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Topic:
Clarification on the result of the equichordal point problem
Replies:
6
Last Post:
Jan 5, 2004 3:09 PM
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Re: Clarification on the result of the equichordal point problem
Posted:
Dec 31, 2003 7:51 PM
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On 31 Dec 2003, Shinya wrote:
> Hello. While I was doing research on the equichordal point problem,
> I encountered a confusion.
I might be able to clear it up, since I've been interested in this
problem for more than 40 years, and know the state of play. I'll read
on...
> Equichordal Point Problem: Can a plane region have two equichordal
> points?
The answer is definitely "No", as was first established by Rychlik
about 5 years ago. I read on again...
> The source of the confusion is Mathworld. On the one hand, it states
> that the problem was fully solved by Rychlik in 1997
So that's the right one, while in this one:
> on the other hand, it states that "a plane convex region can
> have two equichordal points."
the word "can" is obviously a typographical error for "cannot".
This particular error ("can" for "cannot") is really quite
common. There have been 5 or 6 different instances that have
puzzled me for quite considerable times!
> By the way, the problem was solved in the negative: This problem has
> been fully solved in the negative by the author of this announcement
> just recently. (From abstract of the original paper) i.e.,
>
> No Jordan curve may contain two or more equichordal points.
>
> Could anyone help me?
You seem to have helped yourself pretty well, but might like
to have the reassurance that your guess is the right one.
Regards, John Conway
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