The Magic Triangle - How to Fool Your Teacher

All you need for this very simple magic trick is a piece of paper, a printer, colored pencils and scissors.

Despite the simplicity, it will cause your teacher a lot of problems and you a lot of fun...

Step 1: The Preparations

Print out the 13x5 rectangle with your printer. For your entire school class, print it out accordingly.

Now draw 2 lines connecting the lower left corner and the upper right corner with the point (8; 3) (see red circle in the figure)! Then cut out the 4 parts. That was it....

Step 2: The Magic Trick

First arrange the 4 parts as shown in the form of a triangle with side lengths 13 and 5. The triangle has no free areas.

Now arrange the 4 parts a little differently (see illustration). You will get an identical triangle with sides 13 and 5 again. But what has happened now? The large triangle now has a free square despite the same dimensions! How can that be?

Step 3: The Solution

If you look closely, you will see that it is actually not a triangle at all. It is rather a quadrangle! If you arrange the 4 parts as in the picture above, this creates a quadrangle with a small inward dent. In this way there is no free space within the triangle.
Now arrange the 4 parts as in the illustration below. You get a slightly different quadrangle. This does not have a dent on the top side but a small bump. The entire quadrangle now spans a larger area than before. But since it is made up of the same 4 parts with the same area, there must now be a free area within the square in the form of a single free square!

The trick is that simple if you know the solution ...