Images of Some Discs Under the Linear Fractional Transformation of Special Continued Fractions

Akbaba Ü., Tuylu T., Değer A. H.

CONFERENCE PROCEEDINGS OF SCIENCE AND TECHNOLOGY, vol.1, no.1, pp.232-237, 2021 (Conference Book)


In this paper, considering that the continued fraction Kn(􀀀1= 􀀀 k) is a Pringsheim fraction, with n = 1; 2; 3; ::: for natural
numbers k that are k = 2 and k = 3. The forms of the images of the discs Kn are examined under the linear fractional transformations
fSng of the complex disc D = fw 2 C : jwj  1g. Specially, the relation between Fibonacci numbers and forms of the
images of the Kn are examined for k = 3. The results for these special continued fractions from the images of these discs will also
be compared with the vertex values on the minimal-length paths in the suborbital graphs. Also, an algorithm is created in Python
application language to visually inspect circular discs.