Dear Francois ... P recur ... the third ... isometric ... ratio k > ... If I don't mistake,if P is inside ABC, the third pedal triangle cannot be isometric...
15788
Francois Rideau
francoisrideau
Nov 11, 2007 5:26 pm
Dear Bernard and dear friends It is known that the shapes of repeated triangles wrt a fixed point P recur with period 3 and the Mac Cay cubic is the locus for...
15784
Ignacio Larrosa Ca...
ilarrosa
Nov 10, 2007 11:54 am
... By fact, in the same way it is possible divide a triangle in n^2 + 1 congruent triangles and similar to the initial. The legs of the triangle must be n and...
15783
Quang Tuan Bui
bqtuan1962
Nov 10, 2007 5:44 am
Dear Ignacio Larrosa Cañestro, Thank you very much for your solution. It is interesting that in Vietnamese Yahoo Answer (I posted already some days) they are...
15782
Ignacio Larrosa Ca...
ilarrosa
Nov 9, 2007 8:59 pm
... Yes, a rectangle triangle with legd 2 and 1. Trace the heihgt over the hipotenuse, and divide the greatest resultant triangle in four congruent ones. The...
15781
Quang Tuan Bui
bqtuan1962
Nov 9, 2007 2:43 pm
Dear All My Friends, If exists one triangle which can be divided into five congruent triangles? Thank you and best regards, Bui Quang Tuan ...
15780
garciacapitan
Nov 9, 2007 1:07 pm
Dear Nikos, I have sent to Hyacinthos a response to your message... ... but I haven't seen it published, Thank you for your nice generalization. I have put it...
15779
garciacapitan
Nov 9, 2007 1:06 pm
Dear Nikolaos, thank you for your nice generalization, I have included it at http://garciacapitan.auna.com/problemas/jb/20071108/ Also, since the sum of...
15778
Nikolaos Dergiades
ndergiades
Nov 8, 2007 9:00 pm
Dear Garcia, ... If A'B'C' is the orthic triangle and A1B1C1 is the medial triangle of ABC then the line AbBa is the symmetric line of A'B' relative to C1 the...
15777
garciacapitan
Nov 8, 2007 4:22 pm
Dear all, now in the section 'Charlas con JBRM' (*) of my site you can see: If we construct enclosing rectangles BCCaBa, CAAbCb, ABBcAc to the triangle ABC,...
15776
Jeff
jbrooks_update
Nov 8, 2007 12:54 pm
Good grief! Like a small child just learning to describe the world around him, I see tonight I was asking essentially for the center zx of a direct similitude....
15775
Francois Rideau
francoisrideau
Nov 8, 2007 12:54 pm
Dear friends ... Of course this macro works only with points in the euclidian plane. Now I explain you how to get the image M' = f(M) of any point M by a...
15774
jpehrmfr
Nov 7, 2007 2:46 pm
Dear Alexei ... symmedians of correspondent triangles. So the common point of the diagonals is the Lemoine's point. OK, I was stupid and I see my confusion. ...
15772
Alexey.A.Zaslavsky
zasl@...
Nov 7, 2007 1:34 pm
Dear Jean-Pierre! If the quadrilateral is harmonic then its diagonals are the symmedians of correspondent triangles. So the common point of the diagonals is...
15769
jpehrmfr
Nov 6, 2007 2:26 pm
Dear Alexei ... distances from L to the sidelines, i.e if L_1, L_2, L_3, L_4 are the projections of L then the vector sum of LL_i is zero. Your approach is the...
15768
Alexey.A.Zaslavsky
zasl@...
Nov 6, 2007 12:13 pm
Dear Jean-Pierre! Thanks for your remarks. I considered the case of oriented distances from L to the sidelines, i.e if L_1, L_2, L_3, L_4 are the projections...
15767
jpehrmfr
Nov 5, 2007 6:09 pm
Dear Alexei and other Hyacinthists in fact, it is not difficult to construct when A,B,C,L are given the points D such as ABCD is a Lemoine quadrilateral with L...
15766
jpehrmfr
Nov 5, 2007 12:44 pm
Dear friends, I've uploaded in Hyacinthos files a figure (Lemoine quadrilateral) showing the locus of D such as ABCD is a Lemoine quadrilateral : - the...
15765
Francois Rideau
francoisrideau
Nov 5, 2007 12:44 pm
Dear friends In the affine choo-choo theory, I had to think how a metric structure can give a new look at it and that's why I was led up to this famous "3...
15764
jpehrmfr
Nov 5, 2007 1:34 am
Dear Alexei ... there exists the point L such that the distances from L to the sidelines of ABCD are proportional to respective sides. Does anybody know which...
15763
Quang Tuan Bui
bqtuan1962
Nov 4, 2007 10:50 pm
Given triangle ABC, one point U with barycentrics (u : v : w), one point P with barycentrics (p : q : r) and point X with barycentrics (x : y : z). A line from...
15762
Eisso J. Atzema
atzemae
Nov 3, 2007 12:13 pm
Dear Hyacinthians, I did some computations on the Lemoine quadrilateral as defined by Alexey Zaslavsky. I find that this class of quadrilaterals is broader ...
15761
Jeff
jbrooks_update
Nov 3, 2007 12:13 pm
Dear Friends, There exists well-known JAVA export capabilities with our mainstream geometry software, but is anyone aware of a low-cost dynamic geometry ...
15760
Francois Rideau
francoisrideau
Nov 3, 2007 12:13 pm
Dear friends To show you how this theorem is useful, I will give you some of its applications but first I write it again more symmetrically: Let (A, B, C) and...
15759
Quang Tuan Bui
bqtuan1962
Nov 2, 2007 4:59 pm
Dear Peter, Thank you very much for your verification and plentiful results, information about Steiner deltoid. It is interesting that we have one common idea:...
15758
Moses, Peter J. C.
peter_mows
Nov 2, 2007 3:39 pm
Dear Tuan, Your point is indeed on the Steiner Deltoid. Copied below are some Deltoid bits that I sent Clark a while ago. (Some bits may be irrelavent to...
15757
Quang Tuan Bui
bqtuan1962
Nov 2, 2007 2:59 pm
Dear All My Friends, Consider one point P with first barycentric coordinates: (b^2 - c^2)^2*(-a^6*(b^2 + c^2) + (b^2 - c^2)^2*(b^4 + 3*b^2*c^2 + c^4) +...
15756
Francois Rideau
francoisrideau
Nov 1, 2007 11:05 pm
Dear friends I give you an strange theorem that I have found in a french book of exercices published more than 10 years ago. As it links euclidian and circular...
15755
Francois Rideau
francoisrideau
Nov 1, 2007 11:05 pm
Dear friends Sorry, I mixed up the labels of my points because of too much burgundy, hence I restore the true text: Let <s> be a direct similitude of center...
15754
Jean-Louis Ayme
jeanlouisayme
Nov 1, 2007 11:01 am
Dear Tuan thanks you very much for your verification and also for your nice email wrote for some months ago about "A little result". I continue my rechearch in...
