Computation and Analysis of Explicit Formulae for the Circumradius of Cyclic Polygons ∗

Content Provider	Semantic Scholar
Author	Moritsugu, Shuichi
Copyright Year	2018
Abstract	This paper describes computations of the circumradius of cyclic polygons given by the lengths of the sides. Extending the author’s previous paper in 2011, we mainly discuss the computation and analysis of the formulae for cyclic heptagons and octagons. As a result of the present work, we have succeeded in explicitly computing the circumradius of cyclic heptagons, which is converted into an expression in the form of elementary symmetric polynomials for the first time. We have also succeeded in computing 25 out of 39 coefficients in the circumradius formula for cyclic octagons. Moreover, investigating the formulae by the total degree of each term, from triangles to octagons, we have discovered a characteristic structure in common among them, which should be helpful for computing the other huge coefficients remaining in the octagon formula.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www.jssac.org/Editor/CJssac/V03/V3_101.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article