Show that a planar curve has infinitely many Bertrand mates.
Can anyone give hints or direction on how to prove this? Thanks
2026-04-03 14:25:24.1775226324
planar curve has infinitely many Bertrand mates
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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.