Geometry With Applications And Proofs

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Geometry with Applications and Proofs

Aad Goddijn,Martin Kindt,Wolfgang Reuter
Geometry with Applications and Proofs Book PDF

Author : Aad Goddijn,Martin Kindt,Wolfgang Reuter
Publisher : Springer
Page : 342 pages
File Size : 40,9 Mb
Release : 2014-12-03
Category : Education
ISBN : 9789462098602

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Geometry with Applications and Proofs by Aad Goddijn,Martin Kindt,Wolfgang Reuter Pdf

This book shows how geometry can be learned by starting with real world problems which are solved by intuition, common sense reasoning and experiments. Gradually the more formal demands of mathematical proofs get their proper place and make it possible to explore new applications. This process helps students to feel the need for precise definitions and procedures, to contribute to the construction of an axiomatic system, and to experience the power of systematic reasoning. The course is designed for students in a Nature & Technology strand which prepares for studying the sciences or technology at university level. Its goal was basically to reintroduce ‘proof’ in a meaningful way in the late 1990s Dutch secondary education curriculum. Following the educational view of the Freudenthal Institute this is not done by stating Euclid’s axioms on page one, but rather a starting point is chosen in students’ intuitions and tentative solutions of problems that are experienced as real and relevant. The photograph on the cover shows students exploring one of the problems from the midpart of the course in the computerlab.

Geometry with Applications and Proofs

A. J. Goddijn,Martin Kindt,Wolfgang Reuter,Danny Dullens
Geometry with Applications and Proofs Book PDF

Author : A. J. Goddijn,Martin Kindt,Wolfgang Reuter,Danny Dullens
Publisher : Unknown
Page : 267 pages
File Size : 47,5 Mb
Release : 2004
Category : Electronic
ISBN : OCLC:66035642

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Geometry with Applications and Proofs by A. J. Goddijn,Martin Kindt,Wolfgang Reuter,Danny Dullens Pdf

A selection of student texts of the 1995-1999 Profi-project for New matematics for senior Highschool

Geometry and its Applications in Arts, Nature and Technology

Georg Glaeser
Geometry and its Applications in Arts Nature and Technology Book PDF

Author : Georg Glaeser
Publisher : Springer Nature
Page : 694 pages
File Size : 49,7 Mb
Release : 2020-12-18
Category : Mathematics
ISBN : 9783030613983

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Geometry and its Applications in Arts, Nature and Technology by Georg Glaeser Pdf

This book returns geometry to its natural habitats: the arts, nature and technology. Throughout the book, geometry comes alive as a tool to unlock the understanding of our world. Assuming only familiarity with high school mathematics, the book invites the reader to discover geometry through examples from biology, astronomy, architecture, design, photography, drawing, engineering and more. Lavishly illustrated with over 1200 figures, all of the geometric results are carefully derived from scratch, with topics from differential, projective and non-Euclidean geometry, as well as kinematics, introduced as the need arises. The mathematical results contained in the book range from very basic facts to recent results, and mathematical proofs are included although not necessary for comprehension. With its wide range of geometric applications, this self-contained volume demonstrates the ubiquity of geometry in our world, and may serve as a source of inspiration for architects, artists, designers, engineers, and natural scientists. This new edition has been completely revised and updated, with new topics and many new illustrations.

Projective Geometry

Albrecht Beutelspacher,Ute Rosenbaum
Projective Geometry Book PDF

Author : Albrecht Beutelspacher,Ute Rosenbaum
Publisher : Cambridge University Press
Page : 268 pages
File Size : 43,9 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 0521482771

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Projective Geometry by Albrecht Beutelspacher,Ute Rosenbaum Pdf

This book introduces the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader to understand and construct proofs and write clear mathematics. The authors achieve this by exploring set theory, combinatorics and number theory, which include many fundamental mathematical ideas. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all time great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

Spherical Geometry and Its Applications

Marshall Whittlesey
Spherical Geometry and Its Applications Book PDF

Author : Marshall Whittlesey
Publisher : CRC Press
Page : 348 pages
File Size : 55,6 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9781000617542

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Spherical Geometry and Its Applications by Marshall Whittlesey Pdf

Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject. The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world – but a geometric world that is no less real than the geometric world of the plane. Features: A well-rounded introduction to spherical geometry Provides several proofs of some theorems to appeal to larger audiences Presents principal applications: the study of the surface of the earth, the study of stars and planets in the sky, the study of three- and four-dimensional polyhedra, mappings of the sphere, and crystallography Many problems are based on propositions from the ancient text Sphaerica of Menelaus

Tensors: Geometry and Applications

J. M. Landsberg
Tensors Geometry and Applications Book PDF

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 40,5 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780821869079

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Tensors: Geometry and Applications by J. M. Landsberg Pdf

Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Geometry and Its Applications

Walter J. Meyer
Geometry and Its Applications Book PDF

Author : Walter J. Meyer
Publisher : CRC Press
Page : 422 pages
File Size : 53,9 Mb
Release : 2022-06-19
Category : Mathematics
ISBN : 9780429582264

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Geometry and Its Applications by Walter J. Meyer Pdf

This unique textbook combines traditional geometry presents a contemporary approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, introduces axiomatic, Euclidean and non-Euclidean, and transformational geometry. The text integrates applications and examples throughout. The Third Edition offers many updates, including expaning on historical notes, Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. The Third Edition streamlines the treatment from the previous two editions Treatment of axiomatic geometry has been expanded Nearly 300 applications from all fields are included An emphasis on computer science-related applications appeals to student interest Many new excercises keep the presentation fresh

Differential Geometry and Its Applications

John Oprea
Differential Geometry and Its Applications Book PDF

Author : John Oprea
Publisher : MAA
Page : 508 pages
File Size : 42,8 Mb
Release : 2007-09-06
Category : Mathematics
ISBN : 0883857480

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Differential Geometry and Its Applications by John Oprea Pdf

This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.

Proofs from THE BOOK

Martin Aigner,Günter M. Ziegler
Proofs from THE BOOK Book PDF

Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 41,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437

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Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Arakelov Geometry and Diophantine Applications

Emmanuel Peyre,Gaël Rémond
Arakelov Geometry and Diophantine Applications Book PDF

Author : Emmanuel Peyre,Gaël Rémond
Publisher : Springer Nature
Page : 469 pages
File Size : 54,8 Mb
Release : 2021-03-10
Category : Mathematics
ISBN : 9783030575595

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Arakelov Geometry and Diophantine Applications by Emmanuel Peyre,Gaël Rémond Pdf

Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.

The Advanced Geometry of Plane Curves and Their Applications

C. Zwikker
The Advanced Geometry of Plane Curves and Their Applications Book PDF

Author : C. Zwikker
Publisher : Courier Corporation
Page : 316 pages
File Size : 44,9 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 9780486153438

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The Advanced Geometry of Plane Curves and Their Applications by C. Zwikker Pdf

"Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics 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. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.

Machine Proofs in Geometry

Shang-Ching Chou,Xiao-Shan Gao,Jingzhong Zhang
Machine Proofs in Geometry Book PDF

Author : Shang-Ching Chou,Xiao-Shan Gao,Jingzhong Zhang
Publisher : World Scientific
Page : 490 pages
File Size : 49,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9810215843

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Machine Proofs in Geometry by Shang-Ching Chou,Xiao-Shan Gao,Jingzhong Zhang Pdf

This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.

College Geometry

Gary L. Musser,Lynn E. Trimpe,Vikki R. Maurer
College Geometry Book PDF

Author : Gary L. Musser,Lynn E. Trimpe,Vikki R. Maurer
Publisher : Prentice Hall
Page : 0 pages
File Size : 49,6 Mb
Release : 2007-02
Category : Geometry
ISBN : 0131879693

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College Geometry by Gary L. Musser,Lynn E. Trimpe,Vikki R. Maurer Pdf

For courses in Geometry or Geometry for Future Teachers. This popular book has four main goals: 1. to help students become better problem solvers, especially in solving common application problems involving geometry; 2. to help students learn many properties of geometric figures, to verify them using proofs, and to use them to solve applied problems; 3. to expose students to the axiomatic method of synthetic Euclidean geometry at an appropriate level of sophistication; and 4. to provide students with other methods for solving problems in geometry, namely using coordinate geometry and transformation geometry. Beginning with informal experiences, the book gradually moves toward more formal proofs, and includes special topics sections.

Book of Proof

Richard H. Hammack
Book of Proof Book PDF

Author : Richard H. Hammack
Publisher : Unknown
Page : 314 pages
File Size : 41,5 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 0989472116

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Book of Proof by Richard H. Hammack Pdf

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Differential Geometry of Curves and Surfaces

Kristopher Tapp
Differential Geometry of Curves and Surfaces Book PDF

Author : Kristopher Tapp
Publisher : Springer
Page : 366 pages
File Size : 47,8 Mb
Release : 2016-09-30
Category : Mathematics
ISBN : 9783319397993

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Differential Geometry of Curves and Surfaces by Kristopher Tapp Pdf

This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.