... De : "Steve Sigur" <ssigur@...> À : <Hyacinthos@onelist.com> Envoyé : mardi 1 février 2000 05:53 Objet : Re: [EMHL] More on the Jerabek points ...
274
Bernard Gibert
b.gibert@...
Feb 1, 2000 2:48 pm
Dear Antreas and all, ... well, Antreas, this is a very relaxing and easy one but it is fondamental in constructive geometry with conics. Let's name d the line...
275
Floor van Lamoen
f.v.lamoen@...
Feb 1, 2000 3:16 pm
Dear Paul, and all, Yesterday I wrote: <...> ... Well, in fact I did, but I hesitated a bit. The surprising result I got was that the perspector/radical center...
276
Richard Guy
rkg@...
Feb 1, 2000 4:06 pm
If you're doing projective geometry, what's a parallel line? R....
277
Bernard Gibert
b.gibert@...
Feb 1, 2000 4:27 pm
... Let me quote Luigi Cremona (elements of projective geometry, p.5) [begin quote] Two parallel straight lines have the same point at infinity. [end quote] ...
278
Antreas P. Hatzipolakis
xpolakis@...
Feb 1, 2000 7:37 pm
... We have: sin(A/2)sin(3B/2)sin(3C/2) :: = sin(A/2)*[3sin(B/2) - 4sin^2(B/2)]*[3sin(C/2) - 4sin^2(C/2)] :: = (3 - 4sin(B/2))*(3 - 4sin(C/2)) :: Can it be...
279
Paul Yiu
yiu@...
Feb 1, 2000 8:37 pm
Dear Anteas, This perspector of I_1I_2I_3 and ABC is the point X_{79} in Kimberling's list. As such, its TRILINEAR coordinates can be written as 1/(1+2cos A) :...
280
Paul Yiu
yiu@...
Feb 1, 2000 9:17 pm
... From: Paul Yiu[SMTP:yiu@...] Sent: Tuesday, February 01, 2000 4:12 PM To: 'xpolakis@...' Cc: 'Hyancinthos@onelist.com' Subject: Altimedial...
281
Antreas P. Hatzipolakis
xpolakis@...
Feb 1, 2000 9:47 pm
Dear Paul, ... Thanks.. (Clark also pointed out that this point is X(79) in his list) ... Yes it is wonderful. Furthermore, a common chord (r. axis) of any two...
282
Antreas P. Hatzipolakis
xpolakis@...
(Date unavailable)
Dear Ken, You wrote (in MHL on Mon, 31 Jan 2000): [...] ... Let me comment something on Aristotle and Triangle Geometry: The triangle circles named after...
283
Paul Yiu
yiu@...
Feb 2, 2000 12:28 am
Dear Floor and Antreas, From Floor's message: <quote> Construct the circle tangent to the circumcircle in a vertex and tangent to the triangle side opposite to...
284
Antreas P. Hatzipolakis
xpolakis@...
(Date unavailable)
Dear Floor and Paul, The circles with diameters the sides of ABC (in Floor's "a nice little problem") have another property: Let ABC be a triangle and...
285
Richard Guy
rkg@...
Feb 2, 2000 3:48 pm
Perhaps my reaction should be: Least said, soonest mended, or Fools rush in where angels fear to tread, but I feel compelled to answer, in case Antreas...
286
Antreas P. Hatzipolakis
xpolakis@...
(Date unavailable)
May I ask my friends Bernard and Richard (in alphabetical order :-) to not continue that unpleasant discussion? Greetings from Athens Antreas...
287
John Conway
conway@...
Feb 2, 2000 7:06 pm
... I wanted to say something about this. I'm not at all sure what Richard said that upset Bernard, but I very much doubt that he had any intention of doing...
288
Antreas P. Hatzipolakis
xpolakis@...
(Date unavailable)
There is an old (?) theorem whose I don't know the origin: If three congruent circles meet at a point P, and each one is inscribed in an angle of a triangle...
289
John Conway
conway@...
Feb 2, 2000 9:09 pm
... Did you check this again? I did, and don't think it works. ... On thinking about it, I realised that you probably meant "the altitudes inverted in the...
290
John Conway
conway@...
Feb 2, 2000 9:23 pm
... This makes it either the proNagel or proGergonne point - I forget which. If Steve hasn't already done so, I should acquaint the group with the properties...
291
John Conway
conway@...
Feb 2, 2000 9:23 pm
... This makes it either the proNagel or proGergonne point - I forget which. If Steve hasn't already done so, I should acquaint the group with the properties...
292
Floor van Lamoen
f.v.lamoen@...
Feb 2, 2000 9:57 pm
Dear Paul and Antreas, On 31 Jan 2000 Paul mentioned your work on triads of triangles, after my message on mixtilinear circumcircles. Among a lot more Paul...
293
Paul Yiu
yiu@...
Feb 2, 2000 11:04 pm
Dear Floor, ... From: Floor van Lamoen[SMTP:f.v.lamoen@...] Reply To: Hyacinthos@onelist.com Sent: Wednesday, February 02, 2000 4:57 PM To:...
294
Antreas P. Hatzipolakis
xpolakis@...
(Date unavailable)
Two points on the Euler line: Tangents are drawn to the nine-point circle of a triangle at the points where it is touched by the in- and ex-circles. Prove that...
295
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Feb 3, 2000 1:23 pm
... De : "Bernard Gibert" <b.gibert@...> À : <Hyacinthos@onelist.com> Envoyé : vendredi 28 janvier 2000 00:13 Objet : Re: [EMHL] A nice little problem ...
296
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Feb 3, 2000 1:56 pm
... De : "Jean-Pierre.EHRMANN" <Jean-Pierre.EHRMANN@...> À : "Hyacinthe" <Hyacinthos@onelist.com> Envoyé : jeudi 3 février 2000 14:23 Objet : Re:...
297
Paul Yiu
yiu@...
Feb 3, 2000 2:18 pm
Dear Antreas, Just a paraphrase: The Newton line of the Feuerbach quadrilateral coincides with the Euler line. Can you provide a more exact reference? Best...
298
Floor van Lamoen
f.v.lamoen@...
Feb 3, 2000 3:57 pm
Dear Paul, ... Nice to see that the problem has been studied by Clark and Peter Yff. Has the solution been published already? ... The tangents in A_2 to the...
299
Paul Yiu
yiu@...
Feb 3, 2000 4:16 pm
Dear Floor, ... From: Floor van Lamoen[SMTP:f.v.lamoen@...] Reply To: Hyacinthos@onelist.com Sent: Thursday, February 03, 2000 10:57 AM To:...
300
Clark Kimberling
ck6@...
Feb 3, 2000 5:17 pm
"Encyclopedia of Triangle Centers - ETC" is now accessible at http://cedar.evansville.edu/~ck6/encyclopedia . I sincerely thank many HTML correspondents for...
301
Antreas P. Hatzipolakis
xpolakis@...
(Date unavailable)
... Dear Paul, So the points are three. The problem was proposed in the _Educational Times_ by W.F. Beard. The exact reference is: Mathematical Questions and...
302
Bernard Gibert
b.gibert@...
Feb 3, 2000 6:38 pm
... Dear John and all, I checked this again and I did not see any flaw in my proof, but I want to stay humble just in case... Let's see : I will use Clark's...
