the foundations of hydrostatics, and explained the principle of the lever, the device on which mechanics is based. His early advances in calculus included the first known summation of an infinite series with a method that is still used todayThe historians of Ancient Rome showed a strong interest in Archimedes and wrote accounts of his life and works, while the relatively few copies of his treatises that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance.Cite error: A <ref> tag is missing the closing </ref> (see the help page).

Biography

Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a colony of Magna Graecia. The date of birth is based on an assertion by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years. 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. A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children. Archimedes probably spent part of his youth in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries. 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 died c. 212 BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two year long siege. According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. The soldier was enraged by this, and killed Archimedes with his sword. Plutarch also gives a lesser-known account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items. General Marcellus was reportedly angered by the death of Archimedes, as he had ordered him not to be harmed.

The tomb of Archimedes had a carving of his favorite mathematical diagram, which was a sphere inside a cylinder of the same height and diameter. Archimedes had proved that the volume and surface area of the sphere would be two thirds that of the cylinder. In 75 BC, 137 years after his death, the Roman orator Cicero was serving as quaestor in Sicily. He had heard stories about the tomb of Archimedes, but none of the locals was able to give him the location. Eventually he found the tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. 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.Cite error: A <ref> tag is missing the closing </ref> (see the help page). 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. The screw was a machine with a revolving screw shaped blade inside a cylinder. It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. Versions of the Archimedes' screw are still in use today in developing countries. The Archimedes' screw described in Roman times by Vitruvius may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon.Cite error: A <ref> tag is missing the closing </ref> (see the help page).

• Archimedes' Cattle Problem

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 at the University of Alexandria. Archimedes challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. There is a more difficult version of the problem in which some of the answers are required to be square numbers. This version of the problem was first solved by a computer in 1965, and the answer is a very large number, approximately 7.760271×10.

• The Sand Reckoner

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 solar system proposed by Aristarchus of Samos (concluding that "this is impossible"), contemporary ideas about the size of the Earth and the distance between various celestial bodies. By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8×10 in modern notation. 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.

• The Method of Mechanical Theorems

This treatise was thought lost until the discovery of the Archimedes Palimpsest in 1906. In this work Archimedes uses infinitesimals, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume. Archimedes may have considered this method lacking in formal rigor, so he also used the method of exhaustion to derive the results. As with The Cattle Problem, The Method of Mechanical Theorems was written in the form of a letter to Eratosthenes in Alexandria.

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. The scholars T. L. Heath and Marshall Clagett argued that it cannot have been written by Archimedes in its current form, since it quotes Archimedes, suggesting modification by another author. The Lemmas may be based on an earlier work by Archimedes that is now lost.

It has also been claimed by the Arab scholar Abu'l Raihan Muhammed al-Biruni that Heron's formula for calculating the area of a triangle from the length of its sides was known to Archimedes. However, the first reliable reference to the formula is given by Heron of Alexandria in the 1st century  AD.

The treatises in the Archimedes Palimpsest are: On the Equilibrium of Planes, On Spirals, The Measurement of the Circle, On the Sphere and the Cylinder, On Floating Bodies, The Method of Mechanical Theorems and Stomachion.

Legacy

There is a crater on the Moon named Archimedes (29.7° N, 4.0° W) in his honor, and a lunar mountain range, the Montes Archimedes (25.3° N, 4.6° W). The asteroid 3600 Archimedes is named after him.

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).

Archimedes has appeared on postage stamps issued by East Germany (1973), Greece (1983), Italy (1983), Nicaragua (1971), San Marino (1982) and Spain (1963).

The exclamation of Eureka! attributed to Archimedes is the state motto of California. In this instance the word refers to the discovery of gold near Sutter's Mill in 1848 which sparked the California gold rush.

1. T. L. Heath, Works of Archimedes, 1897
2. Plutarch. "Parallel Lives Complete e-text from Gutenberg.org". Project Gutenberg. Retrieved 2007-07-23. {{cite web}}: Text "lives" ignored (help); Text "name" ignored (help)
3. O'Connor, J.J. and Robertson, E.F. "Archimedes of Syracuse". University of St Andrews. Retrieved 2007-01-02. {{cite web}}: Text "andrews" ignored (help); Text "name" ignored (help)CS1 maint: multiple names: authors list (link)
4. Rorres, Chris. "Death of Archimedes: Sources". Courant Institute of Mathematical Sciences. Retrieved 2007-01-02.
5. Rorres, Chris. "Archimedes' Stomachion". Courant Institute of Mathematical Sciences. Retrieved 2007-09-14.
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8. "Archimedes' Book of Lemmas". cut-the-knot. Retrieved 2007-08-07.
9. Wilson, James W. "Problem Solving with Heron's Formula". University of Georgia. Retrieved 2007-09-14.
10. Friedlander, Jay and Williams, Dave. "Oblique view of Archimedes crater on the Moon". NASA. Retrieved 2007-09-13.{{cite web}}: CS1 maint: multiple names: authors list (link)
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13. Rorres, Chris. "Stamps of Archimedes". Courant Institute of Mathematical Sciences. Retrieved 2007-08-25.
14. "California Symbols". California State Capitol Museum. Retrieved 2007-09-14.