Cyclic polygons are critical points of area
G. Panina, G. N. Khimshiashvili

This publication is cited in the following articles:

1. Khimshiashvili G. Panina G. Siersma D., “Area-Perimeter Duality in Polygon Spaces”, Math. Scand., 127:2 (2021), 252–263      
2. Leger J.-Ch., “Area, Perimeter and Cocyclical Polygons”, Tbil. Math. J., 14:1 (2021), 15–40      
3. Mamaev D., “Oriented Area as a Morse Function on Polygon Spaces”, ARS Math. Contemp., 19:1 (2020), 155–171      
4. G. Khimshiashvili, G. Panina, D. Siersma, “Extremal areas of polygons with fixed perimeter”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye i algoritmicheskie metody. XXX, Zap. nauchn. sem. POMI, 481, POMI, SPb., 2019, 136–145  
5. N. Sazandrishvili, “Extremal Connectors for Disjoint Circles”, J Math Sci, 237:1 (2019), 147  
6. Khimshiashvili G., Panina G., Siersma D., Zolotov V., “Point Charges and Polygonal Linkages”, J. Dyn. Control Syst., 23:1 (2017), 1–17          
7. G. Panina, “Oriented area is a perfect Morse function”, St. Petersburg Math. J., 29:3 (2018), 469–474          
8. Sossinsky A., “Configuration Spaces of Planar Linkages”, Handbook of Teichmueller Theory, v. VI, Irma Lectures in Mathematics and Theoretical Physics, 27, ed. Papadopoulos A., Eur. Math. Soc., 2016, 335–373      
9. Khimshiashvili G., “Remarks on Bicentric Quadrilaterals”, Proc. A Razmadze Math. Inst., 168 (2015), 41–52      
10. Khimshiashvili G., Panina G., Siersma D., “Coulomb Control of Polygonal Linkages”, J. Dyn. Control Syst., 20:4 (2014), 491–501            
11. G. N. Khimshiashvili, “Moduli spaces of bicentric quadrilaterals”, Journal of Mathematical Sciences, 211:1 (2015), 31–39      
12. Giorgadze G.K., Khimshiashvili G.N., “Cyclic Configurations of Spherical Polygons”, Dokl. Math., 87:3 (2013), 300–303                
13. Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma, Alena Zhukova, “Critical configurations of planar robot arms”, Open Mathematics, 11:3 (2013)  
14. Panina G.Yu., Khimshiashvili G.N., “On the Area of a Polygonal Linkage”, Dokl. Math., 85:1 (2012), 120–121                
15. A. Zhukova, “Morse index of a cyclic polygon. II”, St. Petersburg Math. J., 24:3 (2013), 461–474              
16. A. M. Zhukova, “Nabory vpisannykh konfiguratsii tipichnykh sharnirnykh pyatiugolnikov”, Tr. SPIIRAN, 21 (2012), 203–227  
17. Panina G., Zhukova A., “Morse index of a cyclic polygon”, Cent. Eur. J. Math., 9:2 (2011), 364–377            
18. A. M. Zhukova, G. Yu. Panina, “Ravnovesnye polozheniya ploskogo poligonalnogo sharnirnogo mekhanizma”, Tr. SPIIRAN, 12 (2010), 226–234