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# Pythagoras

### How does the exhibit work?

Turn the green disc. Turning the green disc moves the liquid from the large square into the two smaller squares and vice versa.

### What is the science behind it?

Can you decipher the relationship between the sides of this right-angled triangle? In the triangle, two sides touch the right angle. These are the rectangular sides a and b. The slanting, longest side is c. The theorem of the Greek mathematician Pythagoras says that a² + b² = c². Or simply a x a + b x b = c x c.

Suppose side a = 3 cm. And side b = 4 cm. You then first multiply 3 x 3, which is 9. Then you multiply 4 x 4, which is 16.

9 + 16 = 25. That means c x c is 25 cm. So c = 5 cm, because 5 x 5 = 25.

If you know how long a and b are, you also know how long c is.

Hmm... a x a is also used to calculate the area of a square. This means that you can also prove the theorem by making squares with the sides! If you spin the wheel, you will see that the area of the largest square is equal to the sum of the areas of the 2 small squares.

**Pythagorean theorem for a slide**

Suppose you want a slide that goes from your bedroom window all the way to the end of your garden. If you know the size of your garden and the height of your window, you can calculate the length of your slide.

### How does the exhibit work?

Turn the green disc. Turning the green disc moves the liquid from the large square into the two smaller squares and vice versa.

### What is the science behind it?

Can you decipher the relationship between the sides of this right-angled triangle? In the triangle, two sides touch the right angle. These are the rectangular sides a and b. The slanting, longest side is c. The theorem of the Greek mathematician Pythagoras says that a² + b² = c². Or simply a x a + b x b = c x c.

Suppose side a = 3 cm. And side b = 4 cm. You then first multiply 3 x 3, which is 9. Then you multiply 4 x 4, which is 16.

9 + 16 = 25. That means c x c is 25 cm. So c = 5 cm, because 5 x 5 = 25.

If you know how long a and b are, you also know how long c is.

Hmm... a x a is also used to calculate the area of a square. This means that you can also prove the theorem by making squares with the sides! If you spin the wheel, you will see that the area of the largest square is equal to the sum of the areas of the 2 small squares.

**Pythagorean theorem for a slide**

Suppose you want a slide that goes from your bedroom window all the way to the end of your garden. If you know the size of your garden and the height of your window, you can calculate the length of your slide.

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