Archimedes was born 287 BC in Syracuse, Sicily.

Archimedes was a famous mathematician whose theorems and philosophies became world known. He gained a reputation in his own time which few other mathematicians of this period achieved. He is considered by most historians of mathematics as one of the greatest mathematicians of all time. He discovered pi.

Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch.

He was best known for his discovery of the relation between the surface and volume of a sphere and its circumscribing cyclinder, for his formulation of a hydrostatic principle Archimedes' principle and for inventing the Archimedes screw (a device for raising water). Archimedes Principal states: an object immersed in a fluid experiences a buoyant force that is equal in magnitude to the force of gravity on the displaced fluid.

He also invented things such as the hydraulic screw - for raising water from a lower to a higher level, catapult, the lever, the compound pulley and the burning mirror.

In mechanics Archimedes discovered fundamental theorems concerning the centre of gravity of plane figures and solids.

Archimedes probably spent some time in Egypt early in his career, but he resided for most of his life in Syracuse, the principal city-state in Sicily, where he was on intimate terms with its king, Hieron II. Archimedes published his works in the form of correspondence with the principal mathematicians of his time, including the Alexandrian scholars Conon of Samos and Eratosthenes of Cyrene.

He played an important role in the defense of Syracuse against the siege laid by the Romans in 213 BC by constructing war machines so effective that they long delayed the capture of the city. But Syracuse was eventually captured by the Roman general Marcus Claudius Marcellus in the autumn of 212 or spring of 211 BC, and Archimedes was killed in the sack of the city.

According to Plutarch, Archimedes had so low an opinion of the kind of practical invention at which he excelled and to which he owed his contemporary fame that he left no written work on such subjects. While it is true that--apart from a dubious reference to a treatise, "On Sphere-Making"--all of his known works were of a theoretical character, nevertheless his interest in mechanics deeply influenced his mathematical thinking. Not only did he write works on theoretical mechanics and hydrostatics, but his treatise Method Concerning Mechanical Theorems shows that he used mechanical reasoning as a heuristic device for the discovery of new mathematical theorems.


The works of Archimedes which have survived are as follows. On plane equilibriums (two books), Quadrature of the Parabola, On the Sphere and Cylinder (two books), On Spirals, On Conoids and Spheroids, On Floating Bodies (two books), Measurement of a Circle, and The Sandreckoner.

He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.


Legend has it that Archimedes discovered his famous theory of buoyancy - Archimedes Principle - while taking a bath. He was so excited that he ran naked through the streets of Syracuse shouting "Eureka, eureka (I have found it)!".

Another legend describes how Archimedes uncovered a fraud against King Hieron II of Syracuse using his principle of buoyancy. The king suspected that a solid gold crown he ordered was partly made of silver. Archimedes first took two equal weights of gold and silver and compared their weights when immersed in water. Next he compared the weights of the crown and a pure silver crown of identical dimensions when each was immersed in water. The difference between these two comparisons revealed that the crown was not solid gold.



This machine for raising water, allegedly invented by the ancient Greek scientist Archimedes for removing water from the hold of a large ship. One form consists of a circular pipe enclosing a helix and inclined at an angle of about 45 degrees to the horizontal with its lower end dipped in the water; rotation of the device causes the water to rise in the pipe. Other forms consist of a helix revolving in a fixed cylinder or a helical tube wound around a shaft.

Modern screw pumps, consisting of helices rotating in open inclined troughs, are effective for pumping sewage in wastewater treatment plants. The open troughs and the design of the screws permit the passage of debris without clogging.


Archimedes invented many machines which were used as engines of war. These were particularly effective in the defence of Syracuse when it was attacked by the Romans under the command of Marcellus.

Image by Stanzino delle Matematiche

During the Roman siege of Syracuse, he is said to have single-handedly defended the city by constructing lenses to focus the Sun's light on Roman ships and huge cranes to turn them upside down. When the Romans finally broke the siege, Archimedes was killed by a Roman soldier after snapping at him ``Don't disturb my circles,'' a reference to a geometric figure he had outlined on the sand.


Other inventions of Archimedes such as the compound pulley also brought him great fame among his contemporaries.

Archimedes had stated in a letter to King Hieron that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king's arsenal, which could not be drawn out of the dock without great labour and many men; and, loading her with many passengers and a full freight, sitting himself the while far off, with no great endeavour, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly as if she had been in the sea.


"Give me a place to stand and rest my lever on, and I can move the Earth."


Archimedes is supposed to have made two "spheres" that Marcellus took back to Rome - one a star globe and the other a device (the details of which are uncertain) for mechanically representing the motions of the Sun, Moon, and planets.

One was a solid sphere on which were engraved or painted the stars and constellations, which Marcellus placed in the Temple of Virtue. Such celestial globes predate Archimedes by several hundred years and Cicero credits the famed geometers Thales and Eudoxos with first constructing them.

The second sphere, which Marcellus kept for himself, was much more ingenious and original. It was a planetarium: a mechanical model which shows the motions of the sun, moon, and planets as viewed from the earth.

Cicero writes that Archimedes must have been "endowed with greater genius that one would imagine it possible for a human being to possess" to be able to build such an unprecedented device.

Many other ancient writers also refer to Archimedes' planetarium in prose and in verse. Several viewed it as proof that the cosmos must have had a divine creator: for just as Archimedes' planetarium required a creator, so then must the cosmos itself have required a creator.

Cicero reverses the argument to contend that since the cosmos had a divine creator, so then must Archimedes be divine to be able to imitate its motions.

The Greek mathematician Pappus of Alexandria, who lived in the fourth century AD, writes that Archimedes wrote a now-lost manuscript entitled On Sphere-making. Pappus also states that it was the only manuscript that Archimedes wrote on "practical" matters. No physical trace of Archimedes' planetarium survives. Cicero refers to it as a "bronze contrivance" while Claudian describes it as "a sphere of glass."

The 1752 engraving of Rowley's orrery suggests how Archimedes' planetarium might have looked. On this orrery the sun, moon and planets revolve along a flat surface driven underneath by a hidden gearworks.

Spherical bands surrounding the flat surface represent the celestial equator, the arctic circle, a movable horizon, and the ecliptic marked with the zodiacal signs.

In 1900 a shipwreck discovered off the shore of the Greek island of Antikythera uncovered an unexpected treasure. The ship dated from the first century BC and was sailing from the Greek island of Rhodes. Amidst its cargo was a complicated gearworks in a deteriorated state about the size of a cigar box.

The device, now called the Antikythera mechanism, was analyzed by Derek De Solla Price of Yale University, who concluded that it was an ancient planetarium in which the positions of the heavenly bodies were indicated by dials on the face of the device.

The gearworks are about as complicated as those in a modern mechanical clock and represent the earliest physical evidence of an advanced metallic mechanism. Price gives evidence that this mechanism was in the Archimedean tradition and strongly suggests that Archimedes' planetarium was its forerunner. A complete presentation of Price's research can be found in Gears from the Greeks.


Archimedes discovered pi.

He performed numerous geometric proofs using the rigid geometric formalism outlined by Euclid, excelling especially at computing areas and volumes using the method of exhaustion.

Archimedes, although he achieved fame by his mechanical inventions, believed that pure mathematics was the only worthy pursuit. He was a brilliant mathematician who helped develop the science of geometry. His methods anticipated the integral calculus 2,000 years before Newton and Leibniz.

Although many solid figures having all kinds of surfaces can be conceived, those which appear to be regularly formed are most deserving of attention. Those include not only the five figures found in the godlike Plato, that is, the tetrahedron and the cube, the octahedron and the dodecahedron, and fifthly the icosahedron, but also the solids, thirteen in number, which were discovered by Archimedes and are contained by equilateral and equiangular, but not similar, polygons.

Truncated Tetrahedron

- The first is a figure of eight bases, being contained by four triangles and four hexagons.


- After this come three figures of fourteen bases, the first contained by eight triangles and six squares,

Truncated Octahedron

- the second by six squares and eight hexagons,

Truncated Cube

- and the third by eight triangles and six octagons.


- After these come two figures of twenty-six bases, the first contained by eight triangles and eighteen squares,

Truncated Cuboctahedron

-the second by twelve squares, eight hexagons and six octagons.


- After these come three figures of thirty-two bases, the first contained by twenty triangles and twelve pentagons,

Truncated Icosahedron

- the second by twelve pentagons and twenty hexagons,

Truncated Dodecahedron

- and the third by twenty triangles and twelve decagons.

Snub Cube

- After these comes one figure of thirty-eight bases, being contained by thirty-two triangles and six squares


- After this come two figures of sixty-two bases, the first contained by twenty triangles, thirty squares and twelve pentagons,

Truncated Icosidodecahedron

- the second by thirty squares, twenty hexagons and twelve decagons.

Snub Dodecahedron

- After these there comes lastly a figure of ninety-two bases, which is contained by eighty triangles and twelve pentagons.


Archimedes was killed in 212 BC during the capture of Syracuse by the Romans in the Second Punic War after all his efforts to keep the Romans at bay with his machines of war had failed. Plutarch recounts three versions of the story of his killing which had come down to him.

The first version:

"Archimedes ... was ..., as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus; which he declining to do before he had worked out his problem to a demonstration, the soldier, enraged, drew his sword and ran him through."

The second version:

"A Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was then at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him."

The third version that Plutarch had heard:

"As Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him."

Archimedes was buried Syracuse, where he was born, were he grew up, where he worked, and where he died.

On his grave their is an inscription of pi, his most famous discovery. They also placed on his tombstone the figure of a sphere inscribed inside a cylinder and the 2:3 ratio of the volumes between them, the solution to the problem he considered his greatest achievement.

His nicknames where, "the wise one", "the master", and "the great geometer."

Scientists decipher Archimedes' work using modern technology

October 14, 2000 - Associated Press

Using modern technology to uncover ancient secrets, scientists have deciphered five pages of the only known copy of a 2,300-year-old Greek text by the mathematician Archimedes.

The scientists hope to complete a translation of the 174-page treatise, "On Floating Bodies," by next September.

Scholars believe the treatise was copied by a scribe in the 10th century from Archimedes' original Greek scrolls, written in the third century B.C.

It was erased about 200 years later by a monk who reused the parchment for a prayer book, creating a twice-used parchment book known as a "palimpsest." In the 12th century, parchment - scraped and dried animal skins - was rare and costly, and Archimedes' works were in less demand.

Two teams of scientists, from Hopkins and the Rochester Institute of Technology, are using digital cameras and processing techniques as well as ultraviolet and infrared filters developed for medicine and space research to reveal the hidden text.

The Hopkins team used "hyperspectral imaging," recovering images of the old Greek text by bombarding it with ultraviolet light, causing the parchment to fluoresce in spots where the vanished 10th-century ink had altered its chemistry.

"This is cutting-edge science for historically and culturally valuable documents," said William Christens-Barry, a physicist at the Hopkins School of Medicine.

The manuscript is the only copy in the original Greek of Archimedes' theory of flotation of bodies. The text and diagrams also contain the roots of modern calculus and gravitational theory.

The two teams have been working on the so-called Archimedes Palimpsest since January in a competition to determine who will analyze the rest of the manuscript. A decision will be made by the end of the year.

An anonymous buyer purchased it at a 1998 auction for $2 million, and entrusted it to a Baltimore gallery.

Hunt for Archimedes' lost words

Manuscript sold for $2m at auction in 1998

July 12, 2000 - BBC

Scientists in upstate New York are working to restore a 10th Century manuscript which is the only known copy of the writings of the Greek mathematician Archimedes.

The text was wiped out by a monk 200 years after it was written and covered by other writing, but the scientists at Rochester Institute of Technology are using some of the latest technology to uncover the original words.

The 170-page manuscript has been described by one expert as Archimedes' "brain in a book".

It details several of his ground-breaking ideas, including his theory of the flotation of bodies and theorems which contain the roots of modern calculus and gravitational principles.

The RIT scientists are now using digital cameras and ultra-violet and infra-red filters to see through the overwritten material to what remains of the original words and drawings.

The text was sold at auction for $2m in 1998 and the scientists are hoping their work will persuade the museum where it is now kept that they should be given the entire manuscript to restore.