Math◆ Rare
Pythagoras' theorem
Pythagoras sats
Discovered 1800 BC · BabylonEUREKA 01
Pythagoras' theorem◆
The ideaIn a right-angled triangle, the squares on the two short sides add up to the square on the long side.
a² + b² = c²
Lets you predictA distance you cannot measure, from two you can.
Tests usually ask
  • Find the missing side
  • Is this triangle right-angled?
Scan for the full explanation and a practice question.
Eureka · 01/10
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Math ◆ Rare: a famous discovery

Pythagoras' theorem

Swedish: Pythagoras sats · Discovered: Babylon, about 1800 BC · proved by Greeks about 500 BC

In a right-angled triangle, the squares on the two short sides add up to the square on the long side.

a² + b² = c²

Why it works

Draw a square on each side of a right-angled triangle. The two small squares together always cover exactly the same area as the big one. That is the whole theorem.

Clay tablets from Babylon list triangles like 3, 4, 5 more than a thousand years before Pythagoras was born. Builders used a rope with 12 equal knots to make a perfect right angle: 3 + 4 + 5 knots.

What it lets you predict

A distance you cannot measure, from two you can.

How tests ask about it

  • Find the missing side
  • Is this triangle right-angled?

Try it

A phone screen is 6 cm wide and 8 cm tall. How long is the diagonal?

Show the answer

6² + 8² = 36 + 64 = 100, so the diagonal is √100 = 10 cm.

Connects to

Newton's second law

Wins these Lab Duel challenges

  • Will a 5 m ladder reach a window 4 m up if its foot must stand 3 m out? see challenge