Given two planar regular convex not-closed curves C and C_1. Let A the set of finite intersections between C and C-1. Then what is the stricter upper bound of |A|?
I would say 2. Thanks.
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6$\begingroup$ Viewed from the Sun, the orbits of both Earth and Moon are convex, yet they cross each other about 25 times a year. $\endgroup$– Gerry MyersonCommented Feb 21, 2017 at 22:22
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1$\begingroup$ @GerryMyerson: That's a cool fact that the orbit of the Moon is convex! $\endgroup$– Joseph O'RourkeCommented Feb 21, 2017 at 23:38
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1$\begingroup$ I'd be amazed if ellipses weren't considered "regular". But even ellipses intersect as many as 4 times. See also Bezout's theorem. $\endgroup$– Todd TrimbleCommented Feb 22, 2017 at 0:38
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2$\begingroup$ It's a bad idea to change the question so much that an answer already given changes from relevant to irrelevant. Better would be to open a new question entirely. $\endgroup$– Todd TrimbleCommented Feb 25, 2017 at 4:02
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1$\begingroup$ Francesco, thanks for explaining. I think what I'll do is roll back to the previous version, and then if you'd like to start a new thread and ask a different question, go right ahead. (However, my suspicion is that part of the question you mean to ask would not get a good reception here, because the basic picture given by Joseph O'Rourke is robust and could be easily modified to get strict convexity, i.e., the question would not be considered "research level" (for mathematicians). Maybe Mathematics StackExchange would be the better site for this type of question.) $\endgroup$– Todd TrimbleCommented Feb 25, 2017 at 20:51
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