Pythagoras' theorem

There are 108 NRICH Mathematical resources connected to Pythagoras' theorem
Circumnavigation
problem

Circumnavigation

Age
14 to 16
Challenge level
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The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
All Tied Up
problem

All tied up

Age
14 to 16
Challenge level
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A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
The Fire-fighter's Car Keys
problem

The fire-fighter's car keys

Age
14 to 16
Challenge level
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A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.
Medallions
problem

Medallions

Age
14 to 16
Challenge level
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Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?
Rectangular Pyramids
problem

Rectangular pyramids

Age
14 to 18
Challenge level
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Is the sum of the squares of two opposite sloping edges of a rectangular based pyramid equal to the sum of the squares of the other two sloping edges?
The medieval octagon
problem

The medieval octagon

Age
14 to 16
Challenge level
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Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Out of the Window
problem

Out of the window

Age
14 to 16
Challenge level
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Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.
Babylon numbers
problem

Babylon numbers

Age
11 to 18
Challenge level
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Can you make a hypothesis to explain these ancient numbers?
Picturing Pythagorean Triples
article

Picturing pythagorean triples

This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.