50 Fun Facts About Pythagoras

On which Greek island was Pythagoras born?

Herodotus and Isocrates agree he was the son of Mnesarchus, said to be a gem-engraver or wealthy merchant.

What does the Pythagorean theorem state about a right-angled triangle?

Babylonians and Indians knew and used the relationship centuries before Pythagoras was born.

In which southern Italian city did Pythagoras found his school around 530 BC?

Today's Crotone in Calabria was then part of Magna Graecia, the Greek colonies of southern Italy.

Pythagoras was reputedly the first man to describe himself with which Greek word?

It means 'lover of wisdom'; Augustine later praised his humility in not calling himself a sage.

Which teaching is most securely identified with Pythagoras himself?

Metempsychosis holds that every soul is immortal and enters a new body at death.

What is the doctrine of musica universalis that Pythagoras may have devised?

Kepler's search for the mathematics behind this 'harmony of the spheres' led to his laws of planetary motion.

How old was Pythagoras when he left Samos, according to Aristoxenus?

He left during the reign of the tyrant Polycrates, giving a birth date around 570 BC.

Which Egyptian pharaoh supposedly taught Pythagoras the Egyptian language, according to a later legend?

He was then said to be the only foreigner allowed to join the priests' worship at Thebes.

Which Greek sage is most often named as Pythagoras's teacher?

One story says Pythagoras returned to Delos to nurse the dying Pherecydes.

What was the name of the school Pythagoras supposedly founded on Samos for public debate?

He himself was said to study in a secret cave.

Which famous wrestler was said to have saved Pythagoras's life when a roof was about to collapse?

The story may confuse the philosopher with an athletics trainer of the same name.

The city's victory over which neighbouring colony in 510 BC was credited to Pythagorean discipline?

After the victory, supporters of democracy turned on the Pythagoreans and burned their meeting house.

Who led the democratic faction that roused the city against Pythagoras's brotherhood?

Cylon was said to be irritated at being excluded from the brotherhood.

In one legend, Pythagoras was caught and killed because he refused to run through what?

Doing so would have violated his teachings; the story was probably originally told about later Pythagoreans.

In Dicaearchus's account, where did Pythagoras and his followers die of starvation after forty days?

They had first pleaded for sanctuary at Locris and been refused.

In Xenophanes' satirical poem, Pythagoras stops a man beating a dog because he recognises what?

It is the earliest source for his belief in reincarnation.

Which minor hero of the Trojan War did Pythagoras claim to have been in a former life?

He said he could remember four previous lives, including one as a fisherman from Delos.

What is the tetractys, which Pythagoras's students swore oaths by?

The Pythagoreans regarded ten as the 'perfect' number.

Which later Pythagorean do scholars usually credit with the number philosophy pinned on Pythagoras?

Walter Burkert argued Pythagoras himself never dealt with numbers at all.

What was the Pythagorean maxim 'koina ta philon'?

Members shared all their possessions and ate communal meals in the Spartan manner.

What were the two groups within early Pythagoreanism called?

'Learners' and 'listeners', traditionally seen as the rationalist and mystical wings.

How long did new initiates supposedly have to stay silent before being allowed to meet Pythagoras?

Those who broke the community's laws were expelled and had tombstones erected for them as if dead.

Which of these was one of the Pythagoreans' surviving 'oral sayings'?

Others forbade breaking bread, poking fires with swords or picking up crumbs.

How many of the 235 famous Pythagoreans listed by Iamblichus were women?

Pythagoras was said to be unusually progressive towards women, who played an active role in the school.

Which food is Pythagoras most famously said to have forbidden his followers to eat?

One theory links the ban to favism, an enzyme-deficiency anaemia common around the Mediterranean.

What did Aristotle say Pythagoras had that he exhibited at the Olympic Games?

He showed it to Abaris the Hyperborean as proof he was the 'Hyperborean Apollo'.

What was Pythagoras supposedly given by the priest of Apollo, which let him fly over long distances?

He was also reportedly seen in two cities at the same time.

According to a fragment of Aristotle, what did Pythagoras do when a deadly snake bit him?

He also reportedly persuaded a bear to swear never to harm a living thing again.

What did the river Kosas supposedly do when Pythagoras crossed it?

'Several witnesses' reported it, according to the legend.

What was Pythagoras said to have sacrificed to the gods after discovering his theorem?

Cicero rejected the story since Pythagoras supposedly forbade blood sacrifice; Porphyry said the ox was made of dough.

What sound supposedly led Pythagoras to realise that music was mathematical?

He concluded the pitch was proportional to the size of the hammer.

Which philosopher has a stronger claim than Pythagoras to first teaching that the Earth is spherical?

Both were also credited with identifying the morning and evening stars as the same object, Venus.

Which philosopher mocked Pythagoras as a clever charlatan practising 'artful knavery'?

He was born a few miles across the sea from Pythagoras's island and may have lived in his lifetime.

Which Pythagorean philosopher and friend of Plato was elected general of Tarentum seven times?

Others were forbidden from serving more than a year; he was also a noted mathematician and musician.

Which of Plato's dialogues most clearly exhibits Pythagorean ideas?

Cicero repeated the saying that 'Plato learned all things Pythagorean'.

The oldest known Pythagorean building, a Rome basilica, dates from which emperor's reign?

The Porta Maggiore Basilica has an interior almost entirely white, the colour Pythagoreans held sacred.

Which astronomer called Pythagoras the 'grandfather' of all Copernicans?

He titled his book on planetary harmony Harmonices Mundi.

Which Roman poet's Metamorphoses gives Pythagoras a speech urging his followers to eat no meat?

Until the word 'vegetarianism' was coined in the 1840s, English vegetarians were simply called Pythagoreans.

Which fraternal society deliberately modelled itself on Pythagoras's community in southern Italy?

Rosicrucians and John Dee also drew on Pythagorean symbolism.

Which Babylonian clay tablet from about 1800 BC lists what can be read as 15 Pythagorean triples?

The rule was in widespread use in the Old Babylonian period, over a thousand years before Pythagoras.

Per Plutarch, the Egyptians identified the sides of the 3:4:5 triangle with which three gods?

The Berlin Papyrus of about 1800 BC includes the triple 6:8:10 without mentioning a triangle.

Which future US president published a proof of the Pythagorean theorem while serving as a congressman?

His proof uses a trapezoid instead of a square.

How many proofs of the theorem does the book The Pythagorean Proposition contain?

The theorem may have more known proofs than any other, rivalled only by quadratic reciprocity.

Where in Euclid's Elements is the theorem proved?

Euclid's construction of squares on each side depends on the parallel postulate.

What happens to a Pythagorean cup when it is filled beyond a certain point?

Also called a greedy cup, its hidden siphon was described by Hero of Alexandria; the link to Pythagoras is a recent folk tradition.

What is the meaning of the maxim 'Ex pede Herculem', linked to a story about Pythagoras?

He supposedly estimated the hero's height from the length of a racecourse at Pisae.

What trade is Pythagoras's father Mnesarchus said to have followed?

Other sources call him a wealthy merchant; his mother Pythaïs was claimed to descend from Ancaeus, Samos's mythical founder.

Which Roman building, with its oculus symbolising the monad, was designed on Pythagorean numerology?

Its twenty-eight ribs stand for the moon, matching the months of the Pythagorean lunar calendar.

Which Samian astronomer did Copernicus pointedly omit when crediting Pythagoreans for his heliocentric model?

That non-Pythagorean had worked out a fully heliocentric model in the fourth century BC, which spoiled the story.

By what name is the right-triangle relation known in China?

The Zhoubi Suanjing, with contents known long before its surviving 1st-century BC texts, reasons it out for the 3-4-5 triangle.