円内接多角形の外接円半径公式の計算と解析 (Computer Algebra : Theory and its Applications)

Abstract

This paper describes computations of the circumiadius 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, we have found a more efficient method for computing the circumradius of cyclic heptagons than before. 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.