Dear Hyacynthians, looking for variations of the Van Lamoen-Grinberg-Wolk-transform I discovered the following properties: Consider a point P and a triangle...
7222
Darij Grinberg
darij_grinberg
Jun 1, 2003 4:36 pm
... It seems that the line joining these points touches the common inscribed conic of the two triangles (i. e., the conic centered at the center of symmetry...
7223
Darij Grinberg
darij_grinberg
Jun 2, 2003 5:16 am
Dear Eric Danneels, ... Do you have a synthetic proof? The property was established by Paul Yiu with barycentrics in Hyacinthos message #3957, but I think that...
7224
Darij Grinberg
darij_grinberg
Jun 2, 2003 5:55 am
... Barry Wolk has pointed out that it doesn't. Also, it doesn't lie on the Brocard axis. I have just noted that if Ma, Mb, Mc are the midpoints of BaCa, CbAb,...
7225
Darij Grinberg
darij_grinberg
Jun 2, 2003 11:00 am
... More is true. If X, Y, Z are the midpoints of AbAc, BcBa, CaCb, respectively, then it is well-known that the lines AX, BY, CZ concur at the Longchamps...
7226
jpehrmfr
Jun 2, 2003 3:42 pm
Dear Eric and Darij, ... I think that these points S and T have been discussed on Hyacinthos : If P* = isogonal conjugate of P S is the isogonal conjugate of...
7227
ForumGeom
ForumGeom@...
Jun 2, 2003 3:46 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2003volume3/FG200313index.html The Editors, Forum...
7228
Alexey.A.Zaslavsky
zasl@...
Jun 4, 2003 9:12 am
->>> Let the triangles ABC and A'B'C' are centrjsymmetric. ... I have a proof. It is sufficiently to proof next fact. Let l is the line touching the inscribed...
7229
Darij Grinberg
darij_grinberg
Jun 4, 2003 3:08 pm
Dear Hyacinthians, Given triangle ABC, how many points P are there so that BA' * A'C = CB' * B'A = AC' * C'B, where A'B'C' is the cevian triangle of P ? ...
7230
Darij Grinberg
darij_grinberg
Jun 4, 2003 3:17 pm
Dear Hyacinthians, ... Namely, of the cubics (z+x)²y / b² = (x+y)²z / c², (x+y)²z / c² = (y+z)²x / a², (y+z)²x / a² = (z+x)²y / b². Each of these...
7231
Bernard Gibert
bernardgibert
Jun 4, 2003 4:56 pm
Dear Darij, ... your cubics are what I call isotomic cK cubics ie conico-pivotal isocubics. they have a singularity at one vertex of the antimedial triangle. ...
7232
Darij Grinberg
darij_grinberg
Jun 4, 2003 7:52 pm
dear Bernard, ... thanks very much for these properties. i guess the points are not ruler-and-compass constructible. is there an easy method to see if the...
7233
jpehrmfr
Jun 4, 2003 10:27 pm
Dear Darij ... There exist three lines tangent to the inscribed parabola with focus the Steiner point such as your 6 points form the three pairs of points...
7234
jpehrmfr
Jun 5, 2003 10:45 am
Dear Darij ... Here a possible conic construction of your points : Consider the isotomic conjugates of the common points - apart K - of Stammler hyperbola and...
7235
Darij Grinberg
darij_grinberg
Jun 5, 2003 3:18 pm
Dear Jean-Pierre Ehrmann, ... Aha. And the pair of isotomic conjugates on a given line is constructed as the intersections of the line with its isotomic...
7236
Sergei Markelov
sergeimarkelov
Jun 5, 2003 6:02 pm
Dear Jean-Pierre, Nikos, Paul and all Hyacinthos! In the October of 2002 we discussed the problem in subject. ... I have found this Euler's 200 years old paper...
7237
jpehrmfr
Jun 6, 2003 8:13 am
Dear Darij, Consider a point P = p:q:r (in barycentrics) and suppose that M = x:y:z and the isotomic conjugate of M lie on the line px+qy+rz=0, ie that...
7238
Darij Grinberg
darij_grinberg
Jun 6, 2003 10:49 am
Dear friends, especially Floor, Antreas and Paul who have made so interesting investigations concerning the squares-on-the-sides configuration, I have found...
7239
Darij Grinberg
darij_grinberg
Jun 6, 2003 11:05 am
Dear Jean-Pierre, ... ... I didn't. I also don't know of any special name for this circle, but it is coaxal with the circumcircle and the Parry circle (the...
7240
Darij Grinberg
darij_grinberg
Jun 7, 2003 6:02 pm
The paper "Harcourt's Theorem" by Nikolaos Dergiades and Juan Carlos Salazar in Forum Geometricorum 3 (2003), pages 117-124, reminded me of the extangents...
7241
Dick Klingens
dklingens
Jun 7, 2003 8:11 pm
Dear all, I would like to know the date of birth and the date death of Antoine Gob He was a teacher in Hasselt (Belgium) and published with J. Neuberg a paper ...
7242
Antreas P. Hatzipolakis
xpolakis
Jun 7, 2003 8:26 pm
... An article with a reference to that paper is available online in pdf format: Francis E. Greulich: The Barycentric Coordinates Solution to the Optimal Road...
7243
Darij Grinberg
darij_grinberg
Jun 8, 2003 5:06 pm
I have extended two results of Victor Thébault presented by Antreas P. Hatzipolakis in Hyacinthos messages #1102 and #1551. What came out was a very...
7245
Darij Grinberg
darij_grinberg
Jun 11, 2003 11:51 am
In the following, I am going to establish some results of Alexei Myakishev, Jean-Pierre Ehrmann and me in Hyacinthos messages #6338, #6339, #6340, #6341,...
7246
Nikolaos Dergiades
ndergiades
Jun 11, 2003 1:06 pm
Dear Darig Grinberg, perhaps you may find the following proof not very complicated. The circles (c1) (B*, B*B) and (c2) (C*, C*C) pass through A and are...
7247
jpehrmfr
Jun 11, 2003 3:44 pm
Dear Hyacinthists, here is a little problem. A'B'C' is the orthic triangle of ABC. Consider three points U,V,W respectively on the half lines AA', BB', CC'...
7248
Darij Grinberg
darij_grinberg
Jun 11, 2003 5:04 pm
Dear Nikolaos Dergiades, Thank you very much - a nice proof. ... Please don't call me by the surname. I am a school student and try to write as politely as...
7249
Darij Grinberg
darij_grinberg
Jun 12, 2003 4:24 pm
On the sides BC, CA, AB of a triangle ABC, erect similar isosceles triangles BA'C, CB'A, AC'B, with equal base angles angle A'BC = angle A'CB = angle B'CA =...
7250
John Conway
conway@...
Jun 12, 2003 4:52 pm
... Yes, at least to me. It's much more general than the Kiepert situation. Erect what I call (alpha,beta,gamma)-Napoleons on the edges, namely triangles...
7251
Darij Grinberg
darij_grinberg
Jun 12, 2003 6:30 pm
Dear John Conway, I am very glad to see you posting at Hyacinthos again! Thanks for the reply. ... A little historical digression. I think this is what you and...
