Abstract
Fibonacci numbers and the Golden Mean are numbers and thus 0-dimensional objects. Usually, they are visualized in the Euclidean plane using squares and rectangles in a spiral arrangement. The Golden Mean, as a ratio, is an affine geometric concept and therefore Euclidean visualizations are not mandatory. There are attempts to visualize the Fibonacci number sequence and Golden Spirals in higher
dimensions [11], in Minkowski planes [12], [4] and in hyperbolic planes (again [4]). The latter has to replace the not existing squares by sequences of touching circles. This article aims at visualizations in all Cayley-Klein planes and makes use of three different visualization ideas: nested sets of squares, sets of touching circles and sets of triangles that are related to Euclidean right angled triangles.
dimensions [11], in Minkowski planes [12], [4] and in hyperbolic planes (again [4]). The latter has to replace the not existing squares by sequences of touching circles. This article aims at visualizations in all Cayley-Klein planes and makes use of three different visualization ideas: nested sets of squares, sets of touching circles and sets of triangles that are related to Euclidean right angled triangles.
Original language | English |
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Pages (from-to) | 36-44 |
Journal | KoG |
Volume | 18 |
Issue number | 8 |
DOIs | |
Publication status | Published - 2014 |
Fields of Expertise
- Sonstiges
Treatment code (Nähere Zuordnung)
- Theoretical