Dear Paul, ... Just to small comments: Since the circles passing through A and tangent to BC at B,C, resp., have another intersection A', means that the same...
2692
xpolakis@...
Apr 1, 2001 6:19 pm
Dear Paul, ... Here is my proof: Assume that AC > AB or b > c A /\ / \ / \ / \ / \ K / M | / \ | / Q...
2693
xpolakis@...
Apr 1, 2001 6:29 pm
Let P be a point and P', P" its isogonal, isotomic conjugates, resp. We have six lines: PP', PP", P'P", tripolars of P,P',P", which can form C(6,3) = 20 triads...
2694
Floor van Lamoen
f.v.lamoen@...
Apr 1, 2001 6:58 pm
Dear all, ... This particular example has been discussed in the thread "Don Wallace Locus". Kind regards, Floor....
2695
Dick Tahta
d.tahta@...
Apr 2, 2001 11:19 am
Paul recently asked for a synthetic proof of a neat construction ... ... He mentioned a construction by inversion and I wondered whether this would not also...
2696
Steve Sigur
ssigur@...
Apr 2, 2001 1:18 pm
... Floor is not mentioning that, before Hyacinthos, he also posted (and solved) this in the geometry forum. Steve...
2697
xpolakis@...
Apr 2, 2001 2:56 pm
... [I changed the notation of the points. Similarly we define the points B', C'; B", C"; Pb, Pc] 1. Let Ma, Mb, Mc be the centers of Paul's circles (ie...
2698
xpolakis@...
Apr 3, 2001 11:27 am
Given a systen of cubics passing through the six corners of a quadrilateral and through another fixed point O, prove that all those that touch a given line...
2699
Wilson Stothers
wws@...
Apr 5, 2001 9:29 am
... You can add to the list the Theroems of Ceva and Menelaus (well, the definition of ratio needs attention). In fact the above results are all related to the...
2700
Ignacio Larrosa Ca...
ignacio.larrosa@...
Apr 5, 2001 10:15 am
Jules Finoulst (a belgician?) post the following message in the newsgroup es.ciencia.matematicas, in italian! I suppose thjat it is known for the most of you. ...
2701
Paul Yiu
yiu@...
Apr 5, 2001 6:10 pm
Dear Ignacio and Jules, I do not have [TCCT] in front of me. Very likely the perspectivity of the tangential triangle and the circumcevian point of P is there....
2702
Alexander Bogomolny
alexb@...
Apr 7, 2001 2:36 am
Dear Richard and Hyacinthians: ... There is a curious observation. The demonstration is dynamic, whereas the result, the Lighthouse theorem, is static. It then...
2703
Richard Guy
rkg@...
Apr 7, 2001 2:34 pm
Hyacinthians not on the math-fun list may be amused by this bit of oddball triangle geometry, especially the 3,4,5 clock. R. ... Date: Sat, 7 Apr 2001...
2704
yiu@...
Apr 7, 2001 7:51 pm
Dear Richard and friends, I do not know if I interpret correctly; but it seems to me that a reasonable clock pivot P point is one such that angle BPC : angle...
2705
yiu@...
Apr 7, 2001 8:20 pm
Dear Richard and friends, [PY]: I do not know if I interpret correctly; but it seems to me that a reasonable clock pivot P point is one such that angle BPC :...
2706
yiu@...
Apr 7, 2001 8:52 pm
Dear Richard and friends, [PY](2704): I do not know if I interpret correctly; but it seems to me that a reasonable clock pivot P point is one such that angle...
2707
yiu@...
Apr 7, 2001 9:05 pm
Dear Richard and friends, ... Of course it is nonsense to throw in the isodynamic point!!! Best regards Sincerely, Paul and the point ... get ... the ... get ...
2708
yiu@...
Apr 7, 2001 11:38 pm
Dear Richard and friends, This is a correction for the coordinates of the clock pivot point in message 2704. Given triangle ABC, let P be the point such that ...
2709
yiu@...
Apr 7, 2001 11:49 pm
Dear Richard and friends, (2708): Given triangle ABC, let P be the point such that angle BPC : angle CPA : angle APB = a : b : c. The homogenous barycentric...
2710
Paul Yiu
yiu@...
Apr 9, 2001 9:35 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2001volume1/FG200109index.html The Editors Forum...
2711
Barry Wolk
wolkb@...
Apr 10, 2001 8:56 pm
... And this generalizes to angle ratios that are not related to triangle ABC. Given X, Y, Z with X+Y+Z = 2 Pi, let P be the point such that angle BPC = X,...
2712
Lambrou Michael
lambrou@...
Apr 11, 2001 4:33 pm
After some time I return to a thread we had concerning three dimensional proofs of two dimensional results. Thank you all for the marvelous examples. In...
2713
Richard Guy
rkg@...
Apr 11, 2001 5:00 pm
Are there two ells in `calissons' ? I'd like to know, `cos we're putting them in The Inquisitive Problem Solver than Loren Larson & I are writing. They are...
2714
Lambrou Michael
lambrou@...
Apr 11, 2001 5:55 pm
Dear Richard, regards ... It is one ell. Sorry. ... I will ask my French friends to bring me some. ... Right. Sorry for my typo. ... Unfortunately I don't have...
2715
Richard Guy
rkg@...
Apr 11, 2001 6:51 pm
From the 1994 Crux, I've located the references. The `proof without words' is due to Guy David \& Carlos Tomei, The problem of the calissons, {\it Amer.\...
2716
Alexander Bogomolny
alexb@...
Apr 12, 2001 3:02 pm
... Dear Michael, thank you. I found it in Nelsen's book on page 142. It's by Guy David and Carlos Tomei (Monthly, v 95, n 5 (May 1989), pp 429-430.) All the...
2717
Richard Guy
rkg@...
Apr 13, 2001 5:10 pm
There's even more to the Lighthouse theorem than I at first suspected, and I'll say more about it when it's better organized. Meanwhile One of various...
2718
Richard Guy
rkg@...
Apr 13, 2001 5:40 pm
In a recent message, for `sequence', read `cycle'. R....
2719
Steve Sigur
ssigur@...
Apr 16, 2001 4:10 am
Antreas, I thought these were results interesting and as they floated by, I noted them for future reference. I am making pictures of these which I will post...
2720
Bernard Gibert
b.gibert@...
Apr 17, 2001 11:06 am
Dear Antreas and Steve, ... This is only a special case of the more general theorem : If W (p,q,r) is the pole of the isoconjugation P(x,y,z) ---->...
