KoG, Vol. 29 No. 29, 2025.
Original scientific paper
https://doi.org/10.31896/k.29.3
On Fuss’ Relations for Bicentric Polygons with an Odd Number of Vertices
Mandi Orlić Bachler
orcid.org/0000-0002-9011-1892
; University of Applied Sciences, Zagreb, Croatia
*
* Corresponding author.
Abstract
This paper presents novel analytical forms of Fuss’ relations for bicentric polygons with an odd number of sides and higher rotation numbers. The method is based on Poncelet’s theorem and Radić’s theorem and conjecture concerning the connection between Fuss’ relations for different rotation numbers. Explicit analytical expressions are obtained for the bicentric triskaidecagon with k = 2,4,6 and for the bicentric pentadecagon with k = 2, while complete sets of relations are established for the bicentric heptadecagon (k = 1,2,3,4,5,6,7,8) and enneadecagon (k = 1,2,3,4,5,6,7,8,9). The proposed approach simplifies the derivation and enables a systematic extension of known Fuss’ relations to higher-order bicentric polygons and new rotation numbers, confirming the validity of Radić’s conjecture.
Keywords
bicentrični poligon; Fussova relacija; rotacijski broj; trinaesterokut; petnaesterokut; sedamnaesterokut; devetnaesterokut
Hrčak ID:
341601
URI
Publication date:
19.12.2025.
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