Geometric Modeling of Closed Steiner Chain in Micro-Scale Structures

Abstract

Many functional properties of living and non-living materials around us depend on the size,
shape and therefore geometric models of their smaller parts. The geometric models of these parts are factors
that affect their distribution and settlement patterns in the area where they are located. The settlement
patterns of geometric models of materials are not simple and random, and most of them are concepts that
we can define with formulas. We can detect geometric models of some materials that we can observe with
the naked eye. However, it is more difficult to detect geometric models that make up materials at micro
scales. Such studies will provide information about the efficiency of the whole of these materials by
knowing their microstructures. At the same time, when the micro mathematical properties and geometric
structures of these materials are known and taken into consideration, the efficiency parameters at the macro
scale can also be easily determined. In this study, it was tried to determine the definitions of geometric
structures based on mathematical rules in some microstructures that we can only observe with a microscope.
In our research, different plant micro geometric modeling was used to define geometric models. In
mathematical evaluations, mathematical concepts determined in the light of literature were used to describe
the geometric models of microstructures.