Following Wison's lead and using his notation, I think I am getting a handle on this "supplement" operation. I am interested in this because the classical...
I have been reading Salmon's books and (for my half angle project) using trilinear coordinates so I have been thinking about coordinate systems. Salmon's books...
The cevian and excevian triangles of ABC are bounded by four lines. This means that they form a complete quadrilateral for which ABC is the diagonal triangle. ...
... getting ... As before, we write sP for the supplement of P, aP for the antisupplement of P, gP for the isogonal conjugate of P. ... Not quite, I find that...
I've been enjoying current mails on supplements etc. Stepping in where even angels would fear to tread I wonder why we can't use cevian product * as we are...
dick tahta
dick@...
Oct 2, 2005 6:40 pm
11593
Hi Dick, It's nice to know someone (else) is interested in this topic. As you say, sP = g(P*I), so gsP = P*I = cevapoint of P,I. I think that we were coming to...
Wilson, and now Dick, I first owe a bit of an apology. I have been rereading my old French books and the "supplementaire" of a point is not :z+x: in...
Hey Dick and Wison, ... Yea, we seem to have put everyone else to sleep! ... If I remember the ETC glossary correctly, the cevapoint operation is an involution...
... I have looked at your translation of Mineur. From this, I think that your apology is not needed. The two notions coincide. If you look at a result in...
Wiison, Thanks for all this. This is good news but if the aO = X(46), it is not the circumcenter of the excentral triangle, which is X(40). This means that the...
Wilson, ... I do not know these operations, and am initially suspicious of them, but I should know about them. I tend to think in terms of more primary...
Hi No doubt to everyones relief, this is not (overtly) related to supplements. I would appreciate some help with a problem related to the nine-point circle. I...
Dear Wilson [WS] ... Please feel free to post your results to Hyacinthos. Even if none in the current list of members is interested (I do NOT think so!),...
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 : /TCCT.jpg ...
Hyacinthos@yahoogroup...
Oct 8, 2005 5:07 am
11602
A late question on my part Vladimir, but what are spiral similarities? ... 9548 -- ... of P. ... BPC' and ... complement ... AX, BY, CZ ... each other ... and...
What's really cool is this: Let give circles X'Y'Z, Y'Z'X, Z'X'Y These circles concur at a point P on the circumcircle of XYZ. The circumcenters of these...
Well, let me please start over again! Let given circles X'Y'C, Y'Z'A, Z'X'B then, these circles concur at a point P on the circumcircle of triangle ABC and the...
Dear Jeff, spiral similarity is the composition of a rotation and dilation with the same center -- the general form of a simililarity transformation preserving...
Dear Vladamir, Do Coxeter and Greitzer say something about the circles X'Y'C etc.? Thank you sincerely, Jeff Brooks ... with the same ... preserving...
Let P = (x:y:z) in Trilinears, and sP defined as (y+z : z+x : x+y). We have the sequence of supplements sP, ssP, sssP,..... with trilinears : sP: y+z...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/FG200520index.html The editors Forum...
ForumGeom
ForumGeom@...
Oct 10, 2005 9:03 pm
11611
The line from the incenter of ABC to the orthocenter of the incentral triangle is parallel to the Euler line of ABC. I can see it on Sketchpad. I can verify...
Antreas, Neat! and this happens the same way for complements in barycentrics. Steve ... Couldn't figure out the primes but looking at this sequence mod 3, ...
Hi This is a very common sequence - see Sloane's list It is called the Jacobsthal sequence: and given by a(n) = a(n-1) + 2a(n-2). One of Sloane's references...
... For every n we have that G(n+1) + G(n) = 2^n From this we get that, G(3(k+1)) = 3 * 2^(3k) - G(3k) [1] For k = 1 : G(3) = 3 Now, if it is true for 3k,...
... I believe that the problem of finding infinitely many prime G(n) will be intractable. The analogue for the Fibonacci numbers has not been solved as far as...
Dear all, there are a triangle ABC and some circumellipse with center S. There are also three ellipses j, k, l with the center S and the same excentricity like...
... incentral ... I think we met this before in #11564. This contained more information. Suppose we write Ix (x = o,a,b,c) for the in- and ex-centres, and...
