Dear Francisco, I can follow your reasoning and it looks like you are quite right. So that's why I constructed your way and my way together. After doing this I...
Sorry, Jeff. I draw tour sketch and I don't see your lines are parallell but maybe I don't understand your strange notations. Better is you send me your own...
Let ABC be a triangle, P a point on the Euler line of ABC, and Pa,Pb,Pc the P-points of PBC,PCA,PAB, resp. (If, for example, P = O of ABC, then Oa,Ob,Oc are...
Dear Francisco. I understand what you are saying. It is an interesting question. Everything is allright for me. Except for your statement "The line PQR here is...
[APH] ... Let's call this line as L(ABC). A natural question is: Which is the locus of point Q such that the lines L(QBC), L(QCA), L(QAB) are concurrent? APH...
We have recently finished writing up a several year project in geometry titled "Synthetic Cevian Geometry". Starting from work of Grinberg, Ehrmann, and Yiu...
Dear Igor If I understand you, you give the affine plane a metric structure, in order to P would be the Gergonne point, P' the Nagel point and Q the center ...
Dear Francois, We work in the extended Euclidean plane, and use Euclidean, affine, and projective arguments. If we understand your question correctly, you are...
Dear Igor and Dear Patrick I was only joking for I knew that point P was allowed to go everywhere it could inside as well outside the reference triangle ABC. ...
Dear Cosmin and Hyacinthists, following the article of Léon Bankoff, an article with the "same" title appears on my website : http://perso.orange.fr/jl.ayme...
More Concurrent circles: Let ABC be a triangle and P a point. Denote: La,Lb,Lc := the cevian lines of P. Lbc := the Reflection of Lb in Lc Mbc := the parallel...
Dear All My Friends, It is well-known some following properties of pedal triangle A'B'C' of P wrt reference triangle ABC: 1. ABC and A'B'C' are orthologic with...
Dear Quang Tuan Bui [QBT] ... There is nothing new : an inscribed triangle orthologic with ABC is obviously allways a pedal triangle (of an orthologic center) ...
Let ABC be a triangle, P a point and A'B'C' the cevian triangle of P. The perpendiculars from A to BB',CC' intersect BC at Ab,Ac, resp. The perpendiculars from...
Let ABC be a triangle, A'B'C' the cevian triangle of the incenter I, and MaMbMc the medial triangle of ABC. Denote: Ab,Ac := The intersections of MbMc with...
Be careful, Jeff, strains and shears are not the "same" affine map, that is to say a strain and a shear are not conjugate in the affine group. A strain can be...
Dear Francois, Thank you very much. Somebody really should add that reference to Wikipedia: http://en.wikipedia.org/wiki/Affine_transformation Sincerely, Jeff...
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the Hyacinthos group. File : /groupe...
Hyacinthos@yahoogroup...
Mar 9, 2009 9:00 am
17346
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2009volume9/FG200904index.html The editors Forum...
ForumGeom
ForumGeom@...
Mar 9, 2009 2:49 pm
17347
Can someone please remind me the definition of areal center? Something is not right here; that is I construct the areal center following Quim Castellsaguer's...
Let ABC be a triangle, F the Feuerbach point, F* the antipodal of F on the incircle, and f,f* the tangents to incircle at F,F*, respectively. Which points (on...
[APH] ... [FJ] ... Dear Francisco Thanks. Let's call this line (ie X(106)X(109)) as Feuerbach-Miquel line of the incircle (I). I am wondering if the similar...
[APH] ... [FJ] ... [APH] ... [FJ] ... Dear Francisco Hmmmmm... It seems 3G [= Great God of Geometry] did not make everything perfect in the Euclidean Space...
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