Dear friends of Hyacinthos: A new edition in spabish lenguage of http://www.personal.us.es/rbarroso/trianguloscabri/index.htm review of triangles with two...
Jeff, I cannot look at your code and see a definition of conjugacy. I have always figured that we are not all speaking of the same thing when we use that word....
To Hyacinthians, I have been coming to the end of my investigations of the excentral triangle, which is part of my larger "mining the Kimberling points" ...
Dear Steve, Another term I have seen used is "involution" as in "An operation, such as negation, which, when applied to itself, returns the original number...
The Euler lines of the 4 triangles fomed from ABCIo concur at the Schiffler point of ABC. Likewise for the extraversions. Intotal there are 12 triangles and 12...
... No, you are not making a mistake since conjugacy is such a general word. Note that Kimberling calls everything a something conjugate. But if a new person...
Is'nt this the truth. Look at some of Alexey's prior messages to which I was the only one who responded (some were off-line -- wrongly on my part.) Jeff ... ...
Let ABCD be a convex quadrilateral with area is "S".Let construck new quadrilateral which vertices midpoints of [AC],[AD],[BD],[BC] line segments.Show that...
... new ... Let the midpoints of AB, BC, CD, DA, AC, BD are P, Q, R, S, M, N respectively. By Varignon's Theorem, PQRS and SMQN are paralellograms and the area...
Antreus, Kapetis uses 3 coordinate systems in his book: normals, barycentrics, and a third for which the coordinates are the three Cevian ratios. He gives them...
Dear Hyachintos, Given two intersecting lines and a point not on the line, draw a line through the point that cuts off from the lines a segment of minimal ...
What I hope to find by this project are relationships in triangle geometry that can only be seen by having such a large collection of points. I think I have...
If I understand the question, there are 4 angles from 2 intersecting lines. In general 2 are acute and 2 obtuse. If P is in the interior of the acute one, the...
Dear Steve, Thanks for the prompt reply. And yes, you understood the question right. However, I have a problem with the proposed solution. Consider the point...
Dear Steve and Barukh ... line ... In fact, such a line is not ruler and compass constructible : Consider the hyperbola with asymptots your two lines and going...
Dear Barukh , Steve and Jean-Pierre in other words the problem is the following: If ABC is a triangle and P is a point inside angle A which is the segment AbAc...
... I do not read Greek but am leaning a lot of key words and I get help at local Greek restaurants when needed. I will see if I can find your problem. ...
Dear all, How can we calculate the image of a rotation of x:y:z by a rotation with center u:v:w and angle alpha? Best regards, Francisco Javier García...
Dear Francisco ... I suppose that you barycentric coordinates and that ABC is direct; then the first line of the matrix M of the rotation is M[1,1] =...
For any set of points with three homogeneous coordinates, there is a "fourth coordinate" in the sum of the first three. If the point be a center, then this...
Dear Jean-Pierre, when you say cyclically, you mean cyclicity for letters and for index? e.g. from M[1,3] = u(1-cos(alpha))+(u cotC+v(cotB+cotC))sin(alpha) we...
Dear Nikolaos ... Yes!! Note that, if you put k.cos(alpha) and k.sin(alpha) everywhere instead of cos(alpha) and sin(alpha), you get the matrix of the direct...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/FG200522index.html The editors Forum...
ForumGeom
ForumGeom@...
Nov 8, 2005 3:16 pm
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Dear Francisco, First, let me apologize for not writing your name properly last night. I looked today at possibly using complex arithmetic to describe the...
Dear friends ... This point is X(69) ... This is page 248 of Kapetis Triangle geometry volume 1 that has to do the brachystotransversal (Philo line) ... This...
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