APPROXIMATE SOLUTION TO THE CIRCLE SQUARING PROBLEM

This paper presents a formal geometric construction and analytical validation for an approximate solution to the classical circle-squaring problem. While exact quadrature using a compass and straightedge is impossible due to the transcendental nature of π, we demonstrate a highly accurate geometric approximation suitable for practical applications, such as mathematical puzzles and structural design. Furthermore, we show how this construction provides a practical framework for Tarski’s circle-squaring challenge by decomposing the circle and square into a finite set of geometric pieces. Crucial to this decomposition is proving the exact area equivalence between the boundary segment cut by the square into the circle (the Lune) and the corner region cut by the circle into the square (the Anvil). Both regions are analytically verified to converge precisely to