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0|0|0|||||Menelaus%3A an unnecessary requirement in a proof%3F|ram||14:03:02|07/08/2009|Hello Alex%2C%0D%0A%0D%0AI have a comment concerning a proof of Menelaus%27s Theorem that is presented during the discussion of Einstein%27s remarks on elegant and ugly proofs %28%5Ba%5Dhttp%3A%2F%2Fwww.cut-the-knot.org%2FGeneralization%2FMenelausByEinstein.shtml%23Carnot%5B%2Fa%5D%29. It is the proof that is marked %22Proof %233%22 in the corresponding applet%2C and which serves as an impressive example of a proof which is elegant despite involving auxiliary constructions...%0D%0A %0D%0AThe proof starts %22Draw a line perpendicular to the transversal EDF ...%22. My comment is this%3A the proof does not seem to make%2C actually%2C any use of the fact that the auxiliary line %28call it l%5Bsub%5D1%5B%2Fsub%5D%29 is %5Bi%5Dperpendicular%5B%2Fi%5D to the transversal. The proof does use the following principle%3A %22the segments cut on two lines by a family of parallel lines are in the same ratio%22. Therefore it is required that the segments aKa%2C bKb%2C cKc are all parallel to the transversal. But for that they don%27t seem to have to be perpendicular to l%5Bsub%5D1%5B%2Fsub%5D. The only requirement from l%5Bsub%5D1%5B%2Fsub%5D seems to be that it intersects the transversal EDF.%0D%0A %0D%0AOr perhaps I%27ve missed something.%0D%0A %0D%0ARam%0D%0A
1|1|0|||||RE%3A Menelaus%3A an unnecessary requirement in a proof%3F|alexb||18:00:14|07/08/2009|%3EOr perhaps I%27ve missed something. %0D%0A%0D%0ANo%2C that%27s a good remark. The only thing that matters is that the lines through the vertices come out parallel to the transversal. Surely this might be the starting point with a line crossing the four as the second stage.%0D%0A%0D%0AMany thanks%2C%0D%0AAlex
2|2|1|||||RE%3A Menelaus%3A an unnecessary requirement in a proof%3F|ram||07:20:56|07/09/2009|By the way%2C when I posted%2C I marked the check-box to get email notifications %22when a new message is submitted%22. Also for my previous post. But I didn%27t get any such notifications. Do you know perhaps why%3F%0D%0AI verified that they weren%27t held by gmail%27s spam filter.%0D%0A%0D%0ARam
4|3|2|||||RE%3A Menelaus%3A an unnecessary requirement in a proof%3F|alexb||08:00:58|07/09/2009|Thank you for taking the trouble. There is certainly a problem with the forum software. The program is quite old and is no longer supported. I am planning to switch to a new program in a short while and thus resolve several outstanding problems%2C this one in particular.%0D%0A