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Oct 30, 2022 at 15:27 history edited Alexandre Eremenko CC BY-SA 4.0
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Oct 30, 2022 at 15:14 comment added Alexandre Eremenko @Josif Pinelis: you are right: 4 straight segments is enough. On how to round the corners, I will add to my ans.
Oct 30, 2022 at 14:00 comment added Iosif Pinelis On the other hand, if the smoothness condition is disregarded, it is unclear to me why you need $8$ (rather than $4$) straight segments and why you need the curve to be of zero index.
Oct 30, 2022 at 2:00 comment added Iosif Pinelis I am wondering how this can be done: "to round the corners, and keep integral zero".
Oct 29, 2022 at 1:59 comment added Alexandre Eremenko It is piecewise smooth. But it is possible to round the corners, and keep integral zero.
Oct 28, 2022 at 22:27 comment added Iosif Pinelis The OP requested that the curve be smooth. Is your curve smooth?
Oct 28, 2022 at 19:30 vote accept Ali
Oct 28, 2022 at 19:26 history answered Alexandre Eremenko CC BY-SA 4.0