... The conjecture was: Let ABC be a triangle. From A we draw parallels to b- and c- altitudes intersecting the BC at Ba, Ca respectively. Similarly, we define...
63
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 2, 2000 8:10 pm
... Dear Bernard, Neither I am, but JHC has already provided one. This message is about another coordinates Floor once used, namely Bottema's r-coordinates. ...
64
Bernard Gibert
b.gibert@xxxx.xxx
Jan 3, 2000 5:22 am
Dear Antreas and all, ... Those coordinates are called "tripolar coordinates" by Trajan Lalesco (la géométrie du triangle, p.28. excellent small book written...
65
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 3, 2000 8:47 am
... Jacques Gabay Editions: Les Editions Jacques Gabay sont specialisees dans la reedition de grands textes scientifiques concernant principalement les...
66
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 3, 2000 11:14 pm
The coordinates x,y,z being proportional to the perpendicular distances from the sides of a triangle ABC, prove that (1) the locus of a point (x,y,z) such that...
67
Julio Gonzalez Cabillon
jgc@xxxxxx.xxx.xxx
Jan 3, 2000 10:40 pm
... Well... I haven't checked it right now, but that's how I remember it from my mid-teens. Synthetic geometry was (and still is) *very* popular at my ...
68
Floor van Lamoen
f.v.lamoen@xxx.xxx
Jan 4, 2000 2:25 pm
Hi, all, On december 29, 1999, I gave a locus that described Kiepert's hyperbola. Here is another locus variant of Kiepert's hyperbola, for the fun of it!: ...
69
Bernard Gibert
b.gibert@xxxx.xxx
Jan 4, 2000 5:01 pm
Dear Antreas and all, ... there is a whole book to write about this stuff and I just want to make a few comments : 1). this cubic belongs to a family of...
70
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 4, 2000 6:39 pm
... Dear Bernard I have a question about a locus which probably is included in the book above, a book which I heve not seen: Who is the author of this problem...
71
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 4, 2000 7:15 pm
An old discussion on homogeneous coordinate systems, between John H. Conway and Steve Sigur, can be found in the geometry-research archive: ...
72
wolkb@xx.xxxxxxxxx.xx
Jan 4, 2000 7:19 pm
... According to my calculations, no three of those four lines are concurrent. I used Maple to do the messy algebra. Incidentally, onelist.com suppresses email...
73
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 4, 2000 7:37 pm
... Thanks, Barry. Hope that the other conjecture (about the perpendicular bisectors of BaCa, CbAb, AcBc) is true! Antreas...
74
wolkb@xx.xxxxxxxxx.xx
Jan 4, 2000 7:54 pm
on 12/25/99 12:18 PM Bernard Gibert wrote ... Almost all of those collinearities given in 1) can be summarized by: n'* m* n' m n* m'* n m' K...
75
Paul Yiu
yiu@xxx.xxxx
Jan 4, 2000 8:18 pm
Dear Antreas, As Barry just pointed out, these Euler lines do not concur. The same is true for the Brocard axes. However, your original conjecture [Message 3...
76
Paul Yiu
yiu@xxx.xxxx
Jan 4, 2000 9:26 pm
Dear Antreas, I should have remarked a simple geometric property of this intersection of the ``first'' perpendicular bisectors of the orthial triangles. Its...
77
Floor van Lamoen
f.v.lamoen@xxx.xxx
Jan 5, 2000 7:52 am
Dear Antreas, This is exactly Adam Bliss' conjecture of last May! I wish I had seen that problem before!! Kind regards, Floor. Antreas P. Hatzipolakis wrote: ...
80
Floor van Lamoen
f.v.lamoen@xxx.xxx
Jan 5, 2000 10:17 am
Dear Bernard and Antreas, Bernard is quite confident in my knowledge! I am quite sure, Bernard, that you know more than I do. Well, let's see what I manage to...
81
Bernard Gibert
b.gibert@xxxx.xxx
Jan 5, 2000 1:26 pm
... Dear Antreas, Sorry, I don't know the author of your problem and it is not in Collet & Griso unless I did not see it ! This book is a real gold-mine...
82
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 5, 2000 8:54 pm
Dear Floor, ... Some months ago I had discovered something like that! See below a letter from John to Steve. ... ...
83
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 5, 2000 10:14 pm
Find the locus of the centers of the rectangles inscribed in a given triangle ABC, whose (: rectangles) the base lies on BC. [1, p. 540, #464] The locus is the...
84
wolkb@xx.xxxxxxxxx.xx
Jan 5, 2000 11:03 pm
... Perhaps I can preserve your next copy of the NYTimes. Here are the results of some messy calculations. Of course, the computer did all the messy work, but...
85
Floor van Lamoen
f.v.lamoen@xxx.xxx
Jan 6, 2000 2:53 pm
Dear Antreas, ... John Conway's argument is almos the same as the one I had in mind. My idea can clearly be extended to fixed form rectangles, as you, Antreas,...
86
GDear55942@xxx.xxx
Jan 6, 2000 6:51 pm
Dear members, I am pleased to be a recent member of your excellent and well-named group. I have recently discovered a solution to Apollonius' problem of...
87
Bernard Gibert
b.gibert@xxxx.xxx
Jan 6, 2000 10:37 pm
Dear Antreas and Floor, ... I am not sure whether I understand your a-Schwatt lines correctly. Last year, I spent a while on the following problem : ABC a...
88
Floor van Lamoen
f.v.lamoen@xxx.xxx
Jan 7, 2000 9:08 am
... If I understand correctly, the a-Schwatt line is the line joining the midpoint of the altitude from A and the midpoint of side BC. <...> ... I am still not...
89
Floor van Lamoen
f.v.lamoen@xxx.xxx
Jan 7, 2000 9:17 am
Dear Mr. Dearing, I am delighted to see that we can compute the radius of the Appolonian circle of three given circles with a simple tool as Heron's formula...
90
GDear55942@...
Jan 7, 2000 6:25 pm
Dear Floor van Lamoen, Thanks very much for your comments of Fri,07 Jan 2000 10:17:10 I am very pleased that you recognised the nice simplicity of the use of...
91
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 7, 2000 10:05 pm
Dear Floor, ... Yes, that is. ... "conic", "cubic" are almost homophonic (= with same voice), hence your typo. On Loci problems: No point is an "island", so...
92
xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
Jan 7, 2000 10:11 pm
... three (I wrote "four" because the FOUR Euler lines of the triangles ABC, IBC, ICA, IBA concur). Antreas...
93
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@x...
Jan 8, 2000 1:16 am
Antreas wrote in message 1 of Jan 1 : ? Theorem The lines AF_a, BF_b, CF_c are concurrent where the nine-point circle touches the excircles at F_a, F_b, F_c. ...
