Dear Hyacinthists with my best greetings for 2011 for you, your family and your friends, I have a little question : Consider a quadrilateral A_1,A_2,A_3,A_4 ...
19636
Chris Van Tienhoven
chris.vantie...
Jan 1, 2011 2:16 pm
Dear Jean-Pierre, ... I do not know a special name for point M. However I noticed this. Maybe you know it already. Let T(A_1,A_2,A_3,A_4) = Transform...
19637
Antreas Hatzipolakis
xpolakis
Jan 1, 2011 4:59 pm
Dear Jean-Louis Yes, the result is correct. I have a proof but the "margin" is too small to contain it! So I have put it ...
Dear Hyacinthos: I recently showed some of my students the fact that every point F on the circumcircle of a triangle ABC is the focus of a unique parabola that...
19640
jpehrmfr
Jan 2, 2011 8:29 am
Dear Chris [JP] ... [Chris] ... Thank you for your nice remark. In fact, if O_1' is the circumcenter of O_2O_3O_4,..., the same homothecy maps A_i to O_i' and...
19641
Jean-Louis Ayme
jeanlouisayme
Jan 2, 2011 9:49 am
Dear Antreas and Hyacinthists, thank for your mail... For the concurrence, I haven't no doubt... In your message 1663, you say that the point of concurrence...
19642
Lim Sung Hyun
bbblow
Jan 2, 2011 10:14 am
Dear Charles, Now there's this nice property that I discovered, probably done before: Given a circumconic (with perspector P), all the inconic with perspectors...
19643
Lim Sung Hyun
bbblow
Jan 2, 2011 10:33 am
Dear geometers, I'd like to know if there was any previous reference on the following result: Given circumconic with perspector P and arbitrary point Q, take...
19644
Francois Rideau
francoisride...
Jan 2, 2011 3:37 pm
In fact, the locus of the perspector P is the Steiner circumellipse tnat is to say tne circumellipse with center the centroid. Note that the line FP, the join...
19645
jpehrmfr
Jan 2, 2011 5:28 pm
Dear Lim Sung Hyun ... I didn't know your result but I can make some remarks. If Ap,Bp,Cp is the precevian triangle of P, we have 4 pairs of conjugate points...
19646
Chris Van Tienhoven
chris.vantie...
Jan 2, 2011 5:50 pm
Dear Jean-Pierre, ... Thank you for your comments. They helped me to search further. 1. The angular relations can be described some more specific as: Aimj =...
19647
Antreas
xpolakis
Jan 2, 2011 7:42 pm
... This is CLAWSON POINT ... This is wrong. The correct is: in Barycentrics. In trilinears the coordinates are: ((cot(A/2)/cosA ::) ... Obviously 1,1',1" are...
19648
Antreas
xpolakis
Jan 2, 2011 7:45 pm
Dear Jean-Louis It is. I have also posted a follow-up to message #1663 with some corrections. Antreas...
19649
Chris Van Tienhoven
chris.vantie...
Jan 2, 2011 10:47 pm
Dear Jean-Pierre, I am quite thrilled. As always when I find something beautiful. You described a point M depending on the 4 points A1, A2, A3, A4 of a...
19650
Lim Sung Hyun
bbblow
Jan 3, 2011 3:44 am
Dear Jean-Pierre, Thank you for the comment. May I know what you meant by "conjugate point" there? And, do you know any easy proof for the property that I...
19651
Lim Sung Hyun
bbblow
Jan 3, 2011 3:54 am
Dear all, Locus of foci of inconics with perspectors on circumconic seems like a cubic, which is obviously preserved under isogonal conjugation. (Two foci are...
19652
Bernard Gibert
bernardgibert
Jan 3, 2011 6:25 am
Dear Lim Sung Hyun, ... P is the perspector of the circumconic (C). If M lies on (C), the center of the inconic (I) with perspector M lies on a line D which is...
19653
Lim Sung Hyun
bbblow
Jan 3, 2011 7:05 am
Thank you Bernard. I am not very familiar with theory of triangle cubic. May I know how the ... a line D which is the trilinear polar of taP ( isotomic of...
19654
Bernard Gibert
bernardgibert
Jan 3, 2011 7:11 am
Dear Lim Sung Hyun, ... May I suggest you take a look at : http://bernard.gibert.pagesperso-orange.fr/files/isocubics.html Best regards Bernard [Non-text...
19656
jpehrmfr
Jan 3, 2011 5:21 pm
Dear Lim Sung Hyun ... (U,V) are conjugate wrt a conic means that the polar of U goes through V (and the polar of V goes through U) Now, if X lies on the...
19657
Nikolaos Dergiades
ndergiades
Jan 3, 2011 9:23 pm
Dear Hyacinthists, Happy New Year to all of you. I think we must say something beyond mathematics. I don't care about 2012. I think that this year 2011 comes...
19658
Jean-Louis Ayme
jeanlouisayme
Jan 4, 2011 7:43 am
Dear Hyacinthists, ABC a triangle, I the incenter, 1a, 1b, 1c the resp. A, B, C-excercles of ABC, Ia, Ib, Ic the A, B, C-excenters of ABC, 1’a, 1’b, 1’c...
19659
Lim Sung Hyun
bbblow
Jan 4, 2011 7:52 am
Dear Jean-Louis, I am not very sure about my result but my dynamic geometry software seems to answer "no" to your question. Sung Hyun [Non-text portions of...
19660
Francisco Javier
garciacapitan
Jan 4, 2011 8:57 am
Dear Sung Hyun and Jean-Louis, I get that the perspector is X3062=ISOGONAL CONJUGATE OF X165. Best regards, Francisco Javier....
19661
Jean-Louis Ayme
jeanlouisayme
Jan 4, 2011 12:01 pm
Dear Hyacinthists, continuing my research, ABC a triangle, I, the incenter of ABC, (O) the circumcircle of ABC, 1a, 1b, 1c the resp. A, B, C-excercles of ABC,...
19662
Francisco Javier
garciacapitan
Jan 4, 2011 12:27 pm
Not in ETC: {a (a^6 b - 2 a^5 b^2 + a^4 b^3 - a^2 b^5 + 2 a b^6 - b^7 + a^6 c + 2 a^5 b c - 2 a^3 b^3 c + 3 a^2 b^4 c - 4 b^6 c - 2 a^5 c^2 + 4 a^3 b^2 c^2 - 2...
19663
Jean-Louis Ayme
jeanlouisayme
Jan 4, 2011 1:12 pm
Dear Francisco, Clark and Hyacinthists, thank you very much for your help... In consequence, the Clawson's point X19, X3062 (that you have identified) and...
19664
Moses, Peter J. C.
peter_mows
Jan 4, 2011 4:31 pm
Dear Jean-Louis, I reckon your point is on ETC lines {{8, 2893, 2897}, {10, 971}, {19, 3062}, {374, 1903}, {612, 1419}}. Best regards, Peter. [Non-text...
19665
Antreas Hatzipolakis
xpolakis
Jan 4, 2011 5:35 pm
Dear Nikos [ND] ... TI ROMIOSINI MIN TIN KLAIS <http://www.youtube.com/watch?v=vZjtDRVJwdI> ... I think that the following search in ETC would be interesting...
