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Liquid Pythagoras

sinc-e **2013**
Hiša eksperimentov

Ljubljana, Slovenia

### Do and observe!

Slowly rotate the circular board by pressing and holding the buttons below the video.

Observe the flow of the liquid in the triangles!

### What's going on?

Above each side of a rectangular triangle made out of plexi-glass there is an empty square space of equal depth.
The sides of each square are the same size as the separate sides of the triangle.
While the board rotates the liquid pours from one empty space to the next.
You will notice that the liquid from the larger square space will completely fill the two smaller square spaces.

### More...

This characteristic of rectangular triangles was discovered by the Greek mathematician Pythagoras 500 years before Christ.
The Pythagorean theorem, which is taught to pupils in elementary school, states that the area of the square above
the largest side of the triangle is equal to the sum of the areas of both smaller squares.

### Did you know?

Normally the lengths of the sides of a rectangular triangle are not whole numbers. But some exceptions can be found,
namely the triangles with the sides (3, 4 and 5) and (9, 12 and 15). Are the following also rectangular triangles: (6, 8, 10), (9, 10, 14) and (5, 12, 13)?