smjw@rtgvax.UUCP (steve winters) (03/05/86)
Here is a puzzle I was told about many years ago but have not seen since. I have not been able to solve it so am not sure it can be. Take any triangle and trisect its internal angles. The points at which the trisecting lines first intersect each other form another triangle. Prove that that triangle is alway equilateral. I would be very grateful to anyone who can simply prove (or disprove) the above statement. Steve Winters. (I seem to be having this tremendous difficulty with my lifestyle)
tan@ihlpg.UUCP (Bill Tanenbaum) (03/08/86)
> Here is a puzzle I was told about many years ago but have > not seen since. I have not been able to solve it so am not > sure it can be. > > Take any triangle and trisect its internal angles. The points > at which the trisecting lines first intersect each other form > another triangle. > Prove that that triangle is alway equilateral. > > I would be very grateful to anyone who can simply prove > (or disprove) the above statement. > Steve Winters. --- I have seen the above as a (Euclidean) geometry theorem, not a trig problem. As such, it is called Morley's Theorem, and there is a geometric proof. Unfortunately, I don't know the details. The proof is not simple. -- Bill Tanenbaum - AT&T Bell Labs - Naperville IL ihnp4!ihlpg!tan
ins_ampm@jhunix.UUCP (Michael P McKenna) (03/09/86)
In article <35@rtgvax.UUCP> smjw@rtgvax.UUCP writes: > > >Here is a puzzle I was told about many years ago but have >not seen since. I have not been able to solve it so am not >sure it can be. > >Take any triangle and trisect its internal angles. The points >at which the trisecting lines first intersect each other form >another triangle. >Prove that that triangle is alway equilateral. > >I would be very grateful to anyone who can simply prove >(or disprove) the above statement. > You can find a proof of this in _Introduction to Geometry_ by H.S.M. Coxeter. This is a WONDERFUL book that explores many aspects of geometry (introduction is something of a misnomer). If you can't find it in your library COMPLAIN VERY LOUDLY! Dwight S. Wilson P.S. For anyone interested in buying this book: The publisher is John Wiley, & Sons, Inc.