





Contact 

Nicollier Grégoire 



Title 

Dynamics of the Nested Triangles Formed by the Tops of the Perpendicular Bisectors 



Author(s) 

Nicollier G. 



References 

Forum Geometricorum, volume 14, 2014, pp. 3141 



Url 

http://forumgeom.fau.edu/FG2014volume14/FG201403index.html 



Abstract 

Given a triangle, we construct a new triangle by taking as vertices the tops of the interior perpendicular bisectors. We describe the dynamics of this transformation exhaustively up to similarity. An acute initial triangle generates a sequence with constant largest angle: except for the equilateral case, the transformation is then ergodic and amounts to a surjective tent map of the interval. An obtuse initial triangle either becomes acute or degenerates by reaching a rightangled state. 











