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The Golden Ratio and Fibonacci Numbers

The Golden Ratio and Fibonacci Numbers Book
Author : R. A. Dunlap
Publisher : World Scientific
Release : 1997
ISBN : 9789812386304
Language : En, Es, Fr & De

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Book Description :

In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences. Contents: Basic Properties of the Golden Ratio; Geometric Problems in Two Dimensions; Geometric Problems in Three Dimensions; Fibonacci Numbers; Lucas Numbers and Generalized Fibonacci Numbers; Continued Fractions and Rational Approximants; Generalized Fibonacci Representation Theorems; Optimal Spacing and Search Algorithms; Commensurate and Incommensurate Projections; Penrose Tilings; Quasicrystallography; Biological Applications; Construction of the Regular Pentagon; The First 100 Fibonacci and Lucas Numbers; Relationships Involving the Golden Ratio and Generalized Fibonacci Numbers. Readership: Applied mathematicians.

The Golden Ratio

The Golden Ratio Book
Author : Mario Livio
Publisher : Crown
Release : 2008-11-12
ISBN : 0307485528
Language : En, Es, Fr & De

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Book Description :

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.

Digit Ratio

Digit Ratio Book
Author : John T. Manning
Publisher : Rutgers University Press
Release : 2002
ISBN : 9780813530307
Language : En, Es, Fr & De

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Book Description :

Manning (biological sciences, University of Liverpool) argues that the relative lengths of the second and fourth fingers are genetically linked to hormone- and sex-related traits, and by extension with sperm counts, family size, musical genius, sporting prowess, autism, depression, homosexuality, heart problems, and breast cancer. He suggests that the study of the ratio between the lengths of the second and fourth finger can broaden our understanding of human ability, behavior, and health. Three photographs, 38 figures, and eight tables are included. Annotation copyrighted by Book News Inc., Portland, OR.

Ratio Correlation

Ratio Correlation Book
Author : Felix Chayes
Publisher : University of Chicago Press
Release : 1971-09-15
ISBN : 0226102203
Language : En, Es, Fr & De

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Book Description :

Download Ratio Correlation book written by Felix Chayes, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Theoretical Studies on Sex Ratio Evolution

Theoretical Studies on Sex Ratio Evolution Book
Author : Samuel Karlin,Sabin Lessard
Publisher : Princeton University Press
Release : 1986-07-21
ISBN : 9780691084121
Language : En, Es, Fr & De

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Book Description :

This book deals with a key area of population genetics: the ratio of the sexes in a population, or the allocation of resources to male versus female reproductive function. Samuel Karlin and Sabin Lessard establish the formal theoretical aspects of the evolution of sex ratio within the constraints of genetic mechanisms of sex determination. Their results generalize and unify existing work on the topic, strengthening previous conceptions in some cases and, in other instances, offering new directions of research. There are two main approaches to understanding the causes and effects of sex ratio. One approach focuses on the optimization and adaptive functions of sex allocation, while the other emphasizes the consequences of genetic sex determination mechanisms. In discussing the utility of these two approaches, Professors Karlin and Lessard examine the principal sex-determining mechanisms and facts involved in sex ratio representations, the various genetic and environmental factors that contribute to adaptive sex expression, and the evolution of sex determining systems and controls. From a population genetic perspective, the authors derive evolutionary properties in support of the high incidence of 1:1 sex ratio in natural populations and investigate the conditions that can explain the occurrence of biased sex ratio.

FINANCIAL RATIO ANALYSIS

FINANCIAL RATIO ANALYSIS Book
Author : CHANDRA SEKHAR
Publisher : Chandra Sekhar
Release : 2020-06-25
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

It gives me a great pleasure and satisfaction to present this book “FINANCIAL RATIO ANALYSIS”. This book is new version of my old book “Financial Ratio Analysis”. The book will explain the need, purpose, and usefulness of Ratio analysis. I have explained almost all ratios based on latest financial statements of a leading manufacturing company for the financial year ended December 2019. Ratio wise hyperlink will help the reader to go quickly to the desired ratio. The main features of the book are simple understanding and key concepts. This book is useful to everyone in financial accounting field like students, Accounts executives, Financial analysts, etc. I hope that the book will help the readers to study in a focused manner. Any criticism and constructive suggestion in the direction of making the book a better teaching and studying manual will be gratefully acknowledged by the author. Suggestions will be incorporated in the subsequent editions. All the best …

Ratio

Ratio Book
Author : Michael Ruhlman
Publisher : Simon and Schuster
Release : 2009-04-07
ISBN : 1416566120
Language : En, Es, Fr & De

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Book Description :

Michael Ruhlman’s groundbreaking New York Times bestseller takes us to the very “truth” of cooking: it is not about recipes but rather about basic ratios and fundamental techniques that makes all food come together, simply. When you know a culinary ratio, it’s not like knowing a single recipe, it’s instantly knowing a thousand. Why spend time sorting through the millions of cookie recipes available in books, magazines, and on the Internet? Isn’t it easier just to remember 1-2-3? That’s the ratio of ingredients that always make a basic, delicious cookie dough: 1 part sugar, 2 parts fat, and 3 parts flour. From there, add anything you want—chocolate, lemon and orange zest, nuts, poppy seeds, cinnamon, cloves, nutmeg, almond extract, or peanut butter, to name a few favorite additions. Replace white sugar with brown for a darker, chewier cookie. Add baking powder and/or eggs for a lighter, airier texture. Ratios are the starting point from which a thousand variations begin. Ratios are the simple proportions of one ingredient to another. Biscuit dough is 3:1:2—or 3 parts flour, 1 part fat, and 2 parts liquid. This ratio is the beginning of many variations, and because the biscuit takes sweet and savory flavors with equal grace, you can top it with whipped cream and strawberries or sausage gravy. Vinaigrette is 3:1, or 3 parts oil to 1 part vinegar, and is one of the most useful sauces imaginable, giving everything from grilled meats and fish to steamed vegetables or lettuces intense flavor. Cooking with ratios will unchain you from recipes and set you free. With thirty-three ratios and suggestions for enticing variations, Ratio is the truth of cooking: basic preparations that teach us how the fundamental ingredients of the kitchen—water, flour, butter and oils, milk and cream, and eggs—work. Change the ratio and bread dough becomes pasta dough, cakes become muffins become popovers become crepes. As the culinary world fills up with overly complicated recipes and never-ending ingredient lists, Michael Ruhlman blasts through the surplus of information and delivers this innovative, straightforward book that cuts to the core of cooking. Ratio provides one of the greatest kitchen lessons there is—and it makes the cooking easier and more satisfying than ever.

State and Local Ratio Studies and Property Assessment

State and Local Ratio Studies and Property Assessment Book
Author : United States. Bureau of the Census
Publisher : Unknown
Release : 1975
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download State and Local Ratio Studies and Property Assessment book written by United States. Bureau of the Census, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Preferences for Canned Orange Juices that Vary in Brix acid Ratio

Preferences for Canned Orange Juices that Vary in Brix acid Ratio Book
Author : James Arthur Bayton
Publisher : Unknown
Release : 1954
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Preferences for Canned Orange Juices that Vary in Brix acid Ratio book written by James Arthur Bayton, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Ratio Scaling of Psychological Magnitude

Ratio Scaling of Psychological Magnitude Book
Author : Stanley Smith Stevens
Publisher : Psychology Press
Release : 1991
ISBN : 9780805807103
Language : En, Es, Fr & De

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Book Description :

First Published in 1990. Routledge is an imprint of Taylor & Francis, an informa company.

Spinoza s Philosophy of Ratio

Spinoza s Philosophy of Ratio Book
Author : Beth Lord
Publisher : Edinburgh University Press
Release : 2018-03-08
ISBN : 1474420443
Language : En, Es, Fr & De

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Book Description :

These essays explore the surprisingly varied dimensions of ratio: an unacknowledged keystone of Spinoza's thought. They take you from Spinoza's geometrical diagrams to his concepts of mind, body, the emotions and the cosmos.

Field Measurement of Water cement Ratio for Portland Cement Concrete

Field Measurement of Water cement Ratio for Portland Cement Concrete Book
Author : Amy M. Dowell
Publisher : Unknown
Release : 2002
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Field Measurement of Water cement Ratio for Portland Cement Concrete book written by Amy M. Dowell, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

State and Local Ratio Studies Property Tax Assessment and Transfer Taxes

State and Local Ratio Studies  Property Tax Assessment  and Transfer Taxes Book
Author : Anonim
Publisher : Unknown
Release : 1980
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download State and Local Ratio Studies Property Tax Assessment and Transfer Taxes book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Experimental Investigation of the Effect of Aspect Ratio and Mach Number on the Flutter of Cantilever Wings

Experimental Investigation of the Effect of Aspect Ratio and Mach Number on the Flutter of Cantilever Wings Book
Author : E. Widmayer,W. T. Lauten,S. A. Clevenston
Publisher : Unknown
Release : 1960
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Experimental Investigation of the Effect of Aspect Ratio and Mach Number on the Flutter of Cantilever Wings book written by E. Widmayer,W. T. Lauten,S. A. Clevenston, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Impact of Red Fox Predation on the Sex Ratio of Prairie Mallards

Impact of Red Fox Predation on the Sex Ratio of Prairie Mallards Book
Author : Douglas H. Johnson,Alan B. Sargeant
Publisher : Unknown
Release : 1977
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Impact of Red Fox Predation on the Sex Ratio of Prairie Mallards book written by Douglas H. Johnson,Alan B. Sargeant, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Noncavitating and Cavitating Performance of Two Low area ratio Water Jet Pumps with Throat Lengths of 5 66 Diameters

Noncavitating and Cavitating Performance of Two Low area ratio Water Jet Pumps with Throat Lengths of 5 66 Diameters Book
Author : Nelson L. Sanger
Publisher : Unknown
Release : 1968
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Noncavitating and Cavitating Performance of Two Low area ratio Water Jet Pumps with Throat Lengths of 5 66 Diameters book written by Nelson L. Sanger, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Flutter Analysis of Rectangular Wings of Very Low Aspect Ratio

Flutter Analysis of Rectangular Wings of Very Low Aspect Ratio Book
Author : Robert William Fralich,John M. Hedgepeth
Publisher : Unknown
Release : 1958
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

A flutter analysis, employing slender-body aerodynamic theory and thin-plate theory, is made for rectangular wings of very low aspect ratio with a constant thickness. The spanwise variation of wing deflection is assumed to be given by a parabola, and the chordwise variation is allowed complete freedom. The results show the vsriation of flutter speed and male shape with aspect ratio. Comparisons are made with additional resuits obtained by approximating the chordwise deflection shape by use of parabolic or cubic curves. The analysis shows that the cubic approximation gives good resuits for a ratio of chord to semispan less than 3.

Experimental Investigation of Aspect Ratio 1 Supercavitating Hydrofoils at Speeds Up to 185 Feet Per Second

Experimental Investigation of Aspect Ratio 1 Supercavitating Hydrofoils at Speeds Up to 185 Feet Per Second Book
Author : Kenneth W. Christopher,Virgil E. Johnson
Publisher : Unknown
Release : 1960
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Experimental Investigation of Aspect Ratio 1 Supercavitating Hydrofoils at Speeds Up to 185 Feet Per Second book written by Kenneth W. Christopher,Virgil E. Johnson, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Voltage Ratio Detector for Millivolt Signals

Voltage Ratio Detector for Millivolt Signals Book
Author : J. R. Houghton
Publisher : Unknown
Release : 1965
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Voltage Ratio Detector for Millivolt Signals book written by J. R. Houghton, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Dosage Calculations A Ratio Proportion Approach

Dosage Calculations  A Ratio Proportion Approach Book
Author : Gloria D. Pickar,Amy Pickar-Abernethy
Publisher : Cengage Learning
Release : 2015-01-06
ISBN : 1305446011
Language : En, Es, Fr & De

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Book Description :

An excellent resource for anyone in or entering the field, market-leading DOSAGE CALCULATIONS: A RATIO-PROPORTION APPROACH, fourth edition, teaches users how to reduce errors while building their confidence in dosage calculation. Extremely reader friendly, the text includes a comprehensive math review, full-color drug labels, and numerous critical thinking assessments. It carefully examines both basic and advanced calculations, including intravenous medications and those specific to the pediatric patient. Reducing the math anxiety that many readers have, the text's unique three-step method of calculating dosages-Convert, Think, Calculate-trains students to approach calculations logically and with a decreased risk of medication errors. The fourth edition reflects the most current drugs and protocol, regulations on medication abbreviations, medication administration technologies, and safe medication practices. Clinical simulations and Clinical Reasoning Skills scenarios based on QSEN principles help students develop clinical reasoning skills, while Section Examinations include test items formatted like graduate licensure examinations. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.