I was trying to prove for myself the assertion that the locus of the incenter over all triangles with given Euler segment is the interior of the...
946
xpolakis@...
Jun 2, 2000 5:50 am
... I H M G IH^2 + IG^2 = 2IM^2 + (HG^2)/2 Median Theorem Now, IH^2 = 2r^2 + 4R^2 - (a^2 + b^2 + c^2)/2 [Panakis 169,90] IG^2...
947
Lambrou Michael
lambrou@...
Jun 2, 2000 8:39 am
... It seems vectors can do the jog without too much trouble (but I confess I did not do the dirty work to the last line): square of IM = inner product of (...
948
xpolakis@...
Jun 2, 2000 1:23 pm
Dear Michael, Did you know that ANTIPELARGESIS of Kosmas Balanos (1816) will be auctioned in Vergos' auction on next Monday, June, 5? Estimated Price? Well.......
949
Paul Yiu
yiu@...
Jun 2, 2000 2:41 pm
Dear John, The squared distance between the incenter I and the center of the orthocentroidal circle (midpoint of GH) is, in terms of a, b, c: the cyclic sum ...
950
Paul Yiu
yiu@...
Jun 2, 2000 2:46 pm
At 08:22 PM 6/1/00 -0400, you wrote: ... I think this is addressed in Guinand's 1984 Monthly paper. I do not have the Monthly issue in front of me. If I...
951
Paul Yiu
yiu@...
Jun 2, 2000 6:34 pm
Dear John, ... Let I be a point in the interior of the circle with diameter GH, distinct from the point N which divides GH in the ratio GN : NH = 1 : 3. Let O...
952
John Conway
conway@...
Jun 3, 2000 5:38 pm
On Fri, 2 Jun 2000, Paul Yiu wrote: [in answer to my query about the locus of the excenter] ... If this is true, it explains why I was having such a hard time ...
953
John Conway
conway@...
Jun 3, 2000 7:43 pm
... In my view, N really belongs to this set, being the limit that I tends to as the triangle approaches equilaterality. ... Interesting! But can it be...
954
John Conway
conway@...
Jun 4, 2000 3:58 pm
Yesterday I asked a number of questions, most of which I've since been able to solve. First, the loci of the points L,G,D,N,H,No.Ko for all triangles with...
955
Lambrou Michael
lambrou@...
Jun 4, 2000 6:38 pm
Dear Antreas ... Yes, I got the catalogue a few days ago ( I subscribe) and I found out.It is the second time in a short span that this marvelous and rare book...
956
Paul Yiu
yiu@...
Jun 5, 2000 2:00 pm
Dear Jean - Pierre, [Continuing] (1) The nine-point circle and the circumcircle of cev($V$) intersect at $U$ and $V$. Similarly those of cev($V'$) intersect...
957
Paul Yiu
yiu@...
Jun 5, 2000 2:00 pm
Dear Jean-Pierre, [A pdf version of this letter (with diagrams) can be found at http://www.math.fau.edu/yiu/JPE000603.pdf I am breaking the letter into two...
958
Paul Yiu
yiu@...
Jun 5, 2000 3:08 pm
Dear John, ... Yes. ... involves the solution of a cubic, Euler did consider the problem of constructing a triangle with given O, H, and I. He worked out a...
959
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Jun 5, 2000 4:31 pm
... De : "Paul Yiu" <yiu@...> À : <Jean-Pierre.EHRMANN@...> Cc : <Hyacinthos@egroups.com> Envoyé : lundi 5 juin 2000 16:00 Objet : [EMHL] Cevian...
960
xpolakis@...
Jun 5, 2000 5:53 pm
In this remarkable List of Journals that have Mathematical Problem Columns http://www.mathpropress.com/problemJournals.html are listed many journals, and among...
961
Paul Yiu
yiu@...
Jun 5, 2000 7:40 pm
Dear John, ... I think in this limiting case, the triangle is isosceles with a vertex at infinity. Best regards. Sincerely, Paul...
962
xpolakis@...
Jun 5, 2000 7:41 pm
ID Number: A014498 Sequence: 1,2,3,3,6,5,4,10,5,12,7,15,14,6,15,20,9,21,7,18,28,11,8,21, 30,35,22,9,36,24,35,13,42,33,45,10,26,40,44,15,39,11,30,45, ...
963
John Conway
conway@...
Jun 5, 2000 9:48 pm
... What happens is this: if we rescale and reorient all our triangles so that all their Euler segments OH coincide, then as they get closer and closer to...
964
F.Gremmen
F.Gremmen@...
Jun 6, 2000 9:40 am
... Dear Jean Pierre and all, Let O be the centre of the circumcircle of ABC. V and W are the common points of the circumcircle and the 9pt circle. V is the...
965
Floor van Lamoen
f.v.lamoen@...
Jun 6, 2000 1:32 pm
Dear Frans, Jean-Pierre, Paul and Hyacinthians, Frans describes the transformation that brings the Cevian triangle of O - the medial triangle - to the Cevian...
966
Dick Tahta
d.tahta@...
Jun 6, 2000 4:23 pm
John Conway recently found that Io meets the Euler line at E(p) where 2/7<p<1/3. For what it is worth I have slogged out the exact value using complex...
967
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Jun 6, 2000 5:24 pm
... De : "F.Gremmen" <F.Gremmen@...> À : <Hyacinthos@egroups.com> Envoyé : mardi 6 juin 2000 11:40 Objet : [EMHL] Re: Cevian triangles similar to...
968
John Conway
conway@...
Jun 6, 2000 7:33 pm
... If you'd looked at the argument I gave, Dick, you'd've seen that this was how I found it: 2/7 and 1/3 are just lower and upper bounds for the above...
969
xpolakis@...
Jun 6, 2000 9:02 pm
... Someone asked me what Conway's extraversion is. In my understanding, it is a metatheorem: When you come across a theorem on the incircle/incenter/angle...
970
John Conway
conway@...
Jun 6, 2000 11:38 pm
... An "expectation" wouldn't deserve to be called either a "theorem" or a "metatheorem". "Extraversion" is my name for the study of what happens to theorems...
971
Floor van Lamoen
f.v.lamoen@...
Jun 7, 2000 6:40 am
Dear Jean-Pierre et al, ... I don't see this? Is there a center of similitude in all cases? ... Let me be more clear on the Miquel connection, although I...
972
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Jun 7, 2000 10:05 am
Dear Paul Floor, Frans and other Hyacinthists, a remark about the Cevian triangle similar to ABC - but not in the same order -. Any Tucker circle C(t)...
973
Dick Tahta
d.tahta@...
Jun 7, 2000 12:38 pm
... Yes, that was clumsy of me. I was rather tickled by the way the complex number treatment worked out, though of course much more brutishly than ...
974
John Conway
conway@...
Jun 7, 2000 2:23 pm
... I like "Enclave", but probably won't use it here because it doesn't give a nice term for its center. The best plan I've come up with so far is to call the...
