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Supplementary Text: Discrete Generative Definition of Circle Perimeter and Area Based on Radial Layerwise Growth

Authors: lihong;

Supplementary Text: Discrete Generative Definition of Circle Perimeter and Area Based on Radial Layerwise Growth

Abstract

2.5 Deduction of Discrete Perimeter via Layer-by-Layer Radial Propagation and Circumferential Extension Factor This subsection develops discrete perimeter formulas strictly following the dynamic generation rule of point-elements, with the fundamental radial increment fixed to the point-element length The circumferential extension factor is defined via site counting over radially expanding lattice layers without polygonal limit approximation, and discrete circumference is derived directly from the layered growth law. 2.5 径向逐层延伸与周向延伸率的离散周长推演 本节立足于点径动态生成规则,以圆心为基准、点径 为固定拓展步长,通过径向逐层外拓的点位统计定义周向延伸率,不借助多边形极限逼近,由层级延伸规律直接导出离散周长表达式。

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