Mimicry of Geometry and Design from the Nature and Biology to Material Science and Engineering

Abstract

In this paper geometry and design in material science and engineering, which have been an inspiration from nature and biology is investigated. It is found out that symmetry, harmony, and perfection play crucial rule in this mimicry. In the symmetry approach not only symmetry of the crystallography group is included, but also molecular symmetry groups, Kugel and Curie symmetry groups. The criteria of harmony are based on Fibonacci sequences and Fibonacci numbers Φ,-Φ,φ,- φ. Symmetry and harmony are giving beauty to geometry and design in nature, biology, and engineering. However, in this investigation, perfection is also included (based on the perfect numbers) that gives, besides beauty, a new property of “sublime” to the objects and processes. In this paper, a few examples of mimicry in relation to nature-biology-engineering based on symmetry, harmony, and perfection are presented. One of the examples of that kind of mimicry is a spiral galaxy- centrioles-solar plants. The second one is molecule C60 in space (in cosmic dust), clathrin in the human brain, and C60 in nanophotonics, nanocosmetics, and medicine. However, more examples of biomimicry (from biology to engineering) are presented. One of the more interesting examples is a container for cosmetically use with complex geometry and design based on the pentagonal-hexagonal organization of collagen in human tissue. According to our investigation, we can conclude that optimization of mass-energy, energyinformation, and information-control (regulation) in the nature, biology, and engineering are principle which determinate geometry and design of objects.