Abstract
For a positive integer , let
In 2000 Bean and Laugesen proved that for every the area bounded by the curve is equal to , where is the beta function. We provide an elementary proof of this fact based on the polar formula for the area calculation. We also prove that
and demonstrate that is the smallest positive integer such that the binary form has integer coefficients. Here denotes the -adic order of .
Citation
Anton Mosunov. "On the area bounded by the curve $\prod_{k = 1}^n\left|x\sin\frac{k\pi}{n} - y\cos\frac{k\pi}{n}\right|=1$." Rocky Mountain J. Math. 50 (5) 1773 - 1777, October 2020. https://doi.org/10.1216/rmj.2020.50.1773
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