Let ABC be a triangle and A'B'C' the cevian triangle of I. In an old discussion we have seen that the reflections of AA' in B'C', BB' in C'A' and CC' in A'B'...
Dear Paul ... Hope that in the following, the answer will not be "they are not" :-) Denote La, Lb, Lc the above reflections of B'C' in AA', C'A' in BB', A'B'...
Let ABC be a triangle and A'B'C' its orthic triangle. The reflection of B'C' in AA' intersects AC,AB at Ac,Ab, resp. Let Na be the Nine Point Circle Center of...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/FG200517index.html The editors, Forum...
ForumGeom
ForumGeom@...
Sep 2, 2005 5:41 pm
11512
... We don't need this difference ! We need the differences of the angles (AAbAc) - A and (AAcAb) - A ... In fact, by applying the theorem we get: sin(BANa) /...
To Jean-Louis Ayme and all at Hyacinthos Please forgive the last abortive post. It is almost two years since the original post, but there is something to add ...
[APH] ... Let's see some variations Let ABC be a triangle, and A*B*C*, A'B'C', and A"B"C" its orthic, medial and antimedial triangles, resp. The reflection of...
We have a resource unknown to older geometers, the collections of geometric objects that are being compiled by Kimberling and others. With all this information...
Dear Jean-Pierre and all, Let a,b,c,p,q be the complex affixes of the reference triangle A,B,C and points P and Q respectively. In Mathematica, write p=P; ...
One way to look at the thousands of Kimberling X points is to look negatively, to look for what is not there. Last year at this time John and I had just...
In Mineur's book on cubics the barycentric operation : y : -> : z + x : is called the "complementaire." The trilinear operation : y : -> : z + x : is...
Dear Steve, Could I maybe get a copy of the material of "Mineur." OSU-Tulsa has an inter-library loan thing going. Thanks, Jeff ... operation ... comments...
... z ... operation ... comments ... Dear Steve, Although not one of the wise geometers, I thought that I might make a few comments on this. Oddly enough, a...
Jeff, I am translating it on my site. It is a copy of a handwritten monograph I found in the very old books at Princeton. It had never been checked out and I...
Wilson, Yours was the perfect response to feed my ideas. Thanks ... I am inordinately fond of the P^2 point. Now a question I have hits to the nature of...
... Wison, I have this conic before as the 9 point conic ... Mineur calls this the 9 pt conic Here is his description. ... When the point P describes the line ...
... complement of ... (Y)..... ... Rephrasing Mineur's description : the nine point conic of D is the locus of centres of circumconics with perspector on T(D)...
Let ABC be a triangle, P a point, PaPbPc the pedal triangle of P. Na := The Nine Point Circle Center of APbPc. Nb := The Nine Point Circle Center of BPcPa. Nc...
[APH] ... Generalization : Let ABC be a triangle, P a point and PaPbPc the pedal triangle of P. Let Q = (cosA - tcosBcosC ::), in trilinears, be a point on the...
Wison, I am still trying to digest your first posting on this. It does some things I have been trying to do, such as find new ways of constructing the...
Let ABC be a triangle and P a point. Which is the locus of P such that the reflections of: PA in BC, PB in CA, and PC in AB, are concurrent? Antreas --...
Dear Antreas I found for locus the cubic with barycentric equation: (b^2+c^2-a^2)x(y^2-z^2) +(c^2 +a^2-b^2)y(z^2-x^2)+(a^2+b^2-c^2)z(x^2-y^2)=0 François...
Dear Antreas and François, ... I find that it looks more like Bernards K060, a^3 y z (b^2 z Cos[B] Sin[3 C]- c^2 y Cos[C] Sin[3 B]) + cyclic = 0 with...
... Now, let A'B'C' be the medial triangle of ABC. Which is the locus of P such that the reflections of: PA in B'C', PB in C'A', and PC in A'B', are...
