From Pascal Triangle to Golden Pyramid

Mamombe, Lovemore

doi:10.9734/arjom/2017/29964

“…Most striking is the number of elements in the pyramid levels of silver pyramids which follows the sequence = (4.1), thereby representing an important law of mathematical beauty. These silver pyramids, like the golden pyramids [2], have got important applications, the obvious ones being in communication.…”

Section: Resultsmentioning

confidence: 99%

Universal Computing Machine for Number Genetics in the Proportiones Perfectus Theory

Mamombe¹

2019

JAMCS

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The proportiones perfectus law states that σ_x^y=(x+√(x^2+4y))/2 is a proportione perfectus if 1≤y≤x such that for an arbitrary positive integer , there exists an integer sequence defined simultaneously by the quasigeometric relation h_(n+1)=round(σ_x^y h_n ),n≥1 and the arithmetic relation h_(n+2)=〖xh〗_(n+1)+〖yh〗_n,n≥1. When x=y=1 σ_x^y is the golden mean. When x=2,y=1,σ_x^y is the silver mean. In previous works we introduced the theory of number genetics – a framework of logic within which the golden section is studied. In this work we apply the concept to all proportiones perfectus. Let be defined as above. Furthermore, let h1 satisfy {█(round(h_1/(σ_x^y ))=w@round(wσ_x^y)≠h_1 ). ┤Now let H'nbe Hn with h1=1 Again let be defined as A robust universal computing machine is herein developed for the purpose of establishing the relationship h_i=g_(n+i-1)±h_i^',i,n≥1, which relationship is key to the logic protocol. It is clear therefore that this system of logic presents as the building block of every (including itself) within a particular σ_x^y regime. Clearly number genetics takes central place in the proportiones perfectus theory.

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“…Mamombe demonstrates the link between 137 and 117 in his analysis of the Fibonacci sequence and describes "its significance to the theory of the golden section and its relationship with the fine-structure constant," [61], also see the discussion of Eq. (17) and [62]. Also, 144/85 e/φ 1/4A.…”

Section: The Golden Ratio and Ne-structure Constantmentioning

confidence: 93%

Fine-Structure Constant from Golden Ratio Geometry

Sherbon¹

2018

Preprint

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After a brief review of the golden ratio in history and our previous exposition of the finestructure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. This research is extended and the fine-structure constant is then calculated in powers of the golden ratio to an accuracy consistent with the most recent publications. The mathematical constants associated with the golden ratio are also involved in both the calculation of the fine-structure constant and the proton-electron mass ratio. These constants are included in symbolic geometry of historical relevance in the science of the ancients.

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“…Mamombe demonstrates the link between 137 and 117 in his analysis of the Fibonacci sequence and describes "its significance to the theory of the golden section and its relationship with the fine-structure constant," [61], also see the discussion of Eq. 17and [62]. Also, 144/85 e/φ 1/4A.…”

Section: The Golden Ratio and Ne-structure Constantmentioning

confidence: 95%

Fine-Structure Constant from Golden Ratio Geometry

Sherbon¹

2018

SSRN Journal

1

0

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After a brief review of the golden ratio in history and our previous exposition of the finestructure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. This research is extended and the fine-structure constant is then calculated in powers of the golden ratio to an accuracy consistent with the most recent publications. The mathematical constants associated with the golden ratio are also involved in both the calculation of the fine-structure constant and the proton-electron mass ratio. These constants are included in symbolic geometry of historical relevance in the science of the ancients.

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From Pascal Triangle to Golden Pyramid

Cited by 3 publications

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Universal Computing Machine for Number Genetics in the Proportiones Perfectus Theory

Universal Computing Machine for Number Genetics in the Proportiones Perfectus Theory

Fine-Structure Constant from Golden Ratio Geometry

Fine-Structure Constant from Golden Ratio Geometry

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