Euclid Trivia
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50 free Euclid trivia questions with answers — science & nature quiz, new questions added Aug 2026.
Almost nothing is known about Euclid the man, but everything is known about his book, and this quiz covers both: the geometer of Alexandria around 300 BC, the thirteen books of the Elements, the five postulates and five common notions, the proof that primes never run out, the algorithm still used to find greatest common divisors, and the two thousand years of translations, printings and rebellions that followed. Easy questions ask what Euclid is called and what his famous book is named; harder ones dig into the philosopher he was long confused with, the pons asinorum, the first printed edition of 1482, Oliver Byrne's coloured Euclid, the mathematicians who broke the parallel postulate and the space telescope that carries his name. It suits maths teachers and students, history-of-science fans and quiz nights that want a science round with a classical flavour. Every answer has been checked against the Wikipedia articles on Euclid, the Elements and the geometry that grew from them, and each question shows its source once you have answered.
30 of 50 questions with answers and explanations. Play the quiz
Q 01Euclid is traditionally known by what title?
The father of geometry
The father of geometry set out a system that went unchallenged until the early 19th century; only when rival geometries appeared did his need a name of its own, Euclidean.
Q 02What is the Greek title of Euclid's great treatise, the Elements?
Stoicheia
Stoicheia was also the Greek word for the letters of the alphabet, and Proclus said its leading theorems serve the rest of geometry as letters serve a language.
Q 03How many books make up the Elements?
Thirteen
Thirteen books are Euclid's own, yet for centuries editions ran to fifteen: two extra books by later hands, the first of them by Hypsicles, travelled with the text.
Q 04In which city is Euclid generally accepted to have spent his career?
Alexandria
Alexandria: Pappus records that a later geometer spent years there with Euclid's pupils, the main evidence that Euclid taught in the city and founded its school of mathematics.
Q 05Under which ruler's reign did Proclus place Euclid's activity?
Ptolemy I
Ptolemy I was one of Alexander the Great's generals and made himself a king when the empire was carved up; Proclus, writing seven centuries later, dated Euclid by his reign.
Q 06Which famous line is Euclid said to have spoken?
"There is no royal road"
"There is no royal road" to geometry, he reportedly told a king who wanted a shortcut. The tale is doubtful: the same story is told of Menaechmus and Alexander the Great.
Q 07Which US president wrote that he had 'nearly mastered' the first six books of Euclid after serving in Congress?
Abraham Lincoln
Abraham Lincoln had less than a year of schooling in all, and wrote that he took up Euclid because he regretted his want of education and did what he could to supply it.
Q 08Scholars long confused Euclid with a namesake from Megara who reportedly sneaked into Athens dressed as a woman to hear whom?
Socrates
Socrates was the draw: as Aulus Gellius tells it, Athens had banned Megarians on pain of death, so this other Euclid walked some twenty miles by night in a woman's tunic and veil.
Q 09What do we now call the division of a line that Euclid named 'extreme and mean ratio'?
The golden ratio
The golden ratio first appears in Book 2, where Euclid makes the cut before he has even defined what a ratio is, and he later uses it to build a regular pentagon.
Q 10Medieval Arabic sources, considered unreliable, claimed Euclid was born in which city?
Tyre
Tyre was his birthplace and Damascus his home in the Arabic accounts, which also name his father as Naucrates; Thomas Heath judged the cities were added to tie a famous Greek to the East.
Q 11Besides a compass, which drawing tool do Euclid's first three postulates allow?
Straightedge
Straightedge: the postulates let you draw a line, extend it and draw a circle, nothing more. It carries no markings, so nothing in a construction is ever measured.
Q 12Which of Euclid's postulates is the famous parallel postulate?
The fifth
The fifth postulate is far less obvious than the rest, and for more than two thousand years geometers tried to prove it from them; their failure led to non-Euclidean geometry.
Q 13Euclid's parallel postulate says two lines meet on the side where the interior angles add up to less than what?
Two right angles
Q 21Which is the smallest 'perfect number', a term Euclid defines in Book 7 of the Elements?
6
6 equals the sum of its divisors 1, 2 and 3. Euclid went on to give a recipe for building such numbers, and two thousand years later Euler proved it catches every even one.
Q 22Which of Euclid's surviving works is the earliest Greek treatise on perspective?
Optics
Optics treats sight as straight rays fanning out from the eye in a cone, and starts from the assumption that an object looks smaller the narrower the angle it fills.
Q 23Which lost four-book work of Euclid was superseded by a fuller treatise of the same name from Perga?
Conics
Conics is known mainly through Pappus, who says the geometer from Perga built the first four books of his own treatise on Euclid's.
Two right angles, or 180 degrees: if the inside angles total less, the two lines lean toward each other and must cross. Change that rule and you get the hyperbolic and elliptic geometries.
Q 14What does the first definition in Euclid's Elements define?
A point
A point comes first, as 'that which has no part'; modern geometry has stopped trying to define it and leaves 'point' as a primitive term whose meaning comes only from the axioms.
Q 15Which famous theorem does Euclid prove at the climax of Book 1 of the Elements?
The Pythagorean theorem
The Pythagorean theorem is Proposition 47, proved with no numbers at all: Euclid cuts the big square into two rectangles and shows each equals one of the smaller squares.
Q 16Which result is the pons asinorum, Proposition 5 of Book 1 of Euclid's Elements?
The isosceles triangle theorem
The isosceles triangle theorem, that the base angles are equal, became the 'bridge of asses' either for its bridge-like diagram or as the first hurdle slower students could not cross; nobody is sure which.
Q 17What does the Euclidean algorithm, set out at the start of Book 7 of the Elements, find?
The greatest common divisor
The greatest common divisor of two numbers falls out by subtraction alone: keep taking the smaller from the larger until one divides the other. It is among the oldest algorithms still in common use.
Q 18What does Euclid's theorem, in Book 9, prove?
There are infinitely many prime numbers
There are infinitely many prime numbers because any finite list can be beaten: multiply its primes together, add one, and the result has a prime factor the list left out.
Q 19Book 10 of Euclid's Elements, its longest, deals in modern terms with which kind of number?
Irrational numbers
Irrational numbers, handled as lengths with no common measure, fill about a quarter of the Elements, a bulk historians find out of proportion to what the book delivers.
Q 20The final book of the Elements is devoted to which five shapes?
The Platonic solids
The Platonic solids end the Elements with a proof that no sixth can exist, and Proclus claimed that building them was the goal of the whole work.
Q 24How did ancient Greek mathematicians usually refer to Euclid?
As "the author of Elements"
As "the author of Elements" he was little more than a byline; some medieval Arabic writers even explained the name 'Euclid' as a compound meaning 'key of geometry'.
Q 25A papyrus scrap of Euclid's Elements, among the oldest known, was dug from the ancient rubbish dumps of which Egyptian town?
Oxyrhynchus
Oxyrhynchus gave up the scrap, a Book 2 proposition with its diagram, in 1897. Its finders dated it to about AD 300, but later study moved it back some two centuries.
Q 26The edition of Euclid's Elements that the Greek world copied for centuries was made by Theon, the father of which philosopher?
Hypatia
Hypatia's father Theon tidied and corrected the text, and his version was the only Greek one anyone knew until a copy his editing had not touched turned up in the Vatican.
Q 27Which Jesuit missionary worked with the scholar Xu Guangqi to publish the first Chinese edition of Euclid's Elements, in 1607?
Matteo Ricci
Matteo Ricci and Xu stopped after the first six books, and Chinese readers waited more than two centuries for the rest.
Q 28Erhard Ratdolt's 1482 Euclid, the first in print, solved which printing problem?
Diagrams
Diagrams had defeated earlier printers, Ratdolt wrote, which is why almost no mathematics was in print; he boasted that his figures could be set as easily as letters.
Q 29Euclid ends his proofs with a Greek phrase that Latin turned into Q.E.D.; what does it mean?
Which was to be demonstrated
"Which was to be demonstrated" became a badge of rigour beyond mathematics: Spinoza closed the proofs of his Ethics with Q.E.D., a work of philosophy laid out in geometrical order on Euclid's model.
Q 30Which adviser to Elizabeth I wrote the celebrated 'Mathematical Preface' to the first English edition of Euclid's Elements?
John Dee
John Dee, the queen's astronomer and astrologer, aimed it at readers outside the universities, and it became his most reprinted work; the translator, Henry Billingsley, ended up Lord Mayor of London.