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Show that a planar curve has infinitely many Bertrand mates.

Can anyone give hints or direction on how to prove this? Thanks

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  • $\begingroup$ Your question "Show q(t,ϕ) defines a parametrized surface" seemed good to me. Why did you delete it? $\endgroup$ – Robert Lewis Apr 10 '15 at 4:02
  • $\begingroup$ Oh, I figured it out. Should I have not deleted but instead answered it myself? $\endgroup$ – lll Apr 11 '15 at 21:46
  • $\begingroup$ I think that would be cool. To my mind it is a good question; I had halfway worked out an answer when you deleted it! I for one would like to see what you've got. Note that there's even a check box on the "ASK" page for answering your own question and sharing what you know. Of course, it's up to you . . . Cheers! $\endgroup$ – Robert Lewis Apr 11 '15 at 21:51
  • $\begingroup$ Note that there's no policy or rule that says you have to delete a question just because you've figured out the answer. Also, other MSE users might like to see what you've got. More Cheers! $\endgroup$ – Robert Lewis Apr 11 '15 at 21:52
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A parallel Bertrand curve is obtained by erecting a normal of constant length at each point on a curve C. Any smooth continuous curve C is a set of infinite connected points, so correspondingly there are infinitely many curved parallels.

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