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Jun 18, 2010 at 12:00 history edited Anton Petrunin
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Jun 17, 2010 at 20:24 comment added Andrey Rekalo It's not clear from the question if cusps are allowed.
Jun 17, 2010 at 20:19 answer added Joel David Hamkins timeline score: 6
Jun 17, 2010 at 19:56 comment added Robin Chapman My first instinct is there must be points where at least three copies of $C$ meet, and there one of them must have an "angle", so no unique tangent. I don't entirely trust my instincts on this one though.
Jun 17, 2010 at 19:44 answer added Tom Goodwillie timeline score: 6
Jun 17, 2010 at 19:28 history asked Garabed Gulbenkian CC BY-SA 2.5