Abstract
The geometric condition that n complex numbers are the vertices of a regular polygon is translated into algebraic equations that symmetric polynomials in these numbers must satisfy.
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Suggested Reading
L V Ahlfors, Complex Analysis, Third edn, McGraw-Hill, New York, 1979.
R Sharma and M Pal, Regular polygons and central moments, Am. Math. Mon., Vol.129, No.10, p.951, 2022.
J V Uspensky, Theory of Equations, McGraw-Hill, New York, 1948.
M Kendall and A Stuart, The Advanced Theory of Statistics, Vol. 1, Fourth edn, Charles Grifin & Company Limited, London & High Wycombe, 1977.
Acknowledgements
The second author thanks Ashoka University for a visit from January to February 2023 when this work was done.
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Rajendra Bhatia is a Professor of mathematics at the Ashoka University and Professor Emeritus at the Indian Statistical Institute. He has written often for the Resonance.
Rajesh Sharma earned his Ph.D. in mathematics in 1992 from H.P. University, Shimla, where at present, he is a Professor. He was a NBHM-Postdoc Fellow at IIT-Bombay (1994–1997). He visited ISI-Delhi (2006–2016) and Ashoka University (2017–2024) year after year for collaborative research work. His research work is focused on Matrix Analysis and Inequalities.
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Bhatia, R., Sharma, R. Regular Polygons and Symmetric Polynomials. Reson 29, 517–526 (2024). https://doi.org/10.1007/s12045-024-0517-3
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DOI: https://doi.org/10.1007/s12045-024-0517-3