Papierfalten

Abstract

In this thesis the properties of the paperfolding sequence are investigated with an emphasis on the application in mathematical education.In ten chapters the sequence is examined in different ways: first and foremost as a sequence of symbols produced by folding a strip of paper repeatedly in halves. The geometric point of view gives a curve that is space-filling and a fractal, known as the Dragon-curve or the Heighway-dragon. This is connected to iterated function-systems (IFS). If the unfolding angle is slightly larger than 90 degrees intersections of the curve occur. This is investigated in detail in chapter 9. The sequence can also be seen as the binary representation of a number of the unit interval. Then the problem of an easy calculation arises. The paperfolding sequence is one of the foremost examples for an automatic sequence, which is looked at in chapter 7. In the last chapter some classic curves are investigated if they can be generated by paperfolding.