MATHEMATICAL MINIMAL SURFACES IN MICROMORPHOLOGICAL STRUCTURES OF PLANTS
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Abstract
In this study, we determined that some micro morphological structures of plants have a mathematical minimal of surfaces. Minimal surfaces arc defined as surfaces with zero mean curvature. A minimal surface parametrized as x = (u,v,h (u, v)) therefore satisfies Lagrange's equation , (1 + h(v)(2))h(uu) - 2h(u)h(v)h(uv) + (1 + h(u)(2))h(vy) = 0. One of the microscopic structures with a mathematically minimal surface examined in the study is glandular hairs. The glandular hairs are aromatic and often used as herbs, spices, folk medicines and fragrances thanks to their secretions, One of the other microscopic structures with a mathematically minimal surfaces examined is the tracheal elements, which are characterized by the formation of lignified cell wall. They serve for upward conduction of water and dissolved minerals in plants. One of the main objectives of the study is to provide concrete examples by showing minimal surfaces, which are the subject of geometry, in the microscopic structures that cannot be seen with the naked eye of plants, Thus, it is extracted from the theoretical form of mathematical formulas and showing concrete examples in nature,