In this paper we propose a novel class of spirals that are based on perfect polygonal formations. The spirals are defined by a fractal of right triangles that delineate their geometry and determine their progression rates and modes. We show how these spirals match naturally occurring ones, including hurricanes and galaxies, much better than already proposed models, allowing for more accurate categorization of these phenomena and better prediction of their physical properties.
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Recently, a 24-based distribution of numbers was used in a novel method for an infinite and accurate prime prediction and factorization. Therefore, further investigation of this particular configuration of numbers, labeled here the icositetragon wheel, is essential if we to expand our understanding of this method and to further improve it. We will show that using the icositetragon wheel is not an arbitrary choice by elaborating on the unique properties this configuration has, not only in regard to prime numbers distribution, but also for the many symmetries and complementary properties that numbers, prime and non-prime, observe in it.
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In this paper, we show how the 12 notes of the octave have inherent decimal references that correspond precisely to the internal angles of regular polygonal shapes that exhibit symmetries found abundantly in nature. This exact correspondence manifests itself only when the standard pitch tuning is set to 432Hz instead of the modern 440Hz, which is an indicator on the importance of this tuning, from a mathematical perspective at least.
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When integers are continuously plotted around each side of an icositetragon (24-side polygon), patterns of primes and a new classification of prime numbers (Quasi-primes) emerge.
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When integers are continuously plotted around each side of an icositetragon (24-sided polygon), patterns of primes and a new classification of prime numbers (Quasi-primes) emerge. This information presents a method to predict prime number incidence.
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When integers are continuously plotted around each side of an icositetragon (24-sided polygon), quaternion sets are demonstrated, allowing the identification of charge-associated quadripolarity.
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Unified mathematical models must establish numerical connections between all types of physical phenomenon. Inherent relationships between geometry and music are shown through the inscription of regular polygons within a unit circle.
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