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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19720277 |
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Table of Contents:
- <p>本文跳出传统割圆术的内逼近研究框架,以定圆直径为固定等腰三角形底边,构建圆内接正n边形紧贴直径的对称侧边向外延长、相交于圆外的几何模型,依托平面几何对称性与三角函数关系完成严谨公式推导,得出圆外等腰三角形面积关于正多边形边数的通项公式;</p> <p>Breaking away from the internal approximation research framework of the traditional circle division method, this paper takes the diameter of a fixed circle as the fixed base of an isosceles triangle, constructs a geometric model in which the symmetrical sides of a regular n-sided circle-inscribed polygon adjacent to the diameter are extended outward and intersect outside the circle, completes rigorous formula derivation based on the symmetry of plane geometry and trigonometric function relations, and obtains the general term formula for the area of the external isosceles triangle with respect to the side number of the regular polygon;</p> <p> </p> <p>通过数值计算、函数单调性分析与极限论证,揭示该三角形面积随正多边形边数增多呈单调递增且趋向无穷大的与割圆术内收敛相反的发散规律。</p> <p>Through numerical calculation, function monotonicity analysis and limit demonstration, it reveals that the area of the triangle increases monotonically with the growth of the sides of the regular polygon and tends to infinity, forming a divergence law opposite to the internal convergence of the circle division method.</p> <p> </p> <p>进一步拓展研究,挖掘模型蕴含的三角函数波形特性、微分极限瞬时状态、双向对偶三角形体系,且证实该几何结构可衍生出全新欧式自相似几何构造,同时挖掘深层数学价值。</p> <p>Further expanded research explores the trigonometric waveform characteristics, differential limit transient states and bidirectional dual triangle system contained in the model, verifies that this geometric structure can derive a new Euclidean self-similar geometric configuration, and explores its in-depth mathematical value at the same time.</p> <p> </p> <p>该研究为平面几何拓展探究、初等数学极限概念等提供了全新的逆向研究视角。</p> <p>This research provides a brand-new reverse research perspective for the extended exploration of plane geometry and the concept of limits in elementary mathematics.</p>