Hello all in geometry, I have always found the Tarry point mysterious. It is opposite the Steiner point in the circumcircle and the intersection of the ...
Dear friends, it is known that if ABC is a triangle and P is a point in the plane of ABC not on the sides of ABC then the isogonal conjugate of the circle PBC ...
Hyacinthians, I have been looking at the group of lines formed by the Schiffler and isotomic Spieker points and the concurrences they produce. My old work on...
Wilson, François, Jean-Pierre, Bernard, Peter, and all, In checking Wilson's statements last night I noticed that there is a point on each axis of the Steiner...
Dear Hyacinthists, consider the rectangular hyperbola through G, O, K (symedian), X[110). His center is the midpoint of GX[110] and the hyperbola goes through ...
Dear all Sorry my chuff-chuffs are causing all this fuss overseas! As for me, I try it but I can't remember one single french soldier and though it was 62...
Dear All, Given four arbitrary points A, B, C, D on the plane. If we take one point as Cevian point and three other as triangle so we have three Cevian foots....
Yes, Jeff, Linear Algebra is an essential tool, even in Triangle Geometry. So concepts like trace or determinant of a matrix are very useful. But as we are in...
I have decided that the problem of points on a conic and the existence of circumconics and inconics can be solved if I can solve the problem of what points are...
A year ago when Penrose was here in Georgia, he told me that when he was very young he had proved a very interesting theorem which proved Pascal, Pappus,...
Dear All Hyacinthians, In the process working with my message "A Small Tour Through Some Small Circles" I see one curve but I don't know what is it and what is...
Dear All, I think a word of caution is in order regarding the file uploaded by Jean-Pierre. The paper uploaded is taken from Poncelet's "Applications (...)"...
I am looking at conics and I think the following circumconic is more significant than it has been taken to be. It has been occasionally mentioned on these...
Dear friends! Let us consider an arbitrary quadrilateral ABCD. Ha is the orthocenter of BCD and Ga is centroid. Let us define Hb,Hc,Hd and Gb,Gc,Gd in the same...
Dear friends Some of you are going on to ask me about references on orthologic maps. As I said in one of my previous posts, it's a long story to tell about and...
Awhile back, Wilson Strothers summarized a Hyacinthos discussion with: [WS]Conway's conic is the isogonal conjugate of the Tarry- Steiner diameter. Then we...
Dear All Hyacinthians, After one working day we are tired some little some more. I am also tired now. By this small tour visiting some small circles I want to...
Dear All Here is a construction which yields a number of useful points (and requires only a staight-edge). This may well have appeared before. If so, I'd...
Consider pi (well 2pi actually) =a/b. Any rational representation is equivalent to a line of length a/b, bent into a regular polygon with b sides of length...
Dear Hyacinthos, I drove John to the airport from the meeting in Atlanta and as his plane was late, we had a long talk about geometry. I got a chance to show...
Dear all, This weekend many famous geometers came to Atlanta. This is from Conway who learned it from one of its namesakes. There are two interesting things...
Dear All, I would like to inform you one my result as follow: Let's P is a point on the plan of triangle ABC with A'B'C' is its Cevian triangle wrt ABC. Then...
Given a triangle ABC and a point P, let A'B'C' the cevian triangle of P. Call X the point of intersection of the circumcircles of triangles BPC' and CPB'...
Dear friends, if i have three points A(xa,ya),B(xb,yb),C(xc,yc). If two of these points (A,B) are given and static, how can I find position xc, yc of third...
Dear friends, finding general perspectivities is not so difficult but the transformation formulae are often rather ugly. I'd like to present a (new?)...
Dear friends! Let ABCD be the cyclic quadrilateral. Let us consider two constructions. 1. P is the intersection of perpendicular from vtrtix A on (BC)-line. Q...
Dear All, Edward Brisse usually distributes a list of triangle centers from the ETC at /pages.infinit.net/spqrsncf/fx3053.htm (This link was down earlier...
Dear Hyacinthists, an article written by myself and intitled "Orthocenter of the Fuhrmann' s triangle, a purely synthetic proof" has been published at ...
