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Geometry: fun facts and quiz
The essentials in 7 ideas, with fun facts, an illustrated story and a quiz to see how much you know.
The essentials
Shapes & Angles
Angles measure turns in degrees. A right angle is 90°, a straight line is 180°, and a full turn is 360°.
Key fact
The 360-degree circle goes back to ancient Babylon.
Triangles
The three angles of any flat triangle add up to 180°. Triangles are rigid, which is why bridges and cranes are full of them.
Key fact
An equilateral triangle has three equal sides and three 60° angles.
Pythagoras’ Theorem
In a right-angled triangle, the square of the longest side equals the squares of the other two added together: a² + b² = c².
Key fact
A 3-4-5 triangle always has a right angle.
Circles
A circle’s diameter goes right across, through the centre; its radius is half that. The circumference is pi times the diameter.
Key fact
The area of a circle is π × radius².
Area & Volume
Area measures flat space in squares; volume measures 3D space in cubes. Double a cube’s sides and its volume grows eight times.
Key fact
A cube 1 metre on each side holds 1,000 litres.
Symmetry
A shape has symmetry if it matches itself when flipped or turned. Butterflies have mirror symmetry; snowflakes usually have six-fold symmetry.
Key fact
A circle has infinitely many lines of symmetry.
Shapes in Nature
Bees build six-sided hexagonal cells that fit together with no gaps and use the least wax. Nature is full of geometry.
Key fact
Only triangles, squares and hexagons tile a floor as the same regular shape.
Fun facts
The Babylonians counted in sixties. That’s why both an hour and a degree are split into 60 minutes.
The Eiffel Tower is a lattice of about 18,000 iron pieces, braced into triangles so it stays stiff in the wind.
Builders in the ancient world may have used knotted ropes forming 3-4-5 triangles to set out right angles.
Pi has been worked out to over 100 trillion digits, yet about 40 are enough to measure the whole observable universe to within an atom.
A sphere holds the most volume for its surface, which is why soap bubbles are round.
Most faces aren’t quite symmetrical, and perfectly mirrored faces often look oddly unnatural.
The Giant’s Causeway in Northern Ireland has about 40,000 stone columns, many of them hexagons.
Story: Don’t Disturb My Circles
Don’t Disturb My Circles
212 BCE. Roman soldiers storm the Greek city of Syracuse. Archimedes, by now an old man, is drawing circles in the sand.
A soldier orders him to come along. Legend says Archimedes barely looked up: “Don’t disturb my circles!”
He was killed, against the Roman general’s orders. On his tomb, as he had wished, was a sphere inside a cylinder.
True or false?
Tap your answer to see if you got it, and why.
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Question 1 of 10
A right angle is 90 degrees.
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True. Like the corner of a square.
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Question 2 of 10
A triangle’s angles add up to 180 degrees.
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True. Every flat triangle, every time.
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Question 3 of 10
In a 3-4-5 triangle, the angle between the two shorter sides is 90°.
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True. 9 + 16 = 25.
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Question 4 of 10
The radius is half the diameter.
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True. From the centre to the edge.
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Question 5 of 10
Doubling a cube’s sides makes its volume eight times bigger.
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True. 2 × 2 × 2 = 8.
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Question 6 of 10
Snowflakes usually have six-fold symmetry.
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True. Because of how water molecules link up.
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Question 7 of 10
Honeycomb cells are hexagons.
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True. Six-sided and tightly packed.
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Question 8 of 10
A triangle’s angles add up to 360 degrees.
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False. They add up to 180°.
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Question 9 of 10
Triangles bend easily, so engineers avoid them.
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False. They’re rigid, so engineers love them.
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Question 10 of 10
Pythagoras’ theorem works for every triangle.
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False. Only for right-angled triangles.
Keep going in the app
KnowSoda learns what you know and brings back what you’re about to forget. Geometry has 6 more ideas at the Advanced and Expert levels.
Sources
- Khan Academy — Geometry
- MacTutor History of Mathematics — Pythagoras, Babylonian mathematics
- Encyclopaedia Britannica — circle, symmetry, tessellation, honeycomb
- Hales (2001), “The Honeycomb Conjecture”, Discrete & Computational Geometry
- Encyclopaedia Britannica — trigonometry, Platonic solid, topology, non-Euclidean geometry
