Hello all Hyacinthers, On Tue, 24 Dec 2002 08:30:53 -0000, "Darij Grinberg <darij_grinberg@...>" ... It was a problem in the Monthly 105/1/jan 1998 problem...
6210
Bernard Gibert
bernardgibert
Dec 26, 2002 11:39 am
Dear Nikos, ... [ND] ... Your locus is the pivotal cubic I call Kn and the locus of the perspector is the Neuberg cubic. X265 is the pivot of Kn. Kn is the...
6211
Bernard Gibert
bernardgibert
Dec 26, 2002 11:39 am
Dear Darij, in your proof, you seem to consider that the conic is a circle. This is a very old problem. I had found something more projective based on the fact...
6212
Bernard Gibert
bernardgibert
Dec 26, 2002 11:39 am
Dear Nikos, ... For informations on conics (and many other things), have a look to the very nice site : http://www.cabri.net/abracadabri/ Best regards Bernard...
6213
Nikolaos Dergiades
ndergiades
Dec 26, 2002 12:12 pm
Dear Bernard, Thank you very much for your solution of the locus and these informations. Best regards Nikos Dergiades ... look to the very...
6214
Darij Grinberg <da...
darij_grinberg
Dec 26, 2002 5:21 pm
Dear Bernard Gibert, ... This comment was true, since I am always working with circles instead of conics, but I think the problem was posed for circles,...
6215
Floor en Lyanne van L...
fvlamoenwxs
Dec 27, 2002 4:17 pm
Dear Hyacinthists, Let ABCD be a cyclic quadrilateral. We can form four triangles from the four points. Sometimes there are amusing things: 1. The nine point...
6216
Darij Grinberg <da...
darij_grinberg
Dec 27, 2002 5:25 pm
Did you know the Longhurst point ? In the problem P 108 of Praxis der Mathematik (PM), the Longhurst point L of a triangle ABC is defined. In the concluding...
6217
Darij Grinberg <da...
darij_grinberg
Dec 27, 2002 6:45 pm
Dear Floor van Lamoen, This is a very interesting problem area, and I had treated it in a little note. I attach the zipped PS file EulerQuad.zip and forward it...
6218
Nikolaos Dergiades
ndergiades
Dec 27, 2002 9:54 pm
Dear Hyacinthists, If P is a point on the plane of a triangle ABC, G1,G2,G3 are the centroids of triangles PBC, PCA, PAB and the circumcenter of triangle...
6219
Paul Yiu
yiuatfauedu
Dec 27, 2002 10:07 pm
Dear Nikos, This is the de Longchamps point of triangle ABC, the reflection of the orthocenter in the circumcenter. Best regards Sincerely Paul...
6220
Darij Grinberg <da...
darij_grinberg
Dec 28, 2002 7:44 am
Dear Floor van Lamoen, and all Hyacinthians, See also http://www.pandd.demon.nl/koordenvierh.htm For example Stelling 6: The incenters of triangles ABC, BCD,...
6221
Darij Grinberg <da...
darij_grinberg
Dec 28, 2002 11:35 pm
Triangle geometers not only find new separate points, but often also work out strange kinds of conjugates or transformations - here is another one. Start with...
6222
Nikolaos Dergiades
ndergiades
Dec 29, 2002 12:08 am
Dear Floor, Darij and all, [FvL] Let ABCD be a cyclic quadrilateral. We can form four triangles from the four points. Sometimes there are amusing things: 1....
6223
jpehrmfr <jean-pie...
jpehrmfr
Dec 29, 2002 12:14 am
Dear Nikos, ... If P' is the homothetic of P in (G,1/4), as P+B+C = 3Ga and A+B+C+P = 4P', it follows that GaGbGc is homothetic of ABC in (P',-1/3); hence the...
6224
Nikolaos Dergiades
ndergiades
Dec 29, 2002 12:28 am
Dear Paul, [PY] ... reflection of the ... [ND] ... Thanks. You are right. I think it can be generalized as follows: Let P be a point on the plane of a triangle...
6225
Aad Goddijn
aadgoddijn
Dec 30, 2002 2:39 am
Dear Floor, ... Let us start with an easier extra question: 3. Let Ga, Gb, Gc, Gd be the centroids of BCD, ACD, ABD and ABC. GaGbGcGd is homethetic with ABCD...
6226
Aad Goddijn
aadgoddijn
Dec 30, 2002 2:39 am
Dear Floor and Jim, ... Let A* , B*, C* be the intersections of AP with BC, BP with AC, CP with AB. If P is the tripole of your line [A'B'C'] the three...
6227
Darij Grinberg <da...
darij_grinberg
Dec 30, 2002 9:17 am
I have recently proven the following theorem, which makes the antipode of A a particularly relevant point: The c-excircle of a triangle ABC touches the side CA...
6228
Darij Grinberg <da...
darij_grinberg
Dec 30, 2002 9:17 am
Once I had copied a problem of J. Steiner from an old issue of Crelle's Journal. Since this problem might be interesting for the newsgroup (since it contains ...
6229
ForumGeom
ForumGeom@...
Dec 30, 2002 4:27 pm
The following paper has been published in Forum Geometricorum: <http://forumgeom.fau.edu/FG2002volume2/FG200223index.htm>Wilfred Reyes, An application of...
6230
Sharygin I. F.
sharygin@...
Dec 30, 2002 6:44 pm
Happy New year! Good Geometry! Igor Sharygin...
6231
RICARDO BARROSO CAMPOS
rbarroso@...
Dec 30, 2002 7:58 pm
A todos: To everyone: Feliz 2003... Happy year 2003 A perimeter-bisecting segment of a triangle originating from the midpoint of one side is a cleaver. Proove:...
6232
Nikolaos Dergiades
ndergiades
Dec 30, 2002 11:55 pm
Dear Ricardo, ... from the midpoint of one side is a cleaver. ... angle bisector of the triangle ... known as the cleavance center ... Math. Mag. 36, 60-62,...
6233
RICARDO BARROSO CAMPOS
rbarroso@...
Dec 31, 2002 8:06 am
My friends Nik: Perfect!... The geometry is beatiful!!! Happy 2003 Ricardo ... Dear Ricardo, ... from the midpoint of one side is a cleaver. ... angle bisector...
6234
Floor en Lyanne van L...
fvlamoenwxs
Dec 31, 2002 11:16 am
Dear hyacinthists, First of all a happy New Year!! Together with Darij I have lately gone through some stuff with the four triangles that can be formed from a...
6235
jpehrmfr <jean-pie...
jpehrmfr
Dec 31, 2002 11:40 am
Dear Floor and other Hyacinthists ... Happy 2003 to all of you!! ... four ... if not ... night ... and ... Your locus is obviously the locus of the focii of...
6236
Gilles Boutte
g_bouttefr
Dec 31, 2002 6:15 pm
Dear Floor ... You give a general description of any circular self-isogonal non-pivotal cubic. Yau can see my paper at...
6237
Darij Grinberg <da...
darij_grinberg
Dec 31, 2002 7:05 pm
Dear friends, Scrolling the archives, I have seen that one subject accompanies our newsgroup the whole time (beginning with Clark Kimberling's message #1): a)...
6238
Nikolaos Dergiades
ndergiades
Dec 31, 2002 11:12 pm
Dear Hyacinthists, Now indeed we entered the new year. HAPPY NEW YEAR to all. To wish to have not a new world war or to wish after all to come soon the day ...
