50 Fun Facts About Archimedes

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

The city was a self-governing Greek colony in Magna Graecia when he was born around 287 BC.

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

The word means "I have found it!" and is now the state motto of California, referring to the 1848 gold discovery.

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

According to Vitruvius the wreath displaced more water than pure gold and less than silver, proving the goldsmith a cheat.

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

A rival 5th-century poem, Carmen de Ponderibus, has him use a balance dipped in water instead.

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 oft-quoted remark about leverage does Pappus of Alexandria attribute to Archimedes?

It arose from a boast to King Hiero that he could move any weight, which the king answered by challenging him to move a ship.

What was the Syracusia, which Archimedes is said to have launched?

Plutarch says he moved it with a block-and-tackle pulley system; Hero of Alexandria credits a windlass called the baroulkos.

What is the modern verdict on whether Archimedes invented the water-lifting screw named after him?

None of the contemporaries who describe its use, including Vitruvius and Strabo, credit him with it.

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

He called Archimedes "a geometrical Briareus" and was reportedly angered by his death.

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

The Romans took the city only after a long siege, greatly delayed by his machines.

What did Archimedes' crane-like machines reportedly do to Roman ships, per Plutarch and Livy?

Other cranes dropped heavy lumps of lead onto the ships from the walls.

The story that Archimedes set Roman ships on fire with mirrors is absent from which group of writers?

Galen is the first to mention mirrors; Descartes rejected the "heat ray" as false and modern reconstructions have had mixed results.

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

The famous last words "Do not disturb my circles" appear in no ancient source; Valerius Maximus has him say "I beg of you, do not disturb this."

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

The carving showed that a sphere's volume and surface area are two-thirds those of the enclosing cylinder.

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

He had it cleaned up and read some of the verses inscribed on it.

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

The sphere is 4/3 pi r cubed and the cylinder 2 pi r cubed; the ratio was his favourite result.

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

He started with hexagons inside and outside a circle and doubled the sides four times.

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

He summed the geometric series 1 + 1/4 + 1/16 + ... to reach it, an early infinite series.

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

He admitted he found results first by a mechanical method using the lever, then proved them this way afterwards.

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?

The point was to prove that mathematics could represent arbitrarily large numbers.

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

The Sand Reckoner is the only surviving work in which Archimedes discusses astronomy.

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

Nothing else is known about him; Plutarch claims the family was related to King Hiero.

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

It states that magnitudes balance at distances reciprocally proportional to their weights.

To which student of Conon of Samos are most of Archimedes' surviving treatises addressed?

The Method and the Cattle Problem, by contrast, were sent to the librarian Eratosthenes.

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

Reviel Netz calculated the pieces form a square in 17,152 ways, an early combinatorics problem.

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

The hardest version's answer is roughly 7.76 × 10^206544, first solved by A. Amthor in 1880.

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

The German dramatist was working as the library's director at the time.

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

They are still called the Archimedean solids.

What is the Archimedes Palimpsest, examined by Johan Ludvig Heiberg in Constantinople in 1906?

It holds seven treatises, including the only surviving Greek text of On Floating Bodies.

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

In it he explains how he used the lever to find results before proving them by exhaustion.

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

It was then studied at the Walters Art Museum in Baltimore with ultraviolet and X-ray imaging.

Which two devices built by Archimedes did Marcellus bring to Rome, according to a Roman statesman?

The 1902 discovery of the Antikythera mechanism showed such geared devices really existed in ancient Greece.

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

Gerard of Cremona later rendered it into Latin from the Arabic; William of Moerbeke translated direct from Greek.

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

Huygens said Archimedes was "comparable to no one", and Leibniz said those who understand him will admire later men less.

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

The Latin inscription around his head reads Transire suum pectus mundoque potiri, "Rise above oneself and grasp the world".

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

There it refers to the discovery of gold at Sutter's Mill in 1848.

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'?

Eric Temple Bell wrote that any list of the three greatest would include Archimedes, usually with Newton and Gauss.

In which dialect were Archimedes' works originally written?

It was the dialect of ancient Syracuse; he made his work known by letters to Alexandria.

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 lie just south of the crater, which sits at 29.7°N 4.0°W.

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

The estimate rests on a Byzantine claim that he lived 75 years before dying in 212 BC, when Syracuse was a self-governing colony in Magna Graecia.

The Method of Mechanical Theorems was written as a letter to which Alexandrian scholar?

The Cattle Problem was addressed to the same man, better known for measuring the Earth's circumference.

After its 1998 sale, the Archimedes Palimpsest was imaged with ultraviolet and X-rays where?

The Baltimore museum's imaging revealed text under the 13th-century prayers; the parchment has since returned to its anonymous owner.

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

The same short work approximates pi by nesting hexagons inside and outside a circle and repeatedly doubling their sides.

Marcellus reportedly called Archimedes 'a geometrical' what, likening him to a hundred-handed giant?

Marcellus valued him as a scientific asset and was angered by his death; the Roman general also carried two of his planetariums to Rome.

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

Johann Herwagen's Editio princeps became an influential source of ideas for Renaissance and 17th-century scientists.

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

He never mentions mirrors, only 'artificial means', which may point to burning projectiles rather than a death ray.

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

Almost nothing else is certain about his life; a biography supposedly written by his friend Heraclides Lembus is lost.