- The following paper has been published in Forum Geometricorum. It can be
Alexei Myakishev, The M-configuration of a triangle,
Forum Geometricorum 3 (2003) 135--144.
Abstract: We give an easy construction of points A_a, B_a, C_a on the sides
of a triangle ABC such that the figure M path BC_aA_aB_aC consists of 4
segments of equal lengths. We study the configuration consisting of the
three figures M of a triangle, and define an interesting mapping of
triangle centers associated with such an M-configuration.
[Non-text portions of this message have been removed]
- Paul Yiu wrote:
>> http://forumgeom.fau.edu/FG2003volume3/FG200315index.htmlIn this article, Alexei Myakishev wrote:
>> Alexei Myakishev, The M-configuration of a triangle,
>> Forum Geometricorum 3 (2003) 135--144.
>> Proposition 1. The lines AAa, BBa, CCa concur at the pointWonderful theorem; although, I believe, the lines should be
>> with homogeneous barycentric coordinates
AAa, BBb, CCc correctly.
>> It follows by Ceva's theorem that the lines AAa, BBa, CCaThe same correction as above.
I fear that it is not shown that an M figure exists (it
shouldn't be difficult, but it isn't obvious).