Practical Conic Sections

The Geometric Properties of Ellipses, Parabolas and Hyperbolas

Author: J. W. Downs

Publisher: Courier Corporation

ISBN: 0486148882

Category: Mathematics

Page: 112

View: 7739

Using examples from everyday life, this text studies ellipses, parabolas, and hyperbolas. Explores their ancient origins and describes the reflective properties and roles of curves in design applications. 1993 edition. Includes 98 figures.
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Geometri?eskie svojstva krivyh vtorogo porâdka

Author: Arseny V. Akopyan

Publisher: American Mathematical Soc.

ISBN: 9780821884324

Category: Mathematics

Page: 134

View: 4936

"Geometry Of Conics deals with the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics."--Publisher's website.
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Analytical Conics

Author: Barry Spain

Publisher: Courier Corporation

ISBN: 0486457737

Category: Mathematics

Page: 145

View: 4397

This concise text introduces students to analytical geometry, covering basic ideas and methods. Readily intelligible to any student with a sound mathematical background, it is designed both for undergraduates and for math majors. It will prove particularly valuable in preparing readers for more advanced treatments. The text begins with an overview of the analytical geometry of the straight line, circle, and the conics in their standard forms. It proceeds to discussions of translations and rotations of axes, and of the general equation of the second degree. The concept of the line at infinity is introduced, and the main properties of conics and pencils of conics are derived from the general equation. The fundamentals of cross-ratio, homographic correspondence, and line-coordinates are explored, including applications of the latter to focal properties. The final chapter provides a compact account of generalized homogeneous coordinates, and a helpful appendix presents solutions to many of the examples.
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Excursions in Geometry

Author: Charles Stanley Ogilvy

Publisher: Courier Corporation

ISBN: 0486265307

Category: Mathematics

Page: 178

View: 3189

A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.
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Conics: Text

Author: Keith Kendig

Publisher: Cambridge University Press

ISBN: 9780883853351

Category: Mathematics

Page: 403

View: 3785

This book engages the reader in a journey of discovery through a spirited discussion among three characters: Philosopher, Teacher and Student. Throughout the book, Philosopher pursues his dream of a unified theory of conics, where exceptions are banished. With a helpful teacher and example-hungry student, the trio soon finds that conics reveal much of their beauty when viewed over the complex numbers. It is profusely illustrated with pictures, worked-out examples, and a CD containing 36 applets. Conics is written in an easy, conversational style, and many historical tidbits and other points of interest are scattered throughout the text. Many students can self-study the book without outside help. This book is ideal for anyone having a little exposure to linear algebra and complex numbers.
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Lines and Curves

A Practical Geometry Handbook

Author: Victor Gutenmacher,N.B. Vasilyev

Publisher: Springer Science & Business Media

ISBN: 1475738099

Category: Mathematics

Page: 156

View: 3066

Broad appeal to undergraduate teachers, students, and engineers; Concise descriptions of properties of basic planar curves from different perspectives; useful handbook for software engineers; A special chapter---"Geometry on the Web"---will further enhance the usefulness of this book as an informal tutorial resource.; Good mathematical notation, descriptions of properties of lines and curves, and the illustration of geometric concepts facilitate the design of computer graphics tools and computer animation.; Video game designers, for example, will find a clear discussion and illustration of hard-to-understand trajectory design concepts.; Good supplementary text for geometry courses at the undergraduate and advanced high school levels
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Conics and Cubics

A Concrete Introduction to Algebraic Curves

Author: Robert Bix

Publisher: Springer Science & Business Media

ISBN: 1475729758

Category: Mathematics

Page: 292

View: 4027

Algebraic curves are the graphs of polynomial equations in two vari 3 ables, such as y3 + 5xy2 = x + 2xy. By focusing on curves of degree at most 3-lines, conics, and cubics-this book aims to fill the gap between the familiar subject of analytic geometry and the general study of alge braic curves. This text is designed for a one-semester class that serves both as a a geometry course for mathematics majors in general and as a sequel to college geometry for teachers of secondary school mathe matics. The only prerequisite is first-year calculus. On the one hand, this book can serve as a text for an undergraduate geometry course for all mathematics majors. Algebraic geometry unites algebra, geometry, topology, and analysis, and it is one of the most exciting areas of modem mathematics. Unfortunately, the subject is not easily accessible, and most introductory courses require a prohibitive amount of mathematical machinery. We avoid this problem by focusing on curves of degree at most 3. This keeps the results tangible and the proofs natural. It lets us emphasize the power of two fundamental ideas, homogeneous coordinates and intersection multiplicities.
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Fundamentals of Astrodynamics

Author: Roger R. Bate,Donald D. Mueller,Jerry E. White

Publisher: Courier Corporation

ISBN: 9780486600611

Category: Technology & Engineering

Page: 455

View: 4687

Teaching text developed by U.S. Air Force Academy and designed as a first course emphasizes the universal variable formulation. Develops the basic two-body and n-body equations of motion; orbit determination; classical orbital elements, coordinate transformations; differential correction; more. Includes specialized applications to lunar and interplanetary flight, example problems, exercises. 1971 edition.
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The Advanced Geometry of Plane Curves and Their Applications

Author: C. Zwikker

Publisher: Courier Corporation

ISBN: 0486153436

Category: Mathematics

Page: 320

View: 8625

This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. 1950 edition.
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The Ellipse

A Historical and Mathematical Journey

Author: Arthur Mazer

Publisher: John Wiley & Sons

ISBN: 111821143X

Category: Mathematics

Page: 320

View: 6214

Explores the development of the ellipse and presents mathematical concepts within a rich, historical context The Ellipse features a unique, narrative approach when presenting the development of this mathematical fixture, revealing its parallels to mankind's advancement from the Counter-Reformation to the Enlightenment. Incorporating illuminating historical background and examples, the author brings together basic concepts from geometry, algebra, trigonometry, and calculus to uncover the ellipse as the shape of a planet's orbit around the sun. The book begins with a discussion that tells the story of man's pursuit of the ellipse, from Aristarchus to Newton's successful unveiling nearly two millenniums later. The narrative draws insightful similarities between mathematical developments and the advancement of the Greeks, Romans, Medieval Europe, and Renaissance Europe. The author begins each chapter by setting the historical backdrop that is pertinent to the mathematical material that is discussed, equipping readers with the knowledge to fully grasp the presented examples and derive the ellipse as the planetary pathway. All topics are presented in both historical and mathematical contexts, and additional mathematical excursions are clearly marked so that readers have a guidepost for the materials' relevance to the development of the ellipse. The Ellipse is an excellent book for courses on the history of mathematics at the undergraduate level. It is also a fascinating reference for mathematicians, engineers, or anyone with a general interest in historical mathematics.
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Geometry: A Comprehensive Course

Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

View: 4079

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.
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The Geometry of René Descartes

with a Facsimile of the First Edition

Author: René Descartes

Publisher: Courier Corporation

ISBN: 0486158179

Category: Mathematics

Page: 272

View: 6410

The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John Stuart Mill.
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Elementary Calculus

An Infinitesimal Approach

Author: H. Jerome Keisler

Publisher: Courier Corporation

ISBN: 0486484521

Category: Mathematics

Page: 913

View: 805

This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems. Additional subjects include transcendental functions, series, vectors, partial derivatives, and multiple integrals. 2007 edition.
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An Imaginary Tale

The Story of √-1

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400833894

Category: Mathematics

Page: 296

View: 5586

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.
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Geometry and the Visual Arts

Author: Daniel Pedoe

Publisher: Courier Corporation

ISBN: 9780486244587

Category: Mathematics

Page: 296

View: 6722

This survey traces the effects of geometry on artistic achievement and clearly discusses its importance to artists and scientists. It also surveys projective geometry, mathematical curves, theories of perspective, architectural form, and concepts of space.
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The Creation of the Universe

Author: George Gamow

Publisher: Courier Corporation

ISBN: 9780486438689

Category: Science

Page: 146

View: 9518

Lively and authoritative, this survey by a renowned physicist explains the formation of the galaxies and defines the concept of an ever-expanding universe in simple terms. 1961 edition. 40 figures.
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Mathematical Thought From Ancient to Modern Times

Author: Morris Kline

Publisher: Oxford University Press

ISBN: 0199770468

Category: Mathematics

Page: 432

View: 5173

The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.
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Mathematical Foundations of Statistical Mechanics

Author: Aleksandr I?Akovlevich Khinchin

Publisher: Courier Corporation

ISBN: 9780486601472

Category: Mathematics

Page: 179

View: 3549

Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.
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Partial Differential Equations for Scientists and Engineers

Author: Stanley J. Farlow

Publisher: Courier Corporation

ISBN: 048667620X

Category: Mathematics

Page: 414

View: 2760

This highly useful text shows the reader how to formulate a partial differential equation from the physical problem and how to solve the equation.
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