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47 free Archimedes trivia questions with answers — science & nature quiz, new questions added Aug 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.
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Q 01On which island was Archimedes' home city, where he was born and killed?
Sicily
Archimedes was born and killed in Syracuse, on Sicily's eastern coast, a Greek city founded by Corinthian settlers in the 8th century BC.
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, king of Syracuse from about 270 BC and Archimedes' patron, suspected his goldsmith had alloyed a votive wreath with silver.
Q 04Which Roman writer, two centuries after Archimedes died, is the source of the bathtub story?
Vitruvius
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.
Q 05Archimedes' principle states that a body immersed in water experiences an upthrust equal to what?
The weight of fluid it displaces
It appears in his treatise On Floating Bodies, which survives in Greek only in the Palimpsest.
Q 06Which saying does Pappus of Alexandria attribute to Archimedes?
"Give me a place to stand on, and I will move the Earth."
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.
Q 07What was the Syracusia, whose construction Archimedes is said to have supervised?
The largest ship built in classical antiquity
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.
Q 08Archimedes proved a triangle's centre of gravity lies where which three lines meet?
Its medians
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.
Q 09Which Roman general besieged Syracuse from 214 BC and later ordered that Archimedes should not be harmed?
Marcus Claudius Marcellus
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.
Q 10During which war did Syracuse switch from Rome to Carthage, prompting the siege Archimedes resisted?
The Second Punic War
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.
Q 11According to Livy's account, what was Archimedes doing when a Roman soldier killed him?
Drawing figures in the dust
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.
Q 12What did Archimedes ask to have placed on his tomb to represent his proudest discovery?
A sphere and a cylinder
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.
Q 13Which Roman statesman 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
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.
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, proved in Propositions 6 and 7 of On the Equilibrium of Planes Book I, says magnitudes balance at distances inversely proportional to their weights.
Q 23To which student of Conon of Samos did Archimedes address several of his treatises?
Dositheus of Pelusium
Cicero
Cicero, serving as quaestor in 75 BC, found the tomb overgrown with brambles outside Syracuse and had the spot cleared and its inscription read.
Q 14What fraction of the enclosing cylinder's volume and surface area did Archimedes show a sphere has?
Two-thirds
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.
Q 15Between which two bounds did Archimedes show pi lies, using polygons of 96 sides?
3 10/71 and 3 1/7
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.
Q 16In Quadrature of the Parabola, a parabolic segment's area is what multiple of its inscribed triangle?
4/3
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 + ...
Q 17What technique, inherited from Eudoxus, did Archimedes use to prove areas and volumes rigorously?
The method of exhaustion
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.
Q 18What Greek term for 10,000 did Archimedes base his large-number system on in The Sand Reckoner?
Myriad
He used powers of a myriad of myriads, that is 100 million, to count sand grains.
Q 19How many grains of sand did Archimedes conclude it would take to fill the universe?
8 × 10^63
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.
Q 20Which heliocentric theorist's model does Archimedes describe in The Sand Reckoner?
Aristarchus of Samos
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.
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.
Q 24What is the Ostomachion, described in a treatise found in the Palimpsest?
A 14-piece dissection puzzle like a tangram
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.
Q 25Archimedes' Cattle Problem challenges Alexandrian mathematicians to count the herd of which deity?
The Sun
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.
Q 26Who found the Cattle Problem in a 44-line Greek poem in the Herzog August Library in 1773?
Gotthold Ephraim Lessing
Gotthold Ephraim Lessing, the German dramatist, was librarian at Wolfenbüttel from 1770 and published the epigram in 1773 among manuscripts he found there.
Q 27How many semiregular polyhedra did Archimedes prove exist, in a lost work described by Pappus?
Thirteen
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.
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 29For how much was the Archimedes Palimpsest sold at auction to an anonymous buyer on 29 October 1998?
$2.2 million
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.
Q 30According to a Roman statesman, what did an Archimedes device carried off to Rome model?
The motions of the planets
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.