Talk:Puzzles/Geometric Puzzles/Rubber Band

One point (A) of the triangle will be the point where the band is fixed to the plane. Get the next point (B) by folding the relaxed band in half (so that it's 3cm long) and marking the endpoint with the pencil. The third point is more tricky. First, stretch out the band completely, hold it down with your finger at B and then draw a half circle (which will have radius 5) to the right. Also, mark the point E on this half circle: E is the point where the second half of the band goes over A (see below). Now repeat the process on the other side: First we measure out the distance 3cm by folding the relaxed band. We get the point D (which lies on the straight line that's going through AE!). Again, we draw the half circle around D with the stretched (8cm) band; but now to the left. The point above A where the two half circles cross is our third triangle point (C). The construction with the two 5cm-radius half circles around B and D guarantees that AC will be in a right angle to AB, thus making ABC into a right-angled triangle (the side lengths will be AB=3cm, AC=4cm, BC=5cm which satisfies Pythagoras' theorem). Thomas

Figure: C   /| / | /  |   B---A.E.D