People were using the rule more than a thousand years before Pythagoras was born. Here's who knew it, and how to see why it works.
Who really knew it
- Babylon, about 1800 BC: a scribe pressed numbers for right-angled triangles into a clay tablet, now known as Plimpton 322.
- China: an ancient book called the Zhoubi showed the rule with a picture of a 3, 4, 5 triangle.
- Greece, about 500 BC: Pythagoras came along, and his name stuck. Nothing he wrote survives. The oldest proof we still have is Euclid's, from about 300 BC.
So what did they all know?
Take a right-angled triangle with short sides 3 and 4. Build a square on each side: 3² is 9 tiles, and 4² is 16 tiles.
Pour them into the square on the longest side. 9 + 16 = 25, and they fill it exactly. So the longest side is 5, because 5² = 25.
That's the rule: a² + b² = c², where c is the longest side (the hypotenuse), opposite the right angle.
Worked example: the ladder
A ladder's foot is 5 m from a wall, and it reaches 12 m up. 5² = 25. 12² = 144. Add them: 169. The square root of 169 is 13, so the ladder is 13 m long.
A right-angled triangle has short sides 6 and 8. How long is the longest side?
Show the answer
6² + 8² = 36 + 64 = 100, and √100 = 10.
Save this for your next test
- Only for right-angled triangles.
- Square the two short sides and add them.
- Square root the total to get the longest side.
- a² + b² = c²
Read the video transcript
- Pythagoras didn't discover Pythagoras' theorem. People were using it more than a thousand years before he was born.
- Around 1800 BC, a Babylonian scribe pressed numbers for right-angled triangles into a clay tablet.
- In China, an ancient book called the Zhoubi showed it with a picture of a 3, 4, 5 triangle.
- Pythagoras came along around 500 BC, and his name stuck.
- So what did they all know? Take a right-angled triangle with sides 3 and 4.
- Build a square on each side. 3 squared is 9 tiles. 4 squared is 16 tiles.
- Now pour them into the square on the longest side. 9 plus 16 is 25. They fill it exactly.
- So the longest side is 5, because 5 squared is 25.
- That's the rule: a squared plus b squared equals c squared.
- Let's use it. A ladder's foot is 5 metres from a wall, and it reaches 12 metres up.
- 5 squared is 25. 12 squared is 144. Add them: 169. The square root of 169 is 13. The ladder is 13 metres long.
- Now you: a right-angled triangle has short sides 6 and 8. How long is the longest side? Tell me in the comments.
- Want maths to click like this? Book a free trial lesson at bloomeducationonline.com.
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