Convergence with Respect to Triangle Shapes -- Elementary Geometric Iterations

When thinking about ‘convergence’ one typically considers number sequences or contexts arising from calculus. However, there are also interesting phenomena of convergence arising from elementary geometry. Cases of convergence in the realm of geometry are useful in that they can readily be visualised using Dynamic Geometry Software (DGS) environments. In this article we explore a number of convergence scenarios that could be used in the school classroom in order to promote conjecturing, exploration, reasoning and proof.