Geometric Modeling in Some Micromorphological Structures

Abstract

In this study, we determined that some micromorphological structures of plants have geometric models and mathematical formulas. There are specialized structures in plants that perform tasks such as making usable, storing and transmitting the products formed as a result of metabolic activities. These structures take different shapes depending on the complexity of their functions. These shapes enable them to perform their duties in the most efficient way. As a result of the examinations under the microscope, it was observed that plant crystals and vascular tissue elements from these structures have special geometric shapes that provide them with important advantages such as small space and durability. In the microscopic observations of the plants we examined, it was determined that the crystals and some transmission tissue elements that serve to transmit water and dissolved minerals in plants show a minimal surface feature, which has an important place in geometry. Minimal surfaces are defined as surfaces with zero mean curvature and expressed with mathematical formulas. In addition, it has been determined that these structures show geometric patterns called helicoid and elongated triangular bipyramid. The schematic shapes of these geometric models and the photographs taken from the plant samples under the microscope as a result of laboratory studies are given in the study.