ON FUSS’ RELATIONS FOR BICENTRIC POLYGONS WITH AN ODD NUMBER OF VERTICES AND ROTATION NUMBER k

izvorni znanstveni rad

izvorni znanstveni rad

ON FUSS’ RELATIONS FOR BICENTRIC POLYGONS WITH AN ODD NUMBER OF VERTICES AND ROTATION NUMBER k

Mandi Orlić Bachler
Vrsta prilog u časopisu
Tip izvorni znanstveni rad
Godina 2026
Časopis KoG : znanstveno-stručni časopis Hrvatskog društva za konstruktivnu geometriju i kompjutorsku grafiku
Volumen Vol. 29
Svesčić No. 29
Stranice str. 22-39
DOI https://doi.org/10.31896/k.29.3
ISSN 1331-1611
EISSN 1846-4068
Status objavljeno

Sažetak

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 Radi´c’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 Radi´c’s conjecture.

Ključne riječi

bicentric polygon, Fuss’ relation, rotation number, triskaidecagon, pentadecagon, heptadecagon, enneadecagon

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