Geometry Trivia
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8correct to beat the crowd
This geometry trivia quiz has 118 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 118 questions with answers and explanations. Play the quiz
Q 01The interior angles of any triangle add up to how many degrees?
180
180 degrees, but only on a flat surface: draw the triangle on a globe and its three angles always add up to more.
Q 02A triangle with all three sides the same length is called what?
Equilateral
Equilateral: equal sides force equal angles, so every corner is exactly 60 degrees, which is why six of them fit around a single point.
Q 03A triangle with all sides of different lengths is called what?
Scalene
Scalene: with no two sides equal, no two angles are equal either, so every scalene triangle is lopsided in its own way.
Q 04What is the name for the longest side of a right-angled triangle?
Hypotenuse
The hypotenuse faces the right angle and is always the longest side; its name is Greek for 'stretching under', because it stretches under that angle.
Q 05How many degrees are in a right angle?
90
90 degrees is a quarter of a full turn, so two lines that cross at a right angle make four equal corners.
Q 06A triangle in which one angle is larger than 90 degrees is called what?
Obtuse
Obtuse comes from the Latin obtusus, 'blunted': the wide corner looks dull beside a pointed one, and the same word is used for a slow-witted remark.
Q 07Which polygon has exactly six sides?
Hexagon
Hexagon comes from the Greek hex, 'six', and gonia, 'angle', so the name actually counts the shape's corners rather than its sides.
Q 08The interior angles of which shape always add up to 540 degrees?
Pentagon
Pentagon: two lines drawn from one corner split it into three triangles, which is where the total comes from; in a regular pentagon every corner measures 108 degrees.
Q 09What is the name for a four-sided shape whose four sides are all the same length?
Rhombus
Rhombus: lean a square over and its sides stay equal while the angles change, giving the diamond of playing cards; the two diagonals still cross at right angles.
Q 10What do Americans call a four-sided shape with exactly one pair of parallel sides?
Trapezoid
In American usage a trapezoid is a quadrilateral with one pair of parallel sides, which the British call a trapezium; the parallel sides are its bases.
Q 11Which four-sided shape has two pairs of equal-length sides that are adjacent rather than opposite?
Kite
A kite: the shape is named after the flying toy, and the toy in turn took its name from the kite, a bird of prey that hangs in the wind.
Q 12What is the sum of the exterior angles of any convex polygon?
360°
The exterior angles of any convex polygon sum to 360°: walk once around it, turning at each corner, and you make exactly one full turn.
Q 13How many sides does a chiliagon have?
1,000
A chiliagon has 1,000 sides, from the Greek chilioi; Descartes used it in his Meditations as a shape one can reason about but not picture.
Q 21Which civilisation's clay tablets show the Pythagorean rule in use over a thousand years before Pythagoras?
The Babylonians
The Babylonians: their scribes listed whole-number right triangles on the tablet Plimpton 322 and worked out a square's diagonal to within one part in a million on another, both over 3,500 years ago.
Q 22Which future physicist proved the Pythagorean theorem for himself at about age 12?
Albert Einstein
Albert Einstein recalled that an uncle told him the theorem before he had seen a geometry book, and that 'after much effort' he proved it with similar triangles; over 300 other proofs are known.
Q 23Which future US president published his own proof of the Pythagorean theorem in 1876?
Q 14Canada's loonie coin has 11 sides, making it which shape?
Hendecagon
Hendecagon, from the Greek hendeka, 'eleven': the coin replaced Canada's one-dollar bill in 1987 and got its nickname from the loon pictured on it.
Q 15Which regular polygon has the fewest sides of any that cannot be drawn with compass and straightedge?
Heptagon
The regular heptagon is the first that cannot be drawn with compass and straightedge alone; it can be built with a marked ruler by neusis.
Q 16Which teenager proved compass and straightedge can draw a regular 17-sided polygon?
Carl Friedrich Gauss
Carl Friedrich Gauss made the discovery in 1796, the first advance of its kind since the ancient Greeks, by turning the drawing problem into one about solving equations.
Q 17Which president taught himself six books of Euclid?
Abraham Lincoln
Abraham Lincoln wrote in an 1860 campaign autobiography that he 'studied and nearly mastered' them after serving in Congress, regretting his want of education and doing what he could to supply it; the Elements has 13 books in all.
Q 18Which of Euclid's five postulates is known as the parallel postulate?
The fifth
The fifth postulate is the parallel postulate; two thousand years of failed attempts to prove it from the other four ended with the discovery of non-Euclidean geometry.
Q 19Euclid, the 'father of geometry', spent his career in which ancient city?
Alexandria
Euclid worked in Alexandria around 300 BC under Ptolemy I; almost nothing else is known of his life, most of it from Proclus and Pappus centuries later.
Q 20The Pythagorean theorem is Proposition 47 in which part of Euclid's Elements?
Book I
Book I ends on it: the Pythagorean theorem is its second-to-last proposition, and the last one turns it around to prove the converse.
James A. Garfield
James A. Garfield, then an Ohio congressman, found his proof by working out one figure's area in two different ways and published it in the New-England Journal of Education five years before he became president.
Q 24In one legend, Hippasus of Metapontum drowned at sea for revealing the existence of what?
Irrational numbers
Irrational numbers: the tale goes that he let slip that the diagonal of a square shares no common measure with its edge; other ancient versions name a different secret.
Q 25How many Platonic solids are there?
Five
Five: at least three faces must meet at every corner and their angles must total less than a full turn, a squeeze only five shapes survive; Euclid ends the Elements by proving it.
Q 26Which Platonic solid has twelve pentagonal faces?
Dodecahedron
The dodecahedron has twelve pentagonal faces; in Plato's Timaeus the other regular solids each stand for an element, while this one is used for the universe as a whole.
Q 27In Plato's Timaeus, which classical element was matched with the cube?
Earth
Plato matched the cube with earth in the Timaeus because of its stability; fire got the tetrahedron, air the octahedron and water the icosahedron.
Q 28The twenty-sided die used in tabletop role-playing games is which solid?
Regular icosahedron
Regular icosahedron: 'icosa' is Greek for twenty, and because all twenty triangular faces are identical, every number has the same chance of landing face up.
Q 29A cube has twelve of which feature?
Edges
Edges: each of a cube's six square faces has four of them, and every edge is shared by two faces, so the count is 6 × 4 ÷ 2 = 12.
Q 30Whose widely read books made π the standard symbol for the circle ratio, decades after William Jones first used it?
Leonhard Euler
Leonhard Euler adopted the symbol in the 1730s, and his books and constant letter-writing spread it across Europe; William Jones, a Welsh maths teacher, had introduced it in 1706.