Dear friends Now I think my "affine construction " of the dual line is false, so forget it but all the rest is still true. PQR and its cofactor triangle beeing...
Let ABC be a triangle, P a point and A'B'C' the pedal triangle of P. AaAbAc := The Orthic Triangle of AB'C' (ie Ab = the Orth. Proj. of B' on AC', Ac = the...
Hello all, Yao Liu has been translating ETC into sketchpad. He currently has the first 360 points, all dynamic. (Nikolaos, this makes it worth upgrading your...
Dear All My Friends, Given triangle ABC, point P with Cevian triangle PaPbPc, point U with Cevian triangle UaUbUc. Let UaPc cuts UB at M; UaPb cuts UC at N. La...
Quang Tuan Bui
bqtuan1962@...
Sep 2, 2006 4:51 pm
14116
Dear All My Friends, I have found some interesting answers for the point mappings: aK*(p^2*v*w + u^2*q*r) + bK*p*u*(v*r+q*w) : : - When aK=1, bK= -1 then after...
Quang Tuan Bui
bqtuan1962@...
Sep 3, 2006 6:36 am
14117
Hello all, My interest of late has been watching how points in the triangle behave. I am using the new Sketchpad version of the first 360 ETC points created...
Dear colleagues! I found a synthetic proof of Kiepert hyperbola's property. Let $A_1$, $B_1$, $C_1$ be the vertex of isosceles triangles $ABC_1$, $BCA_1$,...
Alexey.A.Zaslavsky
zasl@...
Sep 4, 2006 6:29 am
14119
Dear all, There are two points U1 and U2 of the form {0,v,w} (barycentric coordinates) on sideline BC satisfying b^2 w^2 + c^2 v^2 + (b^2 + c^2 - 2*a^2)*v*w =...
Dear All My Friends, I have found two other points T1 and T2 on the circumconic A, B, C, P, U. Details as following: Let the line connected P-Ceva conjugate of...
Quang Tuan Bui
bqtuan1962@...
Sep 4, 2006 12:01 pm
14121
Dear Francisco, I think that U could be thought of as the A-pedal of the Nine point center, X(5). Also reckon on .. U1 = {0, 2 a^2 + b^2 - c^2 - x, 2 a^2 - b^2...
Hello all, The line at infinity is the only affine invariant line; equation x + y + z = 0. The points on this line can be enumerated and computed from special...
Dear Steve I try hard to understand what you said for I know it is important. So let {Gamma} be a circumconic wrt triangle ABC and M any point on {Gamma}. What...
Dear Francisco, ... U1, U2 are the (real or not) intersections of BC and the circle through A, midpoints of AB, AC. Best regards Bernard [Non-text portions of...
Dear Francisco, ... I have added terms in your equation to obtain p u^2 + q u v+r u w +b^2 w^2 + c^2 v^2 + (b^2 + c^2 - 2*a^2)*v*w = 0 and found p, q r to...
... I also work hard to understand yours since I figure they are important. The line at infinity to the Steiner ellipse is indeed a particular case using...
Let ABC be a triangle and P a point. The Parallel to BC through P intersects AB, AC at Ab, Ac, resp. The Parallel to AC through Ab intersects BC at Abb The...
Dear Antreas, You wrote ... In your construction we have 3 equal segments. This point is X(37), the length AbbAcc = abc / (ab + bc + ca) and is the same with...
Dear friends When you look at the Sollertinski and Krasilnikov synthetic proofs of the Sondat theorem, you will see they begin with the same lemma for they...
Dear Steve If we keep the (x + y + z)^2 factor, it means that the conics f = 0 and g = 0 have the same asymptots and this is too strong a condition for shaped ...
Dear All My Friends, Given triangle ABC and point P. Two lines Lab, Lac are passing through A and perpendicular with BP, CP respectively. Similarly define Lbc,...
Quang Tuan Bui
bqtuan1962@...
Sep 10, 2006 4:31 pm
14136
Steve Sigur wrote on Wed Aug 9, 2006 12:24 am, Hardy proved the following correct theorem If a parabola is a rectangular hyperbola, then it is an equiangular ...
Dear friends, Does anyone have some results relating our favorite mathematics discussion (Triangle Geometry) to electrical engineering (EE) principles? I...
Dear Jeff Yes I have a little problem of this kind: Let L1, L2, L3, 3 parallel wires with uniform electrical currents of respective uniform algebraic...
Dear Alexei I give you here a proof of part of the Sondat theorem in case of 2 orthological triangles ABC and A'B'C sharing the same vertice C. These 2...
