# Pythagoras and the Knotted Rope

Now we’ve switched to a full-time living maths approach, we’re actually making time to play with some of the wonderful resources we’ve had on our shelves for years.

On Friday we read What’s Your Angle, Pythagoras, a picture book which tells the story of how the young Pythagoras learns how to make a right-angled triangle using knotted rope, and discovers how to calculate the length of its hypotenuse using square tiles.

Obviously the book is mostly fictional, and it takes some historical liberties – the boy Pythagoras visits Alexandria, for instance, several hundred years before the city was built! – but these are discussed at the back of the book in a way that made my kids laugh and was a handy review of Ancient Greece and Alexander the Great.

### How to make a right-angled triangle using rope

In the book, the young Pythagoras notices what happens when buildings are constructed with less-than-accurate right-angles. On a trip to Alexandria with his father, he learns how the Egyptians use knotted rope to overcome this problem.

We tried it out for ourselves. We tied eleven knots at equal distance along our rope before joining the ends in a final knot, so that we ended up with twelve short lengths of rope between each knot.

Then we used our rope to make different shaped triangles. We counted how many lengths of rope were on each side of each triangle.

To make a right-angled triangle, we found that we needed the sides to be 3 lengths, 4 lengths and 5 lengths of rope respectively.

(Top Tip: Take care to make the knots evenly spaced. C(9)’s rope worked perfectly for making right-angled triangles, whereas the one I helped J(8) make didn’t, oops!)

### Using Lego to demonstrate the Pythagoras Theorem

While playing with floor tiles, the young Pythagoras in the story discovers that if he makes a square along each side of a right-angled triangle, the square on the longest side uses the same number of tiles as the other two sides’ squares put together.

We tried this for ourselves with 2×2 Lego bricks.

Pythagoras uses what he has learned to work out how long a ladder is needed to reach the top of a wall. He also helps his father calculate the sailing distance to Rhodes.   Both excellent demonstrations of the usefulness of maths!

I would never have thought to teach my kids the Pythagoras Theorem at the ages they are (8 and 9) – all we did was read a picture book. But that living book inspired us to play, and before we knew it we were formulating mathematical proofs.  Another living maths success!