Limits of Recursive Triangle and Polygon Tunnels

TL;DR

This paper explores the theoretical limits of recursive triangle and polygon tunnels, introducing generalized concepts like nedians of ratio r and angles, and discusses potential extensions to 3-D and higher dimensions.

Contribution

It presents new unsolved problems involving infinite recursive tunnels of polygons, generalizes the concept of nedians, and proposes future research directions into higher-dimensional tunnels.

Findings

Introduction of generalized nedians of ratio r and angles

Formulation of recursive tunnel problems in 2D polygons

Discussion of potential extensions to 3D and n-D solids

Abstract

In this paper we present unsolved problems that involve infinite tunnels of recursive triangles or recursive polygons, either in a decreasing or in an increasing way. The "nedians or order i in a triangle" are generalized to "nedians of ratio r" and "nedians of angle {\alpha}" or "nedians at angle {\beta}", and afterwards one considers their corresponding "nedian triangles" and "nedian polygons". This tunneling idea came from physics. Further research would be to construct similar tunnel of 3-D solids (and generally tunnels of n-D solids).