Mmm --- wonder why he chose the longest ... WFL On 1/6/10, Dan Asimov <dasimov@earthlink.net> wrote:

In the plane:

Let C be a C^oo simple closed curve.

Let a "double-normal" be a line segment whose endpoints lie on C and which is normal to C at each of them.

C must have a double-normal. (Proof: Consider the longest segment from C to C).

Question: Let a "simple" double-normal be one that intersects C only at its endpoints. Must C have at least one simple double-normal? Prove or find a counterexample.

--Dan _____________________________________________________________ * Thanks to Evan O'Dorney for this quick proof and for asking this question.

_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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