General Mathematics

    

A Simple, Geometric Way to Find the Area of a Circle and the Value of π

Authors: Ramesh Vardhan

This paper outlines a straightforward, step-by-step geometric method to find the area of a circle. Instead of relying on traditional, complex trigonometry, we initiate the framework using a simple right-angled triangle inscribed within one quarter of a circle. By recursively infilling the remaining curved gaps with smaller tiers of triangles, we completely fill the shape. Tracking the mathematical lengths of these expanding bases reveals a pattern of square roots inside square roots (nested radicals) that leads directly to the value of π.

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[v1] 2026-10-31 22:36:17

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