| |
|
|
| |
|
|
| 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. 31-41 |
| |
|
|
| 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 right-angled state. |
| |
|
|
| |
|
|
| |
|
|
| |
|
|