scholarly journals Metallic Means : Beyond the Golden Ratio, New Mathematics and Geometry of all Metallic Ratios based upon Right Triangles, The Formation of the Triples of Metallic Means, And their Classical Correspondence with Pythagorean Triples and p≡1(mod 4) Primes, A

2021 ◽  
Vol 20 ◽  
pp. 250-266
Author(s):  
Dr. Chetansing Rajput
Keyword(s):  
Golden Ratio ◽  
Close Correspondence ◽  
Pythagorean Triples ◽  
Classical Correspondence

This paper brings together the newly discovered generalised geometry of all Metallic Means and the recently published mathematical formulae those provide the precise correlations between different Metallic Ratios. The paper also puts forward the concept of the “Triples of Metallic Means”. This work also introduces the close correspondence between Metallic Ratios and the Pythagorean Triples as well as Pythagorean Primes. Moreover, this work illustrates the intriguing relationship between Metallic Numbers and the Digits 3 6 9.

Discovering Relationships Involving Baravelle Spirals

2006 ◽  
Vol 99 (6) ◽  
pp. 394-400
Author(s):  
Jeffrey J. Wanko
Keyword(s):  
Preservice Teachers ◽  
Performing Arts ◽  
Golden Ratio ◽  
Underlying Structure ◽  
Mathematical Concepts ◽  
Capstone Course ◽  
Visual And Performing Arts ◽  
Pythagorean Triples ◽  
Logarithmic Spirals ◽  
Penrose Tiles

When designing a mathematics capstone course for preservice teachers entitled 'Mathematical Patterns and Structures through Inquiry,” I wanted to include contexts in which mathematics provides the underlying structure for various visual and performing arts. The book Mathematical Quilts: No Sewing Required (Venters and Ellison 1999, p. 78) looks at a number of ways that mathematical concepts—such as the golden ratio, logarithmic spirals, Pythagorean triples, and Penrose tiles—are useful to know when designing various quilt patterns.

A group structure on the golden triples

2021 ◽  
Vol 105 (562) ◽  
pp. 87-97
Author(s):  
Howard Sporn
Keyword(s):  
Mathematics Teachers ◽  
Group Structure ◽  
Golden Ratio ◽  
Fibonacci Numbers ◽  
Mathematics Students ◽  
Pythagorean Triples ◽  
And Mathematics

Some favourite topics of both mathematics teachers and mathematics students are the golden ratio, Fibonacci numbers, groups, and Pythagorean triples. The material of this paper involves the first three, and there are some analogies with the fourth.

On-Line Calculation of Pulmonary Mechanics by Digital Computer

1978 ◽  
Vol 17 (04) ◽  
pp. 261-272 ◽  
Author(s):  
Y. Brault ◽  
G. Atlan ◽  
H. Lorino ◽  
A. Harf ◽  
A.-M. Lorino ◽  
...  
Keyword(s):  
Time Pressure ◽  
Lung Compliance ◽  
Pulmonary Mechanics ◽  
Close Correspondence ◽  
Standard Equipment ◽  
On Demand ◽  
On Line ◽  
The Subject ◽  
Ventilatory Mechanics ◽  
Computerized System

A system was built up around a minicomputer to process in real time pressure and flow signals collected during the course of three ventilatory mechanics tests: the calculation of the lung volume, the evaluation of the static lung compliance, the analysis of the forced expiratory performance. The subject is seated in an open body Plethysmograph, which allows for the instantaneous calculation of changes in the volume of his thorax and abdomen. The system is controlled through a graphics console which displays the sampled curves and the results of data processing. In addition, the signals can be stored on demand onto a magnetic tape so that the method can be tested and improved off line. The results obtained in healthy volunteers are highly reproducible. A close correspondence is found both in patients and volunteers between computer-derived and hand-calculated results. The computerized system has become a standard equipment of our Lung Function Department, where it allows for a rapid quantitative analysis of lung volumes, lung elasticity and bronchial airflow.

On the Origin of Four Pi in Physics

2016 ◽  
pp. 3994-4013
Author(s):  
Aaron Hanken
Keyword(s):  
Black Hole ◽  
Surface Area ◽  
Single Particles ◽  
Pythagorean Triples ◽  
Free Particles ◽  
Close Relationship ◽  
Dimensional Parameters ◽  
Gaussian Surface ◽  
Planck Energy ◽  
The Universe

We find the highest symmetry between the fields intrinsic to free particles (free particles having only mass, charge and spin), and show these fields symmetries and their close relationship to force and entropy. The Boltzmann Constant is equal to the natural entropy, in that it is The Planck Energy over The Planck Temperature. This completes a needed symmetry in The Bekenstein-Hawking Entropy. Upon substitution of Planck Units into The Schwarzschild Radius, we find that the mass and radius of any black hole define both the gravitational constant and the natural force. We find that the Gaussian Surface area about a particle is equal to the surface area of an equally massed black hole if we define the gravitational field of that particle to be the quotient of The Planck Force and the particles mass. By these simple substitutions we find that gravity is quantized in units of surface entropy. We also find Pythagorean Triples are resting within the dimensional parameters of Special Relativity, and show this to be the dimensional aspects of single particles observing one another, coupled with the intrinsic Hubble nature of the universe.

Data visualization quality in a geographic information system using golden ratio properties

2018 ◽  
pp. 46-57
Author(s):  
A. V. Voronin ◽  
G. N. Maltsev ◽  
M. Yu. Sokhen
Keyword(s):  
Information System ◽  
Geographic Information System ◽  
Data Visualization ◽  
Golden Ratio ◽  
Quality Criterion ◽  
Geographic Information ◽  
Control Device ◽  
Video Data ◽  
Geoinformation Systems ◽  
System Operator

Introduction:Data visualization quality is important for the work of a geographic information system operator, determining the conditions under which he or she makes decisions concerning the displayed data. Visual perception patterns associated with the golden ratio properties allow us to formulate a criterion for data visualization quality which would characterize the possibilities of the operator’s complex perception of the video data displayed on a control device screen in the form of an electronic card.Purpose:Substantiation of a data visualization quality criterion for geoinformation systems using the golden ratio properties, and the study of the conditions for providing good visualization quality for geodata and metadata on a video control device screen in accordance with the proposed criterion.Methods:A formal definition of the data visualization quality criterion in geoinformation systems using the coefficient of the screen area information coverage as an index whose optimal value corresponds to the mathematical definition of the golden ratio; and the study of the properties of this criterion. Results: Based on the conducted analysis of visual perception of video data and golden ratio properties during the data visualization, a criterion is proposed for data visualization quality, which uses the golden ratio properties and characterizes the possibilities of complex perception of video data in an electronic map form by a geographic information system operator. Iteration algorithms for choosing the video data display scale are developed, based on the visualization quality criterion and related to the golden ratio properties. These are the basic algorithm used for each geodata layer represented on the electronicmap, and an algorithm of successive analysis of various layers of the displayed geodata. The choice of a video data display scale in accordance with the developed algorithms can be preliminarily carried out by the system operator using the parameters of standard electronic maps and geodata/metadata sets typical for the current applied problem. We have studied how the scale of the geodata and metadata displayed on an electronic map affects their visualization quality on screens of various sizes. For the considered standard volumes of displayed geodata and metadata, the best visualization quality was achieved when they were displayed on a standard computer monitor, as opposed to a portable notebook or visualization screen.Practical relevance:The proposed criterion and the recommendations for choosing a screen size for the video monitoring device or the structures of the displayed geo-objects and metadata can be used in the design of geoinformation systems, or for preliminary choice of the displayed data structure by a geoinformation system operator.

A novel local search method for LSGO with golden ratio and dynamic search step

2020 ◽  
Author(s):  
Havva Gül Koçer ◽  
Sait Ali Uymaz
Keyword(s):  
Local Search ◽  
Golden Ratio ◽  
Search Method ◽  
Local Search Method ◽  
Dynamic Search

scholarly journals Disentangling the enigma of multi-structured economic cycles - A new appearance of the golden ratio

2021 ◽  
Vol 169 ◽  
pp. 120793
Author(s):  
E.A. de Groot ◽  
R. Segers ◽  
D. Prins
Keyword(s):  
Golden Ratio ◽  
Economic Cycles

scholarly journals Complexity of quantum motion and quantum-classical correspondence: A phase-space approach

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Jiaozi Wang ◽  
Giuliano Benenti ◽  
Giulio Casati ◽  
Wen-ge Wang
Keyword(s):  
Phase Space ◽  
Classical Correspondence ◽  
Quantum Motion ◽  
Space Approach

scholarly journals Forecasting and Modelling the Uncertainty of Low Voltage Network Demand and the Effect of Renewable Energy Sources

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2151
Author(s):  
Feras Alasali ◽  
Husam Foudeh ◽  
Esraa Mousa Ali ◽  
Khaled Nusair ◽  
William Holderbaum
Keyword(s):  
Renewable Energy ◽  
Low Voltage ◽  
Renewable Energy Sources ◽  
Golden Ratio ◽  
Clean Energy ◽  
Energy Sources ◽  
Percentage Error ◽  
Ann Model ◽  
Demand Forecast ◽  
Pv System

More and more households are using renewable energy sources, and this will continue as the world moves towards a clean energy future and new patterns in demands for electricity. This creates significant novel challenges for Distribution Network Operators (DNOs) such as volatile net demand behavior and predicting Low Voltage (LV) demand. There is a lack of understanding of modern LV networks’ demand and renewable energy sources behavior. This article starts with an investigation into the unique characteristics of householder demand behavior in Jordan, connected to Photovoltaics (PV) systems. Previous studies have focused mostly on forecasting LV level demand without considering renewable energy sources, disaggregation demand and the weather conditions at the LV level. In this study, we provide detailed LV demand analysis and a variety of forecasting methods in terms of a probabilistic, new optimization learning algorithm called the Golden Ratio Optimization Method (GROM) for an Artificial Neural Network (ANN) model for rolling and point forecasting. Short-term forecasting models have been designed and developed to generate future scenarios for different disaggregation demand levels from households, small cities, net demands and PV system output. The results show that the volatile behavior of LV networks connected to the PV system creates substantial forecasting challenges. The mean absolute percentage error (MAPE) for the ANN-GROM model improved by 41.2% for household demand forecast compared to the traditional ANN model.

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