软细胞和贝的几何结构
Gábor Domokos1,2, Alain Goriely3, Ákos G Horváth2,4
1Department of Morphology and Geometric Modeling, Budapest University of Technology and Economics, Budapest, 1111, Hungary.
PNAS nexus
|September 11, 2024
概括
这项研究引入了"软细胞"和"软",以弥合几何形状和自然形状. 这些新的形状从传统的板上顺利地变形,在自然界中从细胞到贝中出现.
科学领域:
- 几何几何学的几何学
- 数学物理 数学物理
- 自然科学 自然科学自然科学
背景情况:
- 经典几何学依赖于尖的角形状,如多边形和多面体,用于空间.
- 自然构造往往表现出曲的边缘和非平面,偏离理想的几何.
研究的目的:
- 连接经典的尖地板与柔软的,自然存在的形状.
- 介绍和定义一种称为"软细胞"的新类几何形状及其空间布局",软".
主要方法:
- 开发一个数学框架,使多面体平地变形为软.
- 构建二维和三维点格子的迪里克莱特-沃罗诺伊单元软版本.
主要成果:
- 证明无限类的多面体可以连续转化为软.
- 证明存在和构建来自点格子的软.
结论:
- 软细胞和软为理解具有曲线边界的自然形状提供了一个几何模型.
- 这些理想化的柔软形状,源于几何原理,在各种自然结构中普遍存在,包括生物细胞和.
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