45 Fun Facts About Archimedes

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

Sicily was home to Syracuse, where Archimedes' war machines broke the first Roman attack so badly that Rome gave up on a general assault and settled into a blockade.

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 set the puzzle, and in the tale Archimedes' water test caught the goldsmith: the wreath pushed out more water than an equal weight of pure gold, so silver had been mixed in.

Which Roman writer, two centuries after Archimedes died, gave the earliest written account of the bathtub story?

Vitruvius told the tale in De architectura, yet scholars doubt it: a slightly impure wreath would push out so little extra water that no ancient measure could detect it.

Archimedes' principle says a submerged body's upthrust equals what?

The weight of fluid it displaces sets the upthrust, so equal-sized balls of cork and lead get the same push; the cork floats only because it weighs less than that push.

In the boast Pappus attributes to Archimedes, 'Give me a place to stand on, and I will move' what?

The Earth was the boast's target, and in 1963 John F. Kennedy quoted the line at the United Nations, urging nations to take their stand there and move the world toward peace.

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

A giant ship, the Syracusia was reportedly too big for any harbour on its home island, so it was sent to Alexandria as a gift for Egypt's king during a grain shortage there.

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

Its medians, each running from a corner to the middle of the opposite side, meet there: Archimedes showed the balance point lies on every median, so it must sit where they cross.

Which Roman general besieged Syracuse and had ordered that Archimedes should not be harmed?

Marcus Claudius Marcellus wanted Archimedes alive, yet a soldier killed him when Syracuse fell in 212 BC, and Plutarch says nothing afflicted Marcellus so much.

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

The Second Punic War was Hannibal's war; once his agents Hippocrates and Epicydes seized control of Syracuse and sided with Carthage, Rome sent an army to besiege the city.

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

Drawing figures in the dust, Archimedes was killed by a soldier who did not know who he was; Valerius Maximus adds that he shielded the dust with his hands and begged, 'Don't disturb this.'

What is Archimedes said to have wanted placed on his tomb to mark his proudest discovery?

A sphere and a cylinder marked his proudest result: he had proved a sphere holds two-thirds the volume, and has two-thirds the surface, of the cylinder around it.

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

Cicero tracked the tomb down in 75 BC though the Syracusans denied it existed, and sent men with sickles to clear a path so he could read its worn verses.

In On Spirals, Archimedes says two theorems he sent out were impossible, as a warning to whom?

Those claiming results without proofs were the target: anyone who announced a proof of those two statements would be exposed as pretending to discover the impossible.

Which famous number is sometimes called Archimedes' constant?

Pi earned the name because Archimedes' polygon method, which trapped it between 223/71 and 22/7, stayed the best way to compute it for over 1,000 years.

Archimedes found a parabolic segment's area by adding up the terms of what kind of series?

A geometric series did it: each set of triangles he added had a quarter of the area of the last, and 1 + 1/4 + 1/16 + ... gave 4/3 of the first triangle.

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

The method of exhaustion traps a shape between polygons drawn inside and outside it, squeezing the gap as small as needed, and it is seen as a forerunner of calculus.

Which number word did Archimedes build his system on in The Sand Reckoner?

Myriad, 10,000, was as far as Greek number names went, so Archimedes used a myriad myriads, 100 million, as a fresh unit and built ever-higher orders on it.

In The Sand Reckoner, Archimedes worked out how many grains of sand would fill what?

The universe was his choice because some people held that grains of sand were infinite in number, so he named numbers big enough to count every grain that would fit out to the fixed stars.

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

Aristarchus of Samos's own book on the idea is lost, so this passage is a key record of his theory, and his one surviving work assumes an Earth-centred cosmos.

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

Astronomer Phidias is known only from that book, where his son quotes his estimate that the Sun is twelve times as wide as the Moon, beside a figure from Eudoxus.

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

The law of the lever was not new, since an older work from Aristotle's school had a looser proof, but Archimedes rebuilt it from seven postulates and the idea of a centre of gravity.

How does Plutarch say Archimedes regarded the war machines that made him famous?

Mere amusements of geometry were all his machines meant to him, Plutarch says, and he refused to leave any written treatise on engineering, which he thought ignoble and vulgar.

What is the Ostomachion, described in the Archimedes Palimpsest?

A 14-piece dissection puzzle like a tangram, it was played by rearranging the pieces into shapes such as an elephant, and a 2003 search found 536 distinct ways to rebuild its square.

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

The Sun owns the herd in the poem, and the smallest answer runs past 200,000 digits, so no one wrote it out in full until computers at Waterloo managed it in 1965.

Which everyday object follows the pattern of the truncated icosahedron, one of the solids Archimedes described?

A classic soccer ball has this shape of 12 pentagons and 20 hexagons, yet the form became a household sight only when Adidas's Telstar ball was used at the 1970 World Cup.

Which astronomer completed the rediscovery of the 13 solids Archimedes described in a lost book?

Johannes Kepler finished a search begun by Renaissance artists such as Piero della Francesca, who had found some of the shapes again, by setting out all thirteen in his Harmonices Mundi.

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.

Before its 1998 auction, the Archimedes Palimpsest had spent centuries in use as what?

A prayer book was written over Archimedes' scraped-off pages in 1229, perhaps because parchment was scarce, and it stayed in use as one until modern scholars noticed the text beneath.

What did the Archimedes device that Rome carried off from Syracuse reportedly model?

The motions of the planets, Sun and Moon were shown by this bronze model, and one Roman account judged that its maker must have had a genius greater than seemed humanly possible.

Isidore of Miletus, who edited Archimedes' works, helped design which famous building?

The Hagia Sophia was his work with Anthemius of Tralles, but its first dome collapsed about 20 years after the church opened, so his nephew Isidore the Younger rebuilt it higher, with 40 ribs.

Which scientist called Archimedes 'my master'?

Galileo Galilei found the overflow tale too crude for such a genius, so in 1586, at 22, he wrote La Bilancetta, redoing the crown test with a balance instead.

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

The Fields Medal bears Archimedes' portrait, yet in 2006 Grigori Perelman, who had proved the Poincaré conjecture, refused it, saying he was not interested in money or fame.

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

California has carried the word on its seal since 1849, probably for its gold discoveries, yet it became the official motto only in 1963, after a 1957 push for 'In God We Trust'.

What was the SS Archimedes, launched in 1838?

The first seagoing steamship with a screw propeller, she was lent to Brunel, and her trials persuaded him to switch SS Great Britain from paddle wheels to a screw.

In which dialect were Archimedes' works originally written?

Doric Greek was the dialect of his native Syracuse, and because later editors recast some books and stripped it out, scholars judge how faithful a copy is by how much Doric survives.

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

Adopt a spherical form is what any fluid at rest does, he proved, so even a calm sea is not flat but part of a sphere centred on the Earth's centre, fitting a round Earth.

Which country's probe, the first craft to reach the Moon, crashed near the lunar crater named after Archimedes?

The Soviet Union's Luna 2 hit the Moon in September 1959, and on the way it released a cloud of sodium gas so observers on Earth could follow its flight.

What does Plutarch say Archimedes was to the king of Syracuse?

A kinsman and friend of the king, Plutarch says, yet other Roman writers suggest Archimedes came from humble origins, one of them calling him an obscure little man.

Which Alexandrian scholar, famous for measuring the Earth's circumference, received letters from Archimedes?

Eratosthenes was nicknamed Beta by some critics because, for all his range, in every field he seemed to fall just short of first place.

What finally revealed the Archimedes text hidden under forged paintings in the Palimpsest?

Particle accelerator X-rays at Stanford did it, because the imaging that had recovered most of the hidden text was of little use under the forged gold-leaf portraits.

Archimedes proved a circle's area equals that of which shape, with its radius and circumference for sides?

A right triangle is the shape in Measurement of a Circle, one of the books Eutocius brought out with a commentary in the 6th century AD, and only after those editions did Archimedes' treatises become widely known.

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

Briareus and his brothers, in Hesiod's telling, won Zeus's war on the Titans by hurling 300 rocks, and the jest was that Archimedes, shooting many missiles at once, outdid those giants.

What is Archimedes said to have used to set attacking Roman ships on fire?

Mirrors focusing sunlight are the weapon of the legend, and though MIT students set a mock ship alight with 127 mirrors, MythBusters still judged the story busted.

Which Disney film features a talking owl named Archimedes?

The Sword in the Stone gives Merlin an owl called Archimedes, and when young Wart forgets Kay's sword at a locked inn, he pulls the magic blade from the stone instead and becomes king.