ratio

Genre : Mathematics
Publisher : World Scientific
ISBN_10 : 9812386300
Copyright Year : 1997
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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.

đź“’Digit Ratio by John T. Manning

Genre : Science
Publisher : Rutgers University Press
ISBN_10 : 081353030X
Copyright Year : 2002
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DESCRIPTION : Could the length of your fingers indicate a predisposition to breast cancer? Or musical genius? Or homosexuality? In Digit Ratio, John T. Manning posits that relative lengths of the second and fourth digits in humans (2D:4D ratio) does provide such a window into hormone- and sex-related traits. It has been known for more than a century that men and women tend to differ in the relative lengths of their index (2D) and ring (4D) fingers, which upon casual observation seem fairly symmetrical. Men on average have fourth digits longer than their second digits, while women typically have the opposite. Digit ratios are unique in that they are fixed before birth, while other sexually dimorphic variables are fixed after puberty, and the same genes that control for finger length also control the development of the sex organs. The 2D:4D ratio is the only prenatal sexually dimorphic trait that measurably explains conditions linking testosterone, estrogen, and human development; the study of the ratio broadens our view of human ability, talent, behavior, disposition, health, and fertility. In this book, Manning presents evidence for how 2D:4D correlates with traits ranging from sperm counts, family size, musical genius, and sporting prowess, to autism, depression, homosexuality, heart attacks, and breast cancer, traits that are all linked with early exposure to sex hormones.

Genre : Mathematics
Publisher : Broadway Books
ISBN_10 : 0307485528
Copyright Year : 2008-11-12
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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. From the Hardcover edition.

Genre : Health & Fitness
Publisher : Karger Medical and Scientific Publishers
ISBN_10 : 9783805576406
Copyright Year : 2003-01-01
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DESCRIPTION : Studies on the evolutionary aspects of diet and molecular studies included in this volume indicate that human beings evolved on a diet that was balanced in the essential fatty acids (EFA). In fact, the ratio of omega-6/omega-3 EFA was 1/1 whereas present day diets in both developed and developing countries have a much higher ratio, between 5/1 and 50/1. Additional studies show that a high ratio of omega-6/omega-3 EFA is detrimental to health and may lead to the development of chronic diseases. Improving the dietary ratio by decreasing the omega-6 fatty acids and increasing the omega-3 fatty acids is essential for brain function and for the management of cardiovascular disease, arthritis and cancer. A ratio of 4/1 or less leads to lower dosage and to the reduction of adverse effects of drugs. This volume should be of interest to a large and varied audience of researchers in academia, industry, and government; cardiologists, geneticists, immunologists, neuroscientists, and cancer specialists; as well as nutritionists, dietitians, food scientists, agriculturists, economists and regulators.

Genre : Psychology
Publisher : Routledge
ISBN_10 : 9781134724741
Copyright Year : 2006-10-19
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DESCRIPTION : Women who are dominant are more likely to have sons. Demographic studies show that more male children are born after wars, yet most people believe that their baby's sex is a matter of chance - determined by the father's sperm. Valerie Grant presents evidence that the mother's personality - which is related to female testosterone levels - can actually influence which type of sperm fertilises the egg. Using data from human and animal studies Valerie Grant discusses the implications for human evolution, developmental psychology and reproductive biology. Her claims are controversial and the implications of her findings far reaching. Whether mothers have sons or daughters may not be a matter of chance. It may depend on which sex infant the mother is more suited to raise.

đź“’The Jesuit Ratio Studiorum by Vincent J. Duminuco

Genre : Education
Publisher : Fordham Univ Press
ISBN_10 : 0823220478
Copyright Year : 2000-01
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DESCRIPTION : The guiding pedagogical document for Jesuit education worldwide was definitively set out in a 1599 tome entitled Ratio Atque Instituto Studiorum Societatis Jesu, The Plan and Methodology of Jesuit Education.This plan has been praised by scholars from Francis Bacon in the seventeenth century to Harry Broudy and Paul Shore in our day. Some scholars and educators, upon learning of this tradition for the first time, have called it a best-kept secret.And so it was timely that, at the dawn of the new millennium, an invitational 400th anniversary celebration of the Ratio Studiorum would be held at Fordham University in October of 1999. The fruit of the scholarly papers presented there make up the substance of this book. In addition, two key documents of the late-twentieth-century renewal of Jesuit education are included in the appendixes of this volume. Both The Characteristics of Jesuit Education (1986) and Ignatian Pedagogy: A Practical Approach (1993) have been out of print in English and are provided here in full.

Genre :
Publisher : Uitgeverij Æneas BV
ISBN_10 : 9075365500
Copyright Year : 2002
File Format : PDF, EPUB
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Genre : Science
Publisher : Princeton University Press
ISBN_10 : 0691084122
Copyright Year : 1986-07-21
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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.

Genre : Mathematics
Publisher : Wilfrid Laurier Univ. Press
ISBN_10 : 9780889201521
Copyright Year : 1987
File Format : PDF, EPUB
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đź“’Ratio by Michael Ruhlman

Genre : Cooking
Publisher : Simon and Schuster
ISBN_10 : 9781416566120
Copyright Year : 2009-04-07
File Format : PDF, EPUB
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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.