Pedal triangles, self-adjoint affine maps and a two-thirds similarity
Year: 2026
Type: preprint
Abstract: The affine map sending a triangle ABC to an inscribed triangle A1B1C1 is self-adjoint exactly when the perpendiculars to the sides at A1, B1, C1 concur, i.e. when A1B1C1 is the pedal triangle of a point M. It is then a pure strain with principal factors (−1 ± OM/R)/2 along the Simson-line directions of the points where OM meets the circumcircle. Consequently, the points dividing AA1, BB1, CC1 in the ratio 2:1 form a triangle inversely similar to ABC with ratio OM/(3R), a property that characterizes pedal triangles.
Author: Nguyen, Hoang Long
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225338077