Archimedes Trivia
0Loading crowd target
0Loading crowd target
7correct to beat the crowd
45 free Archimedes trivia questions with answers — science & nature quiz, new questions added Sep 2026.
Archimedes of Syracuse worked out the law of buoyancy, the law of the lever, a value of pi accurate to two decimal places and the volume of a sphere, then invented a number system to count the grains of sand it would take to fill the universe. He also built the catapults and cranes that held off a Roman army, and was killed by a soldier while drawing in the dust. This quiz covers the mathematics, the machines, the legends and the astonishing afterlife of his lost manuscripts. Easy questions ask what he supposedly shouted in the bath, what his screw did and where he lived. Harder ones want the king whose wreath he tested, the two bounds he found for pi, the shape carved on his tomb, the number in the Sand Reckoner, the name of his 14-piece puzzle, the treatise that survived only under a book of prayers, the auction price of that Palimpsest, the ship named for his screw and the US state whose motto is his exclamation. Every answer was checked against Wikipedia's article on Archimedes, and each question carries the sentence that supports it. Made for maths and physics teachers, students and quiz hosts. Related quizzes: Ancient Greece, Famous Mathematicians and Physics.
30 of 45 questions with answers and explanations. Play the quiz
Q 01On which island was Archimedes' home city, where he was born and killed?
Sicily
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.
Q 02What did Archimedes supposedly cry as he ran naked through the streets after his bathtub insight?
Eureka!
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.
Q 03Which king of Syracuse asked Archimedes to check whether his gold wreath was cut with silver?
Hiero II
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.
Q 04Which Roman writer, two centuries after Archimedes died, gave the earliest written account of the bathtub story?
Vitruvius
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.
Q 05Archimedes' principle says a submerged body's upthrust equals what?
The weight of fluid it displaces
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.
Q 06In the boast Pappus attributes to Archimedes, 'Give me a place to stand on, and I will move' what?
The Earth
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.
Q 07What was the Syracusia, whose construction Archimedes is said to have supervised?
A giant ship
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.
Q 08Archimedes proved a triangle's centre of gravity lies where which three lines meet?
Its medians
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.
Q 09Which Roman general besieged Syracuse and had ordered that Archimedes should not be harmed?
Marcus Claudius Marcellus
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.
Q 10During which war did Syracuse switch from Rome to Carthage, prompting the siege Archimedes resisted?
The Second Punic War
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.
Q 11According to Livy's account, what was Archimedes doing when a Roman soldier killed him?
Drawing figures in the dust
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.'
Q 12What is Archimedes said to have wanted placed on his tomb to mark his proudest discovery?
A sphere and a cylinder
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.
Q 13Which Roman statesman wrote that he found Archimedes' neglected tomb while quaestor on the island?
Q 21What was the profession of Archimedes' father Phidias, as stated in The Sand Reckoner?
Astronomer
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.
Q 22Which law does Archimedes prove in the first book of On the Equilibrium of Planes?
The law of the lever
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.
Q 23How does Plutarch say Archimedes regarded the war machines that made him famous?
Mere amusements of geometry
Cicero
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.
Q 14In On Spirals, Archimedes says two theorems he sent out were impossible, as a warning to whom?
Those claiming results without proofs
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.
Q 15Which famous number is sometimes called Archimedes' constant?
Pi
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.
Q 16Archimedes found a parabolic segment's area by adding up the terms of what kind of series?
A geometric 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.
Q 17What technique, inherited from Eudoxus, did Archimedes use to prove areas and volumes rigorously?
The method of exhaustion
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.
Q 18Which number word did Archimedes build his system on in The Sand Reckoner?
Myriad
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.
Q 19In The Sand Reckoner, Archimedes worked out how many grains of sand would fill what?
The universe
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.
Q 20Which heliocentric theorist's model does Archimedes describe in The Sand Reckoner?
Aristarchus of Samos
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.
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.
Q 24What is the Ostomachion, described in the Archimedes Palimpsest?
A 14-piece dissection puzzle like a tangram
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.
Q 25Archimedes' Cattle Problem challenges Alexandrian mathematicians to count the herd of which deity?
The Sun
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.
Q 26Which everyday object follows the pattern of the truncated icosahedron, one of the solids Archimedes described?
A classic soccer ball
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.
Q 27Which astronomer completed the rediscovery of the 13 solids Archimedes described in a lost book?
Johannes Kepler
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.
Q 28Which treatise, thought lost forever, is known only from the Archimedes Palimpsest?
The Method of Mechanical Theorems
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.
Q 29Before its 1998 auction, the Archimedes Palimpsest had spent centuries in use as what?
A prayer book
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.
Q 30What did the Archimedes device that Rome carried off from Syracuse reportedly model?
The motions of the planets
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.