# On generalized median triangles and tracing orbits

## TL;DR

This paper explores a generalized concept of median triangles with complex parameters, leading to periodic motions where vertices trace closed orbits, revealing new geometric properties and behaviors.

## Contribution

It introduces a novel generalization of median triangles using complex parameters and analyzes the resulting periodic vertex motions on closed orbits.

## Key findings

- Vertices trace each other on a common closed orbit.
- Generalized median triangles exhibit periodic motion.
- Specialized parameters produce predictable geometric behaviors.

## Abstract

We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices trace each other on a common closed orbit.