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Analytical Derivation of the Fuss Relations for Bicentric Hendecagon and Dodecagon

izvorni znanstveni rad

izvorni znanstveni rad

Analytical Derivation of the Fuss Relations for Bicentric Hendecagon and Dodecagon

Vrsta prilog u časopisu
Tip izvorni znanstveni rad
Godina 2015
Časopis Acta Physica Polonica. A
Nadređena publikacija Acta Physica Polonica. A
Volumen 128
Svesčić 2-B
Stranice str. B-82-B-85
DOI 10.12693/APhysPolA.128.B-82
ISSN 0587-4246
EISSN 1898-794X
Status objavljeno

Sažetak

In this article we present analytical derivation of the Fuss relations for n = 11 (hendecagon) and n = 12 (dodecagon). We base our derivation on the Poncelet closure theorem for bicentric polygons, which states that if a bicentric n-gon exists on two circles then every point on the outer circle is the vertex of same bicentric n-gon. We have used Wolfram Mathematica for the analytical computation. We verified results by comparison with earlier obtained results as well as by numerical calculations.

Ključne riječi

bicentric polygon; Fuss' relations