47 Fun Facts About Archimedes

On which island was Archimedes' home city, where he was born and killed?

Archimedes was born and killed in Syracuse, on Sicily's eastern coast, a Greek city founded by Corinthian settlers in the 8th century BC.

What did Archimedes supposedly cry as he ran naked through the streets after his bathtub insight?

Eureka! is Greek for 'I have found it!'; the tale has Archimedes realising in his bath that displaced water could measure the wreath's volume.

Which king of Syracuse asked Archimedes to check whether his gold wreath was cut with silver?

Hiero II, king of Syracuse from about 270 BC and Archimedes' patron, suspected his goldsmith had alloyed a votive wreath with silver.

Which Roman writer, two centuries after Archimedes died, is the source of the bathtub story?

Vitruvius tells the golden-wreath bathtub story in Book IX of De architectura, written in the first century BC, roughly two centuries after Archimedes' death.

Archimedes' principle states that a body immersed in water experiences an upthrust equal to what?

It appears in his treatise On Floating Bodies, which survives in Greek only in the Palimpsest.

Which saying does Pappus of Alexandria attribute to Archimedes?

Pappus of Alexandria records the saying 'Give me a place to stand on, and I will move the Earth' in Book VIII of his Synagoge (Collection), compiled around AD 320.

What was the Syracusia, whose construction Archimedes is said to have supervised?

The Syracusia, described by Athenaeus from Moschion's account, was the largest ship built in classical antiquity, carrying a gymnasium, gardens and a shrine of Aphrodite; Archimedes supervised its construction.

Archimedes proved a triangle's centre of gravity lies where which three lines meet?

In On the Equilibrium of Planes, Archimedes showed a triangle's centre of gravity lies where its three medians meet, each median dividing the triangle into two equal areas.

Which Roman general besieged Syracuse from 214 BC and later ordered that Archimedes should not be harmed?

Marcus Claudius Marcellus, five times consul, led the siege; Plutarch says he was grieved when a soldier killed Archimedes at the city's fall in 212 BC.

During which war did Syracuse switch from Rome to Carthage, prompting the siege Archimedes resisted?

Syracuse defected to Carthage in 215 BC during the Second Punic War, Hannibal's war; Rome besieged it from 214 and took it in 212 BC.

According to Livy's account, what was Archimedes doing when a Roman soldier killed him?

Livy says Archimedes was absorbed in figures he had drawn in the dust when a soldier killed him; Valerius Maximus has him beg the soldier not to disturb the drawing.

What did Archimedes ask to have placed on his tomb to represent his proudest discovery?

Archimedes wanted a sphere and a cylinder on his tomb, marking his proof in On the Sphere and Cylinder of a fixed ratio between the two solids' volumes and surface areas.

Which Roman statesman found Archimedes' neglected tomb while quaestor on the island?

Cicero, serving as quaestor in 75 BC, found the tomb overgrown with brambles outside Syracuse and had the spot cleared and its inscription read.

What fraction of the enclosing cylinder's volume and surface area did Archimedes show a sphere has?

A sphere's volume is two-thirds that of its circumscribing cylinder, and its surface equals two-thirds of the cylinder's total surface, results Archimedes proved in On the Sphere and Cylinder.

Between which two bounds did Archimedes show pi lies, using polygons of 96 sides?

Archimedes showed pi lies between 3 10/71 (about 3.1408) and 3 1/7 (about 3.1429) by inscribing and circumscribing regular polygons, doubling from hexagons to 96 sides.

In Quadrature of the Parabola, a parabolic segment's area is what multiple of its inscribed triangle?

The segment is 4/3 of the inscribed triangle on the same base and height; Archimedes reached it in Quadrature of the Parabola by summing the series 1 + 1/4 + 1/16 + ...

What technique, inherited from Eudoxus, did Archimedes use to prove areas and volumes rigorously?

The method of exhaustion, developed by Eudoxus, traps a figure between inscribed and circumscribed polygons whose gap can be made arbitrarily small; Archimedes used it to prove his area and volume results rigorously.

What Greek term for 10,000 did Archimedes base his large-number system on in The Sand Reckoner?

He used powers of a myriad of myriads, that is 100 million, to count sand grains.

How many grains of sand did Archimedes conclude it would take to fill the universe?

Archimedes put the count at 8 × 10^63 grains, taking the universe to be a sphere reaching the fixed stars and inventing a notation able to express such numbers.

Which heliocentric theorist's model does Archimedes describe in The Sand Reckoner?

Aristarchus of Samos proposed the heliocentric hypothesis; Archimedes adopted its vastly larger cosmos in The Sand Reckoner so that his sand-grain count would be as large as possible.

What was the profession of Archimedes' father Phidias, as stated in The Sand Reckoner?

In The Sand Reckoner Archimedes names his father Phidias as an astronomer, quoting Phidias's estimate of the solar diameter beside that of Eudoxus; nothing else is known about him.

Which law does Archimedes prove in the first book of On the Equilibrium of Planes?

The law of the lever, proved in Propositions 6 and 7 of On the Equilibrium of Planes Book I, says magnitudes balance at distances inversely proportional to their weights.

To which student of Conon of Samos did Archimedes address several of his treatises?

Dositheus of Pelusium, a pupil of Conon, received On the Sphere and Cylinder, On Spirals, On Conoids and Spheroids and Quadrature of the Parabola after Conon's death.

What is the Ostomachion, described in a treatise found in the Palimpsest?

The Ostomachion is a 14-piece dissection puzzle like a tangram; its pieces can be assembled into a square in 17,152 ways (536 ignoring symmetries), a count computed in 2003.

Archimedes' Cattle Problem challenges Alexandrian mathematicians to count the herd of which deity?

The herd belongs to the Sun, grazing on Thrinacia's plains in the poem; the complete solution has 206,545 digits, its leading figures first found by A. Amthor in 1880.

Who found the Cattle Problem in a 44-line Greek poem in the Herzog August Library in 1773?

Gotthold Ephraim Lessing, the German dramatist, was librarian at Wolfenbüttel from 1770 and published the epigram in 1773 among manuscripts he found there.

How many semiregular polyhedra did Archimedes prove exist, in a lost work described by Pappus?

Pappus reports that Archimedes described thirteen semiregular polyhedra, each with faces of two or more kinds of regular polygon meeting identically at every vertex; they are known as the Archimedean solids.

Which treatise, thought lost forever, is known only from the Archimedes Palimpsest?

The Method of Mechanical Theorems survives only in the Palimpsest, read in 1906; in it Archimedes shows how he balanced figures mechanically to discover results before proving them rigorously.

For how much was the Archimedes Palimpsest sold at auction to an anonymous buyer on 29 October 1998?

The Palimpsest fetched $2.2 million at Christie's in New York on 29 October 1998, bought by an anonymous American collector who then funded its conservation and imaging.

According to a Roman statesman, what did an Archimedes device carried off to Rome model?

In De re publica the author describes the conquering general keeping a device by Archimedes that reproduced the motions of the planets and the two luminaries; a solid star globe went to the Temple of Virtue.

Which 9th-century scholar translated Archimedes' work into Arabic?

Thabit ibn Qurra, a Sabian scholar of Baghdad who died in 901, translated and revised Archimedes in Arabic; the Book of Lemmas survives only through his Arabic text, later Latinised.

Which scientist called Archimedes "superhuman" and "my master"?

Galileo Galilei praised Archimedes repeatedly, calling him 'superhuman' and 'my master'; Galileo's early essay La Bilancetta (1586) reconstructed the hydrostatic balance Archimedes might have used.

Which mathematics prize carries a portrait of Archimedes and a carving of his favourite proof?

The Fields Medal, awarded every four years since 1936, bears Archimedes' head with the Latin inscription Transire suum pectus mundoque potiri, 'Rise above oneself and grasp the world'.

Which US state's motto is the exclamation attributed to Archimedes?

California's motto has appeared on its state seal since 1849 and recalls the 1848 discovery of gold at Sutter's Mill.

What was the SS Archimedes, launched in 1839?

It was named for his work on the screw.

Who named Archimedes, Newton and Eisenstein as the only three 'epoch-making mathematicians'?

Carl Friedrich Gauss is reported to have called Archimedes, Newton and Eisenstein the only epoch-making mathematicians, a remark repeated by E. T. Bell in Men of Mathematics.

In which dialect were Archimedes' works originally written?

Archimedes wrote in Doric Greek, the dialect of Syracuse and other Dorian colonies, rather than the Attic-based Koine of Alexandria, where he sent his treatises.

What did Archimedes' On Floating Bodies prove water would do around a centre of gravity?

The second book analyses floating paraboloids, probably an idealisation of ships' hulls, some floating like icebergs.

What besides a crater is named after Archimedes on the Moon?

The Montes Archimedes, a rugged mountain range, lie just south of the 80-km crater Archimedes on the eastern edge of Mare Imbrium.

In roughly which year is Archimedes estimated to have been born?

Archimedes' birth is placed at 287 BC because a Byzantine writer says he was 75 when killed at the fall of Syracuse in 212 BC.

Which Alexandrian scholar received Archimedes' letter revealing how he first found his results?

Eratosthenes of Cyrene, head of the Library of Alexandria and famed for measuring Earth's circumference, received that letter and was also the addressee of the Cattle Problem.

After its 1998 sale, where was the Archimedes Palimpsest conserved and imaged?

The Walters Art Museum in Baltimore conserved and imaged the Palimpsest from 1999 to 2008, with multispectral imaging on site and X-ray fluorescence scans at Stanford's synchrotron.

Which treatise proves a disc's area equals a right triangle with legs its radius and circumference?

Measurement of a Circle, a short three-proposition work, proves a circle's area equals that of a right triangle whose legs are its radius and circumference.

Which hundred-handed giant did the Roman commander at Syracuse liken Archimedes to?

Briareus was one of the hundred-handed giants of Greek myth; Plutarch has the Roman commander joke that Archimedes, a 'geometrical Briareus', used the Roman ships as cups to ladle water from the sea.

The 1544 first printed edition of Archimedes' works in Greek and Latin was published in which city?

The editio princeps appeared at Basel in 1544 from the press of Johann Herwagen, edited by Thomas Venatorius, with Greek text and Latin translation.

Which 2nd-century satirist gave the earliest account of Archimedes setting Roman ships on fire?

Lucian of Samosata, in his 2nd-century dialogue Hippias, says Archimedes burned the Roman ships by his art without mentioning mirrors, a detail that only later writers supplied.

Which Byzantine scholar's claim that Archimedes lived 75 years fixes his estimated birth date?

John Tzetzes, a 12th-century Byzantine scholar, states in his Chiliades that Archimedes was 75 when he died, the only basis for estimating his birth year.