This deposit contains the PDF version of the article “A Contractive Reformulation of a Geometric Method for the Approximation of π”. The work presents a structural reformulation of a classical geometric iteration for approximating π by introducing a transformed recurrence that defines a contractive dynamical system. Its central contribution is to interpret the update rule as a contraction mapping on an invariant interval, thereby providing a clear explanation for numerical stability, perturbation decay, and convergence of the associated geometric bounds. Within this framework, the approximation process is analyzed through dynamical properties such as monotonicity, invariance, and contraction, connecting classical geometry with ideas from numerical analysis and dynamical systems. Supporting source files, scripts, and additional materials may be linked in a later update.
Francisco Anderson de Sousa Oliveira (Sat,) studied this question.