A Novel and Accurate Method for Squaring the Circle With Compass and Straightedge
Year: 2026
Type: article
Abstract: © Thomas J. O’ConnorIndependent Researcher Abstract This paper presents a novel and accurate geometric method forsquaring the circle using only compass and straightedge. Theconstruction does not require drawing a segment of length π,nor does it contradict the classical impossibility of constructingπ directly. Instead, the ratio π/2 arises naturally and indirectly from the geometry of a specific rectangle together with a quarter circle. A specific point determined solely by circle intersec-tions, midpoints, and diagonal relationships is shown throughexact coordinate equations to lie precisely on the diagonal ofthe rectangle. This point fixes the height of the rectangle allowing the construction of a square whose area is exactlyequal to that of a given circle. The method is fully geometric,requires no approximations, and yields the highest accuracyachieved to date. It demonstrates an elegant relationshipbetween certain circular arcs and rectangular proportions.
Author: O'Connor, Thomas J.
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171835132
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