Talk:Fermat point

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[edit] Incomplete Proof?

As I was reading through the proof, I found it to be (to the best of my knowledge) incomplete. Here is why: "Because AR=AB, AC=AQ, by construction, and because angle RAC = angle BAQ, therefore triangle RAC and BAQ are congruent." Is it assumed that RC = BQ? If not, I do not see any proof that <RAC = <BAQ.

Now, I am no math wiz. If I am missing something here, please forgive my ignorance.

Angle RAC = angle RAB + angle BAC and angle BAQ = angle BAC + angle CAQ. Both angle RAB and angle CAQ are 60 degrees, because the triangles RAB and CAQ are equilateral, and hence <RAC = <BAQ. -- Jitse Niesen (talk) 02:17, 19 March 2006 (UTC)
Ah, yes, that makes sense. Thanks for the quick response! I have updated the main page accordingly.
Wolever 03:37, 19 March 2006 (UTC)

[edit] Incorrect Property?

I think the final property is wrong. The circumcenter of the Napoleon triangle is the centroid, not the Fermat point, of the original triangle .... MRFS 19:39, 11 January 2007 (UTC)

I have no idea, and I don't feel like thinking about it. So, I'm just playing it safe and I'll move the statement here:
"The triangle formed by joining the centers of the three regular triangles in the construction is also a regular triangle(Napoleon's theorem), and the circumcenter of this triangle is the fermat point of the original triangle."
Hopefully, somebody will find a reference for it, or for MRFS's statement. -- Jitse Niesen (talk) 13:59, 9 April 2007 (UTC)

See http://mathworld.wolfram.com/OuterNapoleonTriangle.html. All web statements need to be treated with caution, but if you take ABC to be an isosceles triangle with base angles of 30 degrees then its Fermat point is A and it is quite obvious that A isn't the centroid of the Napoleon! MRFS 18:11, 15 April 2007 (UTC)

Thanks, that's a nice example! I'm happy to have the corrected statement back in the article, but I'm not totally sure it belongs in the article now that the center of Napoleon's triangle does not coincide with the Fermat point. So, I leave it up to you. -- Jitse Niesen (talk) 05:34, 16 April 2007 (UTC)

You're quite right - the statement doesn't belong here so I think it is best omitted! MRFS 19:02, 18 April 2007 (UTC)

[edit] BEC??

What the hell is BEC? E is never mentioned...