Introductory examples

Abstract

We have often been asked questions, by students as well as by established mathematicians, about continued fractions: what they are and what they can be used for. Sometimes the questions have been raised under circumstances where a quick answer is the only alternative to no answer: in the discussion after a talk or lecture, by a cup of co®ee in a short break, in an airplane cabin or on a mountain hike. In responding to these questions we have often been pleased by the sparks of interest we have seen, indicating that we had managed to transmit a glimpse of new and apparently appealing knowledge. In quite a few cases this led to further contact and ‘follow-up activities’.