从生成视角看科赫雪花、曲线缩短流,圆周率的新角度,折线生成空间分类定理A Generative Perspective on the Koch Snowflake, Curve-Shortening Flows, a New View of π, and the Classification Theorem for Polyline-Generated Spaces
Year: 2026
Type: preprint
Abstract: 1. 分形中间态的构造性探索 ——科赫雪花、曲线缩短流与生成视角下的几何过渡 从生成过程而非静态对象的角度,探讨分形曲线在“折线—中间态—圆”谱系中的位置。 2. 从生成过程理解几何 ——均匀折叠、曲线缩短流与分形中间态的认知视角 从生成过程出发,重新审视直线到圆的过渡以及分形曲线在其中的位置。 3. 折线生成空间分类定理 ——从正多边形到分形与螺旋的统一框架 证明折线生成空间的第一分类定理。取一条初始线段,逐段赋予长度与转角,生成折线。 4. 空间折线生成空间分类定理:三维离散动力系统的统一与SO(3)群拓扑相变 折线生成空间分类定理在三维欧氏空间的严格拓展 1. Constructive Exploration of Fractal Intermediate States ——Geometric Transitions from a Generative Perspective: Koch Snowflakes, Curve-Shortening Flows 2. Understanding Geometry Through Generative Processes ——Uniform Folding, Curve-Shortening Flows and the Cognitive Perspective of Fractal Intermediate States 3. Classification Theorem for Polyline-Generated Spaces ——A Unified Framework from Regular Polygons to Fractals and Spirals 4. Classification Theorem for Spatial Polyline-Generated Spaces: Unification of 3D Discrete Dynamical Systems and Topological Phase Transitions on the SO(3) Group
Author: lihong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215879106