Abstract:

The study of mathematics sometimes appears to students to be unfunny and lacking practical relevance. It is true that, for some topics, these connections are hard to find. But students expect them when they are taught. This article shows that motivation can be found not only in practise, but also in mathematics itself. We should not forget that there are also topics in the field of fun or popular mathematics that can be conveniently used in the motivational part of teaching. Selected topics from this part of mathematics will be discussed in this article. This study shows connections between concepts such as the Fibonacci sequence, the golden section, the super-gold section, golden rectangles, rabbit and cattle sequences, Fibonacci p-numbers and the roots of characteristic polynomials of the generalised cattle sequence. The so-called gilded sequence, which is actually the sequence of these roots, is also shown, and its limit is proved to be equal to one. Furthermore, its connection with golden and super-gold rectangles is shown. All solved applications are accompanied by a Matlab script and, where possible, presented graphically. All of the presented applications have been used in teaching applied mathematics at the Faculty of Transport Engineering, University of Pardubice, and can be an inspiration for teaching at other universities of the same or similar orientation.

Keywords:

Golden section, Golden rectangles, Gilded sequence, Applied mathematics, Matlab.