Archimedes facts for kids
Quick facts for kids
Archimedes of Syracuse
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| Ἀρχιμήδης | |
Archimedes Thoughtful
by Domenico Fetti (1620) |
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| Born | c. 287 BC |
| Died | c. 212 BC (aged c. 75) Syracuse, Sicily, Magna Graecia
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| Known for | |
| Scientific career | |
| Fields | |
Archimedes (287 BC–212 BC) was a Greek scientist. He was an inventor, an astronomer, and a mathematician. He was born in the town of Syracuse in Sicily.
Contents
Biography
Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily. Syracuse was a rich Greek city. His father was Phidias, an astronomer, and he may have been in the family of a king of Syracuse. When Archimedes was about ten years old, he left Syracuse to study in Alexandria, Egypt. He was in the school of Euclid, a famous mathematician. Not much is known about the personal life of Archimedes, for example, whether he was married or if he had children. He died during a Roman invasion.
The standard versions of Archimedes' life were written long after his death by Greek and Roman historians. The earliest reference to Archimedes occurs in The Histories by Polybius (c. 200–118 BC), written about 70 years after his death. 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 from the Romans. Polybius remarks how, during the Second Punic War, Syracuse switched allegiances from Rome to Carthage, resulting in a military campaign under the command of Marcus Claudius Marcellus and Appius Claudius Pulcher, who besieged the city from 213 to 212 BC. He notes that the Romans underestimated Syracuse's defenses, and mentions several machines Archimedes designed, including improved catapults, crane-like machines that could be swung around in an arc, and other stone-throwers. Although the Romans ultimately captured the city, they suffered considerable losses due to Archimedes' inventiveness.
Cicero (106–43 BC) mentions Archimedes in some of his works. While serving as a quaestor in Sicily, Cicero found what was presumed to be Archimedes' 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. The tomb carried a sculpture illustrating Archimedes' favorite mathematical proof, that the volume and surface area of the sphere are two-thirds that of an enclosing cylinder including its bases. He also mentions that Marcellus brought to Rome two planetariums Archimedes built.
Plutarch (45–119 AD) wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse. He also provides at least two accounts on how Archimedes died after the city was taken. According to the most popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. This enraged the soldier, who killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by Archimedes' death, as he had ordered that he should not be harmed.
The last words attributed to Archimedes are "Do not disturb my circles" (Latin, "Noli turbare circulos meos"; Katharevousa Greek, "μὴ μου τοὺς κύκλους τάραττε"), a reference to the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. There is no reliable evidence that Archimedes uttered these words and they do not appear in Plutarch's account.
Archimedes the scientist
Archimedes is also well known for being the first person to understand statics, which is a part of applied mathematics. It has to do with loads that do not move, for example in buildings or bridges. He also understood and wrote about what happens when things float in liquids, which is called buoyancy.
Archimedes' principle
The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a crown for a temple had been made for King Hiero II of Syracuse, who supplied the pure gold to be used. The crown was likely made in the shape of a votive wreath. Archimedes was asked to determine whether some silver had been substituted by the goldsmith without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density.
In this account, Archimedes noticed while taking a bath 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 golden crown's volume. Archimedes was so excited by this discovery that he took to the streets, having forgotten to dress, crying "Eureka!" (Greek: "εὕρηκα, heúrēka!, lit. I have found [it]!). For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, its density could be obtained; if cheaper and less dense metals had been added, the density would be lower than that of gold. Archimedes found that this is what had happened, proving that silver had been mixed in.
The story of the golden crown does not appear anywhere in Archimedes' known works. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure water displacement. Archimedes may have instead sought a solution that applied the hydrostatics principle known as Archimedes' principle, found in his treatise On Floating Bodies: a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing it on a scale with a pure gold reference sample of the same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. Galileo Galilei, who invented a hydrostatic balance in 1586 inspired by Archimedes' work, 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."
Archimedes, the inventor and engineer
Archimedes is also famous as an inventor because he made new tools and machines. For example, he made a machine to lift water that could be used by farmers to bring water to their crops. This is called Archimedes' screw.
Archimedes probably also invented a machine to measure distance, an odometer. A cart was built with wheels that turned four hundred times in one mile. A pin on the wheel would hit a 400-tooth gear, so it turned once for every mile. This gear would then make a small stone fall into a cup. At the end of a journey one could count the number of stones in the cup to find the distance.
Archimedes also made a system which one person could pull a large ship with just one rope. This was called the compound pulley. This is an important machine even today, as it helps people in everyday life, although the versions we now use are much more complicated. They still work by the same principle, though.
Archimedes' screw
A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of Syracuse. Athenaeus of Naucratis quotes a certain Moschion in a description on how King Hiero II commissioned the design of a huge ship, the Syracusia, which could be used for luxury travel, carrying supplies, and as a display of naval power. The Syracusia is said to have been the largest ship built in classical antiquity and, according to Moschion's account, it was launched by Archimedes. The ship presumably was capable of carrying 600 people and included garden decorations, a gymnasium, and a temple dedicated to the goddess Aphrodite among its facilities. The account also mentions that, in order to remove any potential water leaking through the hull, a device with a revolving screw-shaped blade inside a cylinder was designed by Archimedes.
Archimedes' screw was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. The screw is still in use today for pumping liquids and granulated solids such as coal and grain. Archimedes' device may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon. The world's first seagoing steamship with a screw propeller was the SS Archimedes, which was launched in 1839 and named in honor of Archimedes and his work on the screw.
Archimedes' claw
Archimedes is said to have designed a claw as a weapon to defend the city of Syracuse. Also known as "the ship shaker", the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it.
There have been modern experiments to test the feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device.
Mathematics
While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics.
Archimedes proved a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.
His other mathematical achievements include deriving an approximation of pi, defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers.
Spherical geometry
On the Sphere and Cylinder is a work that was published by Archimedes in two volumes in about 225 BC. On the sphere, he showed that the surface area is four times the area of its great circle. In modern terms, this means that the surface area is equal to:
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The surface area of a cylinder is equal to:
The volume of the cylinder is:
The volume of the contained ball is two-thirds the volume of a "circumscribed" cylinder. meaning that the volume is
Archimedes at war
Archimedes also invented or made many machines used in war, for example he made better catapults. This was during the Punic Wars, which were between Rome in what is now Italy and the city of Carthage in what is now North Africa. For many years he helped stop the Roman army from attacking Syracuse, his city. One war machine was called the "claw of Archimedes", or the "iron hand". It was used to defend the city from attacks by ships. Ancient writers said that it was a kind of crane with a hook that lifted ships out of the water and caused their destruction.
Another story about Archimedes is that he burned Roman ships from far away using many mirrors and the light from the sun. This is perhaps possible, but it is perhaps more likely that this was done with flaming missiles from a catapult.
Legacy
Sometimes called the father of mathematics and mathematical physics, Archimedes had a wide influence on mathematics and science. Historians of science and mathematics almost universally agree that Archimedes was the finest mathematician from antiquity.
Galileo called him "superhuman" and "my master", while Huygens said, "I think Archimedes is comparable to no one", consciously emulating him in his early work. Leibniz said, "He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times". Gauss's heroes were Archimedes and Newton, and Moritz Cantor, who studied under Gauss in the University of Göttingen, reported that he once remarked in conversation that "there had been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein".
The inventor Nikola Tesla praised him, saying:
Archimedes was my ideal. I admired the works of artists, but to my mind, they were only shadows and semblances. The inventor, I thought, gives to the world creations which are palpable, which live and work.
Honors and commemorations
The Fields Medal for outstanding achievement in mathematics carries a portrait of Archimedes, along with a carving illustrating his proof on the sphere and the cylinder. The inscription around the head of Archimedes is a quote attributed to 1st century AD poet Manilius, 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).
Interesting facts about Archimedes
- Archimedes was the first known Greek to have recorded multiple solstice dates and times.
- The exclamation of Eureka! attributed to Archimedes is the state motto of California.
- Archimedes gives the value of the square root of 3 as lying between 265153 (approximately 1.7320261) and 1351780 (approximately 1.7320512) in Measurement of a Circle. The actual value is approximately 1.7320508, making this a very accurate estimate. Archimedes introduced this result without offering any explanation of how he had obtained it.
- Archimedes discusses astronomical measurements of the Earth, Sun, and Moon, as well as Aristarchus' heliocentric model of the univers without the use of either trigonometry or a table of chords.
- There is a crater on the Moon named Archimedes (29°42′N 4°00′W / 29.7°N 4.0°W) in his honor, as well as a lunar mountain range, the Montes Archimedes (25°18′N 4°36′W / 25.3°N 4.6°W).
- A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.
- Leonardo da Vinci repeatedly expressed admiration for Archimedes, and attributed his invention Architonnerre to Archimedes.
Archimedes quotes
- "Give me a place to stand and with a lever I will move the world."
- "Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible."
- "I have found it!" or "I have got it!", commonly quoted as "Eureka!"
Images for kids
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The Death of Archimedes (1815) by Thomas Degeorge
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Frontpage of Archimedes' Opera, in Greek and Latin, edited by David Rivault (1615).
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Ostomachion is a dissection puzzle found in the Archimedes Palimpsest.
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In 1906, the Archimedes Palimpsest revealed works by Archimedes thought to have been lost.
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The Fields Medal carries a portrait of Archimedes.
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Bronze statue of Archimedes in Berlin
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See also
In Spanish: Arquímedes para niños
