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Sep 4, 2018 at 0:35 vote accept Matheus Andrade
Sep 4, 2018 at 0:06 answer added Joseph O'Rourke timeline score: 6
Sep 3, 2018 at 22:38 comment added Matheus Andrade I hadn't realized that, thanks. I don't want $\alpha \cup \beta$ to be necessarily simple, just smoothness will work well enough.
Sep 3, 2018 at 22:37 history edited Matheus Andrade CC BY-SA 4.0
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Sep 3, 2018 at 22:35 comment added Joseph O'Rourke It appears from your drawing that $\alpha'(0) = -\alpha'(L)$: The tangents are oppositely oriented. Also, do you require that $\alpha + \beta$ be simple, i.e., non-self-intersecting?
Sep 3, 2018 at 22:24 history edited Matheus Andrade CC BY-SA 4.0
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Sep 3, 2018 at 22:23 comment added Matheus Andrade I thought that was implied, but clearly it's not. I'll correct my post.
Sep 3, 2018 at 22:16 comment added Lee Mosher Are you asking how to prove existence of $\beta$? Or what are you asking?
Sep 3, 2018 at 21:35 history asked Matheus Andrade CC BY-SA 4.0