Root Calculation: A Research Notebook

This notebook records an independent search for approximating fractional powers such as 5^(1/n) without computational tools. Starting from a simple observation about the 5-fold change, two independent paths were followed — enlarging the square and balancing the factors — and they were found to be equal to each other. A closed-form series formula was developed, and it was generalized to any base. The work also documents failed attempts, the discrimination test developed to filter them, and the connection to the author's other conceptual models.