... [then a mistake, corrected in:] ... ... after which I snipped some stuff that suggests both Steve and Barry are reinventing some wheels. The rows of these...
1152
Barry Wolk
wolkb@...
Aug 2, 2000 10:40 pm
John Conway wrote: [snip some quoted stuff] ... Well, here's what I said a little further down in my message that you partly quoted: (BW)>Steve, I can prove...
1153
John Conway
conway@...
Aug 2, 2000 11:43 pm
... Obviously I shouldn't have said "both Steve and Barry" - sorry! But it seemed a good idea anyway to set the record straight. ... Yes, I noticed this some...
1154
John Conway
conway@...
Aug 3, 2000 3:03 pm
... Just noticed this again. By the cosine formula, cosB = cc+aa-bb/2ca = SB/ca in my notation, so that this points is (:ca/SB:) = (:1/bSB:). Now didn't we...
1155
xpolakis@...
Aug 3, 2000 8:42 pm
Hi John and All, I returned from Crete, and am glad to meet you again! During my vacation in Crete, I visited a remarkable exhibition with black-and-white...
1156
xpolakis@...
Aug 3, 2000 10:08 pm
Clark Kimberling, in his web page on Triangle Geometers, at: http://cedar.evansville.edu/~ck6/bstud/tg.html writes: <q> Among authors often cited books in...
1157
John Conway
conway@...
Aug 4, 2000 2:18 am
I just noticed that I didn't send this message to Hyacinthos, so am copying it to you, since it might be of general interest.JHC...
1158
Bernard Gibert
b.gibert@...
Aug 5, 2000 3:59 pm
Dear all, as I was working on a cubic related to perpendicular polars, I had to use the point with barycentrics (cos 2A, cos 2B, cos 2C) and was very surprised...
1159
Jim Parish
jparish@...
Aug 5, 2000 5:02 pm
... and proceeds to describe other properties of the orthopolar and orthoconjugate. I also have been studying this area. Another construction of the orthopolar...
1160
Floor van Lamoen
f.v.lamoen@...
Aug 6, 2000 10:40 pm
Dear Hyacinthians, I'm back from holidays, where I did not care about triangles to much. But I was reading in Paul's "Euclidean Geometry" about a...
1161
Floor van Lamoen
f.v.lamoen@...
Aug 7, 2000 11:24 am
Dear Hyacinthians again, ... Aha, I have been mistaken. When given a certain hexagon, the construction gives two congruent equilateral triangles, but not ...
1162
xpolakis@...
Aug 7, 2000 5:17 pm
1. Kantor Point The planes passing through the midpoints of the edges of a tetrahedron, and are perpendicular to resp. opposite edges, meet at a point K called...
1163
Ignacio Larrosa Ca...
ilarrosa@...
Aug 7, 2000 5:28 pm
Dear Hyacinthians, the sixth problem of the 41th International Mathematical Olympiad was: 6) Let AH1, BH2, CH3 the altitudes of an acute triangle ABC. The...
1164
Bernard Gibert
b.gibert@...
Aug 7, 2000 6:30 pm
Dear Ignacio and friends, you will find all the informations in different languages concerning the IMO at: http://www.imo.math.ca/ ... I have found a solution...
1165
xpolakis@...
Aug 7, 2000 10:54 pm
<quote> This is a problem I found on PiF's problem page: http://stud4.tuwien.ac.at/~e8825907/raetsel-eng.html Let ABC be a triangle, and let P be a point in...
1166
Floor van Lamoen
f.v.lamoen@...
Aug 8, 2000 7:10 am
Dear Antreas, Yes, this P is X_176 ``the equal detour point'', aka is the center of the inner Soddy circle. Best regards, Floor....
1167
Ignacio Larrosa Ca...
ilarrosa@...
Aug 8, 2000 8:28 am
In any triangle this 'equal detour point' is X(176), thr inner Soddy point. If the triangle have an angle enough obtuse( >2·arcsin(4/5) if the triangle is...
1168
xpolakis@...
Aug 8, 2000 3:47 pm
... Thanks to Floor and Ignacio for their responses. And another question: Which is the locus of the points P (if exist) such that: PA + PB + t*AB = PB + PC +...
1169
xpolakis@...
Aug 8, 2000 4:06 pm
... This is of course the "equal detour point" APH...
1170
John Conway
conway@...
Aug 8, 2000 6:08 pm
... [and lots more interesting stuff]. Bernard - Is your orthopolar line the same as the orthopolar line of the traditional books? This is something I have...
1171
Bernard Gibert
b.gibert@...
Aug 8, 2000 6:51 pm
Dear John and friends, ... [John] ... I have no idea of what the "traditional" orthopolar is: all is my denomination. Can you please tell me ? I have not even...
1172
xpolakis@...
Aug 8, 2000 8:28 pm
A make a quick search in Zbl for "orthopolar", and got the following references (but I didn't check out them): Galasekharam, F.H.V.: The orthopolar circle. ...
1173
John Conway
conway@...
Aug 8, 2000 8:40 pm
... No! I accidentally "invented" it - I was thinking of the relation between a line and its (traditional) "orthopole" - as far as I know, there's no...
1174
Paul Yiu
yiu@...
Aug 8, 2000 8:51 pm
Dear friends, Bernard [Hyacinthos message 1129] has asked for the construction of triangles with orthocenter lying on the Lemoine axis. To this, Antreas...
1175
Jim Parish
jparish@...
Aug 8, 2000 8:55 pm
... In my work, I've been using the following ad hoc nomenclature: lines through P orthogonal to PA, PB, PC: orthocevians (of P) intersections of orthocevians...
1176
xpolakis@...
Aug 9, 2000 6:33 am
Let ABC be a triangle, and AaBaCa the pedal triangle of the point Pa such that: PaBa = PaCa, PaAa/PaBa = t (:given) [Comment: Pa lies on the internal bisector...
1177
Atul Dixit
atul_dixie@...
Aug 9, 2000 9:25 am
Respected Sir, My name is Atul.A.Dixit and yesterday only I became the member of your group,and today when I opened my account,I was surprised to see a deluge...
1178
Bernard Gibert
b.gibert@...
Aug 9, 2000 10:43 am
Dear Jim, John and all, ... I do not mind at all to change my denominations : they were temporary and maybe a bit clumsy because there is no polarity...
1179
Bernard Gibert
b.gibert@...
Aug 9, 2000 3:55 pm
... it is not the Parry circle but the circle through the Parry point X111 (and G). Sorry best regards Bernard...
1180
xpolakis@...
Aug 9, 2000 5:05 pm
JHC's biography can be found in the St. Andrews Archive (the well-known archive of mathematicians' biographies). The URL is: ...
