Analytical Derivation of the Fuss Relations for Bicentric Hendecagon and Dodecagon

Orlić, M.; Kaliman, Z.

doi:10.12693/APhysPolA.128.B-82

Journal

Acta Physica Polonica A

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

Article title

Analytical Derivation of the Fuss Relations for Bicentric Hendecagon and Dodecagon

Authors

M. Orlić , Z. Kaliman

Content

Full texts:

http://przyrbwn.icm.edu.pl/APP/PDF/128/a128z2bp022.pdf [remote]

Title variants

Languages of publication

Abstracts

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.

Keywords

02.70.Wz

Discipline

02.70.Wz: Symbolic computation (computer algebra)

Publisher

Institute of Physics, Polish Academy of Sciences

Journal

Acta Physica Polonica A

Year

2015

Volume

128

Issue

Pages

B-82-B-85

Physical description

Dates

published

2015-8

Contributors

author

M. Orlić

University of Applied Sciences, Zagreb, Croatia

author

Z. Kaliman

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

DOI

10.12693/APhysPolA.128.B-82

YADDA identifier

bwmeta1.element.bwnjournal-article-appv128n2b022kz