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This article proposes an innovative method based on geometric transformation and limit construction, which successfully solves the problem of "drawing curves as straight". By introducing a linear function of fixed arc length and isosceles trapezoid, we prove that the transformation between a circle and an equal area square can achieve geometric equivalence in finite steps, and provide specific graphical steps and mathematical proof. This study reveals the limitations of traditional ruler drawing constraints and achieves accurate area conversion through an extended toolkit. Finally, the paper discusses the mathematical significance of this solution, including the algebraic treatment of the transcendental number and its supplementation to the Euclidean geometry system.
Comments: 6 Pages.
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[v1] 2025-04-30 21:53:51
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