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2015 | 128 | 2B | B-82-B-85
Article title

Analytical Derivation of the Fuss Relations for Bicentric Hendecagon and Dodecagon

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EN
Abstracts
EN
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.
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EN
Publisher

Year
Volume
128
Issue
2B
Pages
B-82-B-85
Physical description
Dates
published
2015-8
Contributors
author
  • University of Applied Sciences, Zagreb, Croatia
author
  • University of Rijeka, Department of Physics, Rijeka, Croatia
References
  • [1] H. Dörrie, 100 Great Problems of Elementary Mathematics, Dover, New York 1965
  • [2] M. Radić, Z. Kaliman, Rad HAZU, Matematičke znanosti 503, 21 (2009) (in Croatian). http://hrcak.srce.hr/110228
  • [3] M. Radić, Rad HAZU, Matematičke znanosti 519, 145 (2014) (in Croatian). http://hrcak.srce.hr/127655
  • [4] M. Radić, Math. Commun. 19, 139 (2014), doi: 10.1007/s13366-012-0131-5
  • [5] M. Radić, Compt. Rend. Math. 348, 415 (2010), doi: 10.1016/j.crma.2010.02.021
  • [6] Z. Kaliman, M. Orlić, in: 6 Int. Conf. Aplimat 2007, Vol. 3, 2007, p. http://bib.irb.hr/datoteka/595027.Using_Mathematica_in_alternative_derivation_of_fuss_relation_fo.pdf
  • [7] M. Orlić, Z. Kaliman, N. Orlić, in: 6 Int. Conf. Aplimat 2007, Vol. 3, 2007, p. 83. http://bib.irb.hr/datoteka/595027.Using_Mathematica_in_alternative_derivation_of_fuss_relation_fo.pdf
  • [8] http://mathworld.wolfram.com/PonceletsPorism.html
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv128n2b022kz
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