26 Nov
2006
26 Nov
'06
9:40 a.m.
Q2. Are there 10 road lengths that lead to distinct town configurations?
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Q1. Draw a non-isosceles triangle ABC with rational sides. Let M be the midpoint of AB, and let DD' be a segment drawn through M that's perpendicular to CM, such that the distances d(D,M) and d(D',M) are equal and rational.
This implies distinct town configurations A,B,C,D and A,B,C,D' having the same sest of 6 distances.
The fact that DMD' is perpendicular to CM shows that the distances CD and CD' are equal. But I don't see why AD and AD' should be equal in this contstruction. Andy Latto andy.latto@pobox.com