The area of cyclic polygons: Recent progress on Robbins' conjectures

Advances in Applied Mathematics

Volumn 34, Issue 4 SPEC. ISS., 2005, Pages 690-696

  Pak, Igor ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL MATHEMATICS; COMPUTATIONAL GEOMETRY; POLES AND ZEROS; THEOREM PROVING;

CYCLIC POLYGONS; ROBBINS CONJECTURES;

POLYNOMIALS;

EID: 15844425811     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aam.2004.08.006     Document Type: Article

References (13)

1. R. Connelly, The rigidity of suspensions, J. Differential Geom. 13 (1978) 399-408
2. R. Connelly, Handbook of Convex Geometry, North-Holland Amsterdam (1993) 223-271.
3. R. Connelly, Comments on generalized Heron polynomials and Robbins' conjectures preprint, available at http://www.math.cornell.edu/ ~connelly, 2004.
4. R. Connelly, I. Sabitov, A. Walz, The bellows conjecture Beiträge Algebra Geom. 38 (1997) 1-10.
5. M. Fedorchuk, I. Pak, Rigidity and polynomial invariants of convex polytopes Duke Math. J. 2004 in press; available at http://www-math.mit.edu/~pak/research.html
6. P. Landers, Dying mathematician spends last days on area of polygon, WSJ, July 29, 2003, p. 1
7. F.M. Malay, D.P. Robbins, J. Roskies, On the areas of cyclic and semicyclic polygons arXiv:mAth.GM/0407300
8. D.P. Robbins, Areas of polygons inscribed in a circle, Discrete Comput. Geom. 12 (1994) 223-236.
9. D.P. Robbins, Areas of polygons inscribed in a circle, Amer. Math. Monthly 102 (1995) 523-530.
10. I.Kh. Sabitov, The generalized Heron-Tartaglia formula and some of its consequences, Sb. Math. 189 (1998) 1533-1561.
11. I.Kh. Sabitov, The volume as a metric invariant of polyhedra, Discrete Comput. Geom. 20 (1998) 405-425.
12. V.V. Varfolomeev, Inscribed polygons and Heron polynomials, Sb. Math. 194 (2003) 311-331.
13. V.V. Varfolomeev, Galois groups of Heron-Sabitov polynomials for pentagons inscribed in a circle, Sb. Math. 195 (2004) 3-16.