This geometry trivia quiz has 70 free questions with answers and starts with the basics everyone half-remembers from school, the angles in a triangle, the name of the longest side, what a rhombus and a trapezoid are, and then keeps going. There are rounds on the five Platonic solids and the elements Plato assigned to them, on pi and the men who spent their lives computing it (one of them wrongly), and on Euclid's Elements, the textbook that ran for two thousand years. From there it reaches the good stories: the drowned Pythagorean who leaked the irrationals, the president who published his own proof of the Pythagorean theorem, the plague that supposedly started the doubling-the-cube problem, the map-colouring puzzle that needed a computer, and the mathematician who turned down a million dollars. Fractals, the Möbius strip, the Klein bottle and the honeycomb theorem round it out. It suits a maths classroom, a pub quiz science round or anyone who likes shapes. Every answer has been checked against an encyclopaedic or primary source and each question shows its citation once answered.
30 of 70 questions with answers and explanations. Play the quiz
Q 01The interior angles of any triangle add up to how many degrees?
180
That is why a triangle can have at most one right angle or one obtuse angle: the other two must share what is left.
Q 02A triangle with all three sides the same length is called what?
Equilateral
You see one every day: the yield sign at a road junction is one of these.
Q 03A triangle with all sides of different lengths is called what?
Scalene
A triangle with exactly two equal sides is isosceles, which is the shape of most gables and pediments.
Q 04What is the name for the longest side of a right-angled triangle?
Hypotenuse
The word comes from Greek for 'stretching under', because it stretches beneath the right angle.
Q 05How many degrees are in a right angle?
90
The word 'right' comes from the Latin rectus, meaning upright, describing a vertical line meeting a horizontal base.
Q 06A triangle in which one angle is larger than 90 degrees is called what?
Obtuse
If every angle is smaller than 90 degrees, the triangle is acute instead.
Q 07How many sides does a hexagon have?
Six
The name comes from Greek hex, meaning six, and each interior angle of a regular one is 120 degrees.
Q 08What is the sum of the interior angles of a pentagon?
540°
Each corner of a regular pentagon is 108 degrees, which is why five of them will not tile a floor without gaps.
Q 09Which four-sided shape has all four sides the same length but does not need right angles?
Rhombus
The playing-card diamond suit is named after this shape; other names include lozenge and calisson.
Q 10What is the American term for what the British call a trapezium?
Trapezoid
The parallel sides are called the bases and the other two the legs.
Q 11A quadrilateral with two pairs of adjacent equal-length sides is named after which toy?
A kite
When it is not convex, mathematicians call the same shape a dart.
Q 12What is the sum of the exterior angles of any convex polygon?
360°
Walk once around the shape turning at each corner and you end up facing the way you started, one full turn.
Q 13How many sides does a chiliagon have?
1,000
Descartes and Kant both used it as an example of a shape you can reason about but cannot picture.
Q 14Beyond decagons and dodecagons, how do mathematicians usually name polygons?
Q 21Which civilisation used the Pythagorean rule over a thousand years before Pythagoras?
The Babylonians
The clay tablet Plimpton 322, from about 1800 BC, lists what look like fifteen Pythagorean triples.
Q 22The book The Pythagorean Proposition collects how many different proofs of the theorem?
370
That may be more proofs than any other theorem has, though quadratic reciprocity is a rival for the title.
Q 23Which future US president published his own proof of the Pythagorean theorem in 1876?
James A. Garfield
He was still a member of the House of Representatives when it appeared in a weekly mathematics column.
By numerical notation like 17-gon
A regular 17-gon is famous because a 19-year-old Gauss proved in 1796 that it can be built with compass and straightedge.
Q 15Which regular polygon is the simplest one that cannot be constructed with compass and straightedge?
Heptagon
The seven-sided shape can be built with a marked ruler using a neusis construction, but not with the classical tools.
Q 16Gauss proved a regular polygon with how many sides can be built with compass and straightedge?
17
He did it in 1796 at age 19, and it was the first such discovery since the ancient Greeks.
Q 17How many books make up Euclid's Elements?
13
It covers plane and solid geometry, number theory and incommensurable magnitudes, and dominated teaching for two thousand years.
Q 18Which of Euclid's five postulates is known as the parallel postulate?
The fifth
Centuries of failed attempts to prove it from the other four eventually led to hyperbolic and elliptic geometry.
Q 19Euclid, the 'father of geometry', spent his career in which ancient city?
Alexandria
Almost nothing is known of his life; most of it comes from Proclus and Pappus, writing many centuries later.
Q 20The Pythagorean theorem is Proposition 47 in which part of Euclid's Elements?
Book I
Proposition 48, right after it, proves the converse: if the squares add up, the angle is right.
Q 24According to legend, Hippasus of Metapontum was drowned at sea for revealing the existence of what?
Irrational numbers
The offending discovery was probably that the diagonal of a square cannot be measured exactly against its side.
Q 25How many Platonic solids are there?
Five
Theaetetus, a contemporary of Plato, may have written the first proof that no others exist.
Q 26Which Platonic solid has twelve pentagonal faces?
Dodecahedron
Plato said the god used this one for arranging the constellations across the whole heaven.
Q 27In Plato's Timaeus, which classical element was matched with the cube?
Earth
Fire got the spiky tetrahedron, air the octahedron and water the icosahedron.
Q 28The twenty-sided die used in tabletop role-playing games is which solid?
Regular icosahedron
Nature got there first: the adenovirus has the same shape.
Q 29How many edges does a cube have?
12
It has eight corners and six faces; edges are the number people forget.
Q 30Who first used the Greek letter π for the ratio of a circle's circumference to its diameter, in 1706?
William Jones
Euler's later adoption of the symbol is what made it universal.