Rad HAZU, Matematičke znanosti, Vol. 18 (2014), 145-170.

AN IMPROVED METHOD FOR ESTABLISHING FUSS' RELATIONS FOR BICENTRIC n-GONS WHERE n ≥ 4 IS AN EVEN INTEGER

Mirko Radić

Abstract.   In [7] we have given one relatively simple and practical method for establishing Fuss’ relations for bicentric n-gons where n ≥ 3 is an odd integer. In the present article we give one relatively simple and practical method for establishing Fuss’ relations for bicentric n-gon where n ≥ 4 is an even integer. In [7] the rotation numbers for bicentric n-gons have the key role, while in the present article tangent lengths of bicentric n-gons have the key role. So in the present article is described an algorithm to obtain Fuss’ relation for bicentric n-gons where n ≥ 4 is an even integer. Several yet unknown Fuss’ relations are established.

2010 Mathematics Subject Classification.   51E12.

Key words and phrases.   Bicentric polygon, Fuss’ relations.

References:

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3. N. Fuss, De poligonis simmetrice irregularibus calculo simul inscriptis et circumscriptis, NAAPS 1792 (Nova acta), t. XIII (1802), 168-189.

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6. M. Radić and Z.~Kaliman, About one relation concerning two circles where one is inside of the other, Math. Maced. 3 (2005), 45-50.
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7. M. Radić, An improved method for establishing Fuss' relations for bicentric polygons, C. R. Math. Acad. Sci. Paris 348 (2010), 415-417.
   MathSciNet     CrossRef