The Universe of Conics

From the ancient Greeks to 21st century developments

Author: Georg Glaeser,Hellmuth Stachel,Boris Odehnal

Publisher: Springer

ISBN: 3662454505

Category: Mathematics

Page: 488

View: 6214


This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.

Ancient Greece

Author: Thomas R. Martin

Publisher: Yale University Press

ISBN: 0300190638

Category: History

Page: 256

View: 7259


DIVIn this compact yet comprehensive history of ancient Greece, Thomas R. Martin brings alive Greek civilization from its Stone Age roots to the fourth century B.C. Focusing on the development of the Greek city-state and the society, culture, and architecture of Athens in its Golden Age, Martin integrates political, military, social, and cultural history in a book that will appeal to students and general readers alike. Now in its second edition, this classic work now features new maps and illustrations, a new introduction, and updates throughout./divDIV /divDIV“A limpidly written, highly accessible, and comprehensive history of Greece and its civilizations from prehistory through the collapse of Alexander the Great’s empire. . . . A highly readable account of ancient Greece, particularly useful as an introductory or review text for the student or the general reader.�—Kirkus Reviews/divDIV /divDIV“A polished and informative work that will be useful for general readers and students.�—Daniel Tompkins, Temple University/divDIV/div

Observations and Predictions of Eclipse Times by Early Astronomers

Author: J.M. Steele

Publisher: Springer Science & Business Media

ISBN: 9401595283

Category: History

Page: 324

View: 8926


Eclipses have long been seen as important celestial phenomena, whether as omens affecting the future of kingdoms, or as useful astronomical events to help in deriving essential parameters for theories of the motion of the moon and sun. This is the first book to collect together all presently known records of timed eclipse observations and predictions from antiquity to the time of the invention of the telescope. In addition to cataloguing and assessing the accuracy of the various records, which come from regions as diverse as Ancient Mesopotamia, China, and Europe, the sources in which they are found are described in detail. Related questions such as what type of clocks were used to time the observations, how the eclipse predictions were made, and how these prediction schemes were derived from the available observations are also considered. The results of this investigation have important consequences for how we understand the relationship between observation and theory in early science and the role of astronomy in early cultures, and will be of interest to historians of science, astronomers, and ancient and medieval historians.

The Geometrical Beauty of Plants

Author: Johan Gielis

Publisher: Springer

ISBN: 9462391513

Category: Science

Page: 229

View: 4938


This book focuses on the origin of the Gielis curves, surfaces and transformations in the plant sciences. It is shown how these transformations, as a generalization of the Pythagorean Theorem, play an essential role in plant morphology and development. New insights show how plants can be understood as developing mathematical equations, which opens the possibility of directly solving analytically any boundary value problems (stress, diffusion, vibration...) . The book illustrates how form, development and evolution of plants unveil as a musical symphony. The reader will gain insight in how the methods are applicable in many divers scientific and technological fields.

History of Western Philosophy

Collectors Edition

Author: Bertrand Russell

Publisher: Routledge

ISBN: 1135692912

Category: Philosophy

Page: 728

View: 1255


Now in a special gift edition, and featuring a brand new foreword by Anthony Gottlieb, this is a dazzlingly unique exploration of the works of significant philosophers throughout the ages and a definitive must-have title that deserves a revered place on every bookshelf.

Celestial Treasury

From the Music of the Spheres to the Conquest of Space

Author: Marc Lachièze-Rey,Jean-Pierre Luminet,Bibliothèque Nationale de France. Paris

Publisher: Cambridge University Press

ISBN: 9780521800402

Category: Art

Page: 207

View: 7553


A breathtaking survey of the richness of astronomical theories and illustrations through the ages.

Math Tools

500+ Applications in Science and Arts

Author: Georg Glaeser

Publisher: Springer

ISBN: 3319669605

Category: Mathematics

Page: 562

View: 1304


In this book, topics such as algebra, trigonometry, calculus and statistics are brought to life through over 500 applications ranging from biology, physics and chemistry to astronomy, geography and music. With over 600 illustrations emphasizing the beauty of mathematics, Math Tools complements more theoretical textbooks on the market, bringing the subject closer to the reader and providing a useful reference to students. By highlighting the ubiquity of mathematics in practical fields, the book will appeal not only to students and teachers, but to anyone with a keen interest in mathematics and its applications.

A Cultural History of Physics

Author: Károly Simonyi

Publisher: CRC Press

ISBN: 1439865116

Category: Mathematics

Page: 636

View: 336


While the physical sciences are a continuously evolving source of technology and of understanding about our world, they have become so specialized and rely on so much prerequisite knowledge that for many people today the divide between the sciences and the humanities seems even greater than it was when C. P. Snow delivered his famous 1959 lecture, "The Two Cultures." In A Cultural History of Physics, Hungarian scientist and educator Károly Simonyi succeeds in bridging this chasm by describing the experimental methods and theoretical interpretations that created scientific knowledge, from ancient times to the present day, within the cultural environment in which it was formed. Unlike any other work of its kind, Simonyi’s seminal opus explores the interplay of science and the humanities to convey the wonder and excitement of scientific development throughout the ages. These pages contain an abundance of excerpts from original resources, a wide array of clear and straightforward explanations, and an astonishing wealth of insight, revealing the historical progress of science and inviting readers into a dialogue with the great scientific minds that shaped our current understanding of physics. Beautifully illustrated, accurate in its scientific content and broad in its historical and cultural perspective, this book will be a valuable reference for scholars and an inspiration to aspiring scientists and humanists who believe that science is an integral part of our culture.


An Approach Through Problems

Author: B.J. Venkatachala

Publisher: Springer

ISBN: 9811087326

Category: Mathematics

Page: 519

View: 1051


This book discusses about the basic topics on inequalities and their applications. These include the arithmetic mean–geometric mean inequality, Cauchy–Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. The book contains over 400 problems with their solutions. A chapter on geometric inequalities is a special feature of this book. Most of these problems are from International Mathematical Olympiads and from many national mathematical Olympiads. The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students who are consolidating their knowledge of inequalities and their applications.

How Modern Science Came Into the World

Four Civilizations, One 17th-century Breakthrough

Author: H. F. Cohen

Publisher: Amsterdam University Press

ISBN: 9089642390

Category: History

Page: 784

View: 6799


Once upon a time 'The Scientific Revolution of the 17th century' was an innovative concept that inspired a stimulating narrative of how modern science came into the world. Half a century later, what we now know as 'the master narrative' serves rather as a strait-jacket - so often events and contexts just fail to fit in. No attempt has been made so far to replace the master narrative. H. Floris Cohen now comes up with precisely such a replacement. Key to his path-breaking analysis-cum-narrative is a vision of the Scientific Revolution as made up of six distinct yet narrowly interconnected, revolutionary transformations, each of some twenty-five to thirty years' duration. This vision enables him to explain how modern science could come about in Europe rather than in Greece, China, or the Islamic world. It also enables him to explain how half-way into the 17th century a vast crisis of legitimacy could arise and, in the end, be overcome.

The Reception of Darwinism in the Iberian World

Spain, Spanish America, and Brazil

Author: T.F Glick

Publisher: Springer Science & Business Media

ISBN: 9781402000829

Category: History

Page: 272

View: 2082


This book provides both for academic historians and the general reader a broad perspective on Darwin's impact in the Spanish- and Portuguese-speaking worlds. In Latin American countries with black and Amerindian populations, evolutionary theory was quickly mobilized for theorizing racial differences, while in Spain attention was focused on class differentiation, explained by a series of Darwinian, Social Darwinist, and Eugenic hypotheses. The wide variety of approaches to evolutionary and social theory in countries whose culture was very similar points illuminates those issues thought to be of particular significance for national identity, whether political, ethnic, or racial.

Lie Groups and Geometric Aspects of Isometric Actions

Author: Marcos M. Alexandrino,Renato G. Bettiol

Publisher: Springer

ISBN: 3319166131

Category: Mathematics

Page: 213

View: 9501


This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.

Geometry by Its History

Author: Alexander Ostermann,Gerhard Wanner

Publisher: Springer Science & Business Media

ISBN: 3642291635

Category: Mathematics

Page: 440

View: 699


In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.

Aristarchus of Samos, the Ancient Copernicus

A History of Greek Astronomy to Aristarchus, Together with Aristarchus's Treatise on the Sizes and Distances of the Sun and Moon

Author: Thomas Heath

Publisher: Cambridge University Press

ISBN: 1108062334

Category: Mathematics

Page: 440

View: 5252


Prefaced by a history of ancient Greek astronomy, this 1913 edition of Aristarchus' only surviving treatise includes a facing-page translation.

Mathematics Across Cultures

The History of Non-Western Mathematics

Author: Helaine Selin

Publisher: Springer Science & Business Media

ISBN: 9401143013

Category: Mathematics

Page: 479

View: 1909


Mathematics Across Cultures: A History of Non-Western Mathematics consists of essays dealing with the mathematical knowledge and beliefs of cultures outside the United States and Europe. In addition to articles surveying Islamic, Chinese, Native American, Aboriginal Australian, Inca, Egyptian, and African mathematics, among others, the book includes essays on Rationality, Logic and Mathematics, and the transfer of knowledge from East to West. The essays address the connections between science and culture and relate the mathematical practices to the cultures which produced them. Each essay is well illustrated and contains an extensive bibliography. Because the geographic range is global, the book fills a gap in both the history of science and in cultural studies. It should find a place on the bookshelves of advanced undergraduate students, graduate students, and scholars, as well as in libraries serving those groups.

Exploring Mathematics

Problem-Solving and Proof

Author: Daniel Grieser

Publisher: Springer

ISBN: 3319903217

Category: Mathematics

Page: 298

View: 2873


Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.

5000 Years of Geometry

Mathematics in History and Culture

Author: Christoph J. Scriba,Peter Schreiber

Publisher: Birkhäuser

ISBN: 3034808984

Category: Mathematics

Page: 626

View: 2133


The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)