Thanks, Fred! (I didn't see your post until after I replied to Mike's.) Jim Propp On Mon, Apr 6, 2015 at 5:26 PM, Fred W. Helenius <fredh@ix.netcom.com> wrote:
On 4/6/2015 3:51 PM, James Propp wrote:
Back about 30-40 years ago, I posed a problem in Mathematics Magazine (or maybe the Monthly) asking whether any triangle could be linked to a non-congruent similar triangle via a sequence of triangles, each "SSA-congruent" to the one before and the one after. There was a cute solution that pointed out that this is impossible because two SSA-congruent triangles have the same X, where X was some triangle statistic (like perimeter, inradius, or circumradius, but slightly less well-known) that scales linearly under similarity.
Can anyone (a) figure out what X was, or (b) locate my problem and the solution?
Jim Propp
PS: In my original submission I proposed the term "ASS-congruent", which struck me as both more pronounceable and more apt, but the stodgy problems editor who reigned at the time deemed this too vulgar.
Mathematics Magazine, Vol. 57, No. 5, November 1984, page 299. The problem appeared as a "quickie" (Q695); the triangles were called "skew-congruent". The one-line solution on page 305 is credited to John Horton Conway (who observes that circumradius = BC/(2 sin A)).
-- Fred W. Helenius fredh@ix.netcom.com
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