Geometry

Microscopic Mathematics; Tintinnid’s Strategic Survival

In this essay, we explore tintinnids’ survival designs within the context of fundamental mathematics principles. Tintinnids use mathematics concepts for everyday functions such as swimming and self-protection. We delve into tintinnids’ various swimming patterns. We take a close look at the helical swimming motion, or more precisely how that motion…

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Discussion of Nature’s Design Solutions in Tintinnids: Masters of Microzooplankton Survival

In this essay, we explore tintinnids’ survival designs within the context of fundamental physics principles. Tintinnids employ diverse mechanisms to outmaneuver predators, locate prey, and safeguard themselves. To avoid predators, tintinnids utilize specific swimming patterns, attach to groups of particles, develop symbiotic relationships with diatoms, and have undergone morphological adaptations…

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Mathematical Marine Models of Coral Polyps

While coral polyps have been extensively studied across various scientific perspectives, this paper will explore them from a Mathematical perspective. Coral’s spontaneous growth pattern was mathematically modelled and explained from a polyp-oriented perspective, showing how polyps contribute to growth patterns. Moreover, corals are heavily reliant on their environment which contributes…

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Magnetic Marvels: A Mathematical Exploration of Magnetotactic Bacteria

Order can be found within the seemingly complex, and perhaps even disordered, processes and shapes that constitute magnetotactic bacteria (MTB). This order can be explained by the concepts of mathematics. First and foremost, the crystalline structures within the magnetosomes of MTB can be modelled mathematically. Magnetite and greigite crystals consist…

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Mathematical Models of Diatoms: Understanding Their Complex Shape, Reproduction and Chain Formation

Apart from physical and chemical solutions used by the diatom for survival, some features of the unicellular microalgae also could be described in mathematics. For instance, the diatom morphology reveals a striking alignment with the golden ratio and fractal geometry. By examining the silica shells of these unicellular algae, we…

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The Mathematical Principles Pertaining to Coccolithophores

Through their production of protective calcite shells known as coccospheres, coccolithophores are known as one of the ocean’s many architects. These coccospheres can be broken down into smaller and smaller components: individual ‘shields’ known as coccoliths and singular calcite crystals. Both the arrangement of individual calcite crystals in coccoliths and…

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How mathematics governs the nature of tentacles

The tentacle displays a variety of fascinating properties and functions which scientists have attempted to comprehend via mathematical models over the years. In fact, such numerical modeling emphasizes how the appendage has evolved to become optimized for rapid movement, fine-tuned sensation, and skillful predation via its colour-changing abilities. It also…

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Mathematical Modeling of Marine Suction Cups

Many marine animals have evolved to include suction cups, and the suction cups of the natural world continue to inspire synthetic cup technology. Mathematical models can be used to understand the adaptations of different species and the way these operate. By deepening the knowledge of suction mechanisms, new and better…

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Mathematical Space-Filling Models and Applications in Adipose Tissue

The mechanisms describing how objects occupy space are some of the most fundamental topics of study and can be applied to countless chemical, physical, and biological phenomena. This is a topic that people have sought to understand for millennia, and it remains an integral part of our understanding of many…

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Geometry is Key: Mathematical Modeling of Whiskers and Antennae

Abstract Rat whiskers can be  modeled by Euler spirals,  curves with linear change in curvature. One hypothesis explaining vibrissae shape is that the linear growth of rat whiskers creates linear curvature. Another hypothesis is that the Euler spiral is an optimal shape to satisfy its sensory needs. The patterning of…

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The Complexity of Spines and their Mathematical Connections

Physical phenomena seen in nature are often optimized and refined to achieve a particular function. Evaluating spines’ physical and chemical characteristics can only reveal so much in the story of the optimization process. Modeling is an extremely powerful tool to unlock the secrets of developing the hidden strengths of particular…

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Crab Chelae Allometry and Implications on Game-Theoretic Armament Evolution

Pincers (alternatively known as chelae) are an integral component of many arthropod species. Many species, from arachnids to crustaceans, rely on the chelae for survival. Chelae are a highly functional and morphologically diverse group of structures found in crustaceans whose functions range from cracking open coconuts in coconut crabs to…

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