Dear friends Now at last, I have come to construct the fixed points of a direct circular map <f> and today, I begin with the case where <f> is a circular ...
Dear Jean-Pierre, ... I've wondered about using 'complicated numbers' like those defined in [1] below. The author writes in the introduction "At first sight it...
Dear Francois ... central ... Inversive ... fixed ... his own ... hint, ... the fixed ... beautiful to ... I've just looked at Morley's construction - without...
Dear Francois ... the ... the ... (f ... This is not correct; W is not necessarily the internal center of similitude (that was not very clear in Morley's proof...
Dear Jean-Pierre and dear friends Thank you for your help. I have cited Morley for its construction of these fixed points was so beautiful! By the way, there...
Dear Jean-Pierre In fact it was just this choice of the inversion by Morley that I did not understand. In the drawing we have 2 lunes: the first with the arcs...
... Two of them, from 1893 or earlier. George Bruce Halsted, "Elementary Synthetic Geometry". I have the second edition (1893) whose pp. 5-6 clearly...
Ken Pledger
Ken.Pledger@...
Dec 2, 2007 9:59 pm
15894
Dear François ... did not ... AB'A' and ... bounded ... swapped by ... these ... themselves. ... these 2 ... go "inside" ... through the ... no ... bissector ...
Dear friends Now I will look what's going on for a direct circular map f: ABC --> A'B'C' in case points A, B, C are on a line (L) and points A', B', C' are on...
Dear friends In fact, I just see that the old famous construction of the foci of an ellipse given by 2 conjugate diameters is only a special case of the...
Dear François ... circular ... The fixed points are the isodynamic points I1, I2;the other vertices are the inverse M1, M2 of the brocard points in the...
Dear colleagues! What is the number in ETC of Thebault point, i.e the common point of euler lines of triangles AB'C', A'BC' and A'B'C where AA', BB', CC' are...
Alexey.A.Zaslavsky
zasl@...
Dec 3, 2007 4:46 pm
15901
Dear friends For a long time, there exists a very famous construction giving the foci of an ellipse given by 2 conjugate diameters AA' and BB'. So you know...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2007volume7/FG200727index.html The editors Forum...
ForumGeom
ForumGeom@...
Dec 3, 2007 5:22 pm
15904
Dear Alexey, [AZ]: What is the number in ETC of Thebault point, i.e the common point of euler lines of triangles AB'C', A'BC' and A'B'C where AA', BB', CC' are...
Dear Alexey ... euler lines of triangles AB'C', A'BC' and A'B'C where AA', BB', CC' are the altitudes of ABC? Moscow scholar Fyodor Nilov asserts that this ...
Dear Alexey Let T be the Thebault point and (L) the Euler line of ABC. The lines symmetric of (L) wrt the sides BC, CA, AB are on a same point U on the...
Dear friends This paper is very interesting. It looks at cyclic quadrilaterals ABCD such that the middles P of AB, Q of BC, R of CD , S of DA are given. PQRS...
Dear Francois, ... [snip] I've got <s> ... The problem is I still don't have <g> geometrically. Can you help me to construct this (maybe again.) Sincerely,...
Dear Jean-Pierre and all friends As I said in earlier message, I have considered the problem to find the points P(x:y:z)(given in barycentrics), with property ...
Dear Francois, ... [snip] I've got <s> ... The problem is I still don't have <g> geometrically. Can you help me to construct this (maybe again.) Sincerely,...
Dear Jeff If I understand you, your problem is to have a macro giving the image M' = f(M) of any point M, where <f> is a direct circular map with given fixed ...
Dear Ken, Interestingly Johnson mentions Lachlan and a number of other authors (though not Halsted) as having introduced oriented angles. However, he also...
Dear Francois! This problem was proposed at the last Towns tournament. It has an elementary solution. Let K, L, M, N be the midpoints of sides of cyclic...
Alexey.A.Zaslavsky
zasl@...
Dec 5, 2007 12:23 pm
15914
Dear Francois, I'm not waiting for my post to appear -- I already found one of my mistakes. I see you wrote: If P and Q are the fixed points, we know that (P,...
Dear Francois and dear friends, Sorry for the double post, I meant to include a construction below and ask how this might fit here. ... I became interested in...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2007volume7/FG200728index.html The editors Forum...
ForumGeom
ForumGeom@...
Dec 5, 2007 3:14 pm
15917
Dear Alexey Thank you for your interesting remark about the radii of these 4 circles. As for me, I only use this elementary theorem: The locus of the points M...
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