Transformation Geometry

Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry.

Author: George E. Martin

Publisher: Springer Science & Business Media

ISBN: 9781461256809

Category: Mathematics

Page: 240

View: 191


Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.

Geometry Transformed Euclidean Plane Geometry Based on Rigid Motions

[1] William Barker and Roger Howe, Continuous symmetry: From Euclid to Klein, American Mathematical Society, Providence, RI, ... Transformation geometry: An introduction to symmetry, Undergraduate Texts in Mathematics, Springer-Verlag, ...

Author: James R. King

Publisher: American Mathematical Soc.

ISBN: 9781470463076

Category: Education

Page: 258

View: 853


Many paths lead into Euclidean plane geometry. Geometry Transformed offers an expeditious yet rigorous route using axioms based on rigid motions and dilations. Since transformations are available at the outset, interesting theorems can be proved sooner; and proofs can be connected to visual and tactile intuition about symmetry and motion. The reader thus gains valuable experience thinking with transformations, a skill that may be useful in other math courses or applications. For students interested in teaching mathematics at the secondary school level, this approach is particularly useful since geometry in the Common Core State Standards is based on rigid motions. The only prerequisite for this book is a basic understanding of functions. Some previous experience with proofs may be helpful, but students can also learn about proofs by experiencing them in this book—in a context where they can draw and experiment. The eleven chapters are organized in a flexible way to suit a variety of curriculum goals. In addition to a geometrical core that includes finite symmetry groups, there are additional topics on circles and on crystallographic and frieze groups, and a final chapter on affine and Cartesian coordinates. The exercises are a mixture of routine problems, experiments, and proofs.

Geometries and Transformations

Math. Soc. 312, 739–753. W. Magnus. 1974, Noneuclidean Tesselations and Their Groups. Academic Press, New York–London, 1974. G. E. Martin. 1982, Transformation Geometry: An Introduction to Symmetry, Undergraduate Texts in Mathematics.

Author: Norman W. Johnson

Publisher: Cambridge University Press

ISBN: 9781107103405

Category: Mathematics

Page: 438

View: 729


A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.

A Primer for Undergraduate Research

Tamkang J. Math. 10(1), 97–103 (1979) Maclachlan, C., Talu, Y.: p-groups of symmetries of surfaces. Michigan Math. J. 45, 315–332 (1998) Martin, G.: Transformation Geometry: An Introduction to Symmetry. Undergraduate Texts in ...

Author: Aaron Wootton

Publisher: Birkhäuser

ISBN: 9783319660653

Category: Mathematics

Page: 313

View: 532


This highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading. The content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations research), yet have few enough prerequisites that the interested student can start exploring them under the guidance of a faculty member. Whether trying to start an undergraduate thesis, embarking on a summer REU, or preparing for graduate school, this book is appropriate for a variety of students and the faculty who guide them.

Elementary Probability Theory

Undergraduate Texts in Mathematics (continued from page ii) Gamelin: Complex Analysis. ... Hilton/Holton/Pedersen: Mathematical Vistas: From a Room with Many Windows. ... Martin: Transformation Geometry: An Introduction to Symmetry.

Author: Kai Lai Chung

Publisher: Springer Science & Business Media

ISBN: 9780387215488

Category: Mathematics

Page: 404

View: 577


This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales. From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS

Geometry from Isometries to Special Relativity

Anderson, J.: Hyperbolic Geometry. Springer Undergraduate Mathematics Series, 2nd edn. ... Undergraduate Texts in Mathematics. Springer, New York (2000) ... Martin, G.: Transformation Geometry: An Introduction to Symmetry. Undergraduate ...

Author: Nam-Hoon Lee

Publisher: Springer Nature

ISBN: 9783030421014

Category: Mathematics

Page: 258

View: 863


This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.

Groups and Symmetry

(A classic essay which should be read by every mathematics teacher and student.) [2] Lyndon, R.C., Groups and Geometry, Cambridge University Press, Cambridge (England), 1985. ... (An excellent graduate level text.) ...

Author: Mark A. Armstrong

Publisher: Springer Science & Business Media

ISBN: 9781475740349

Category: Mathematics

Page: 187

View: 946


This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.

Measure Topology and Fractal Geometry

Undergraduate Texts in Mathematics Apostol: Introduction to Analytic Number Theory. ... Brickman: Mathematical Introduction to Linear Programming and Game Theory. ... Martin: Transformation Geometry: An Introduction to Symmetry.

Author: Gerald A. Edgar

Publisher: Springer Science & Business Media

ISBN: 9781475741346

Category: Mathematics

Page: 231

View: 327


From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1

Introduction to Analytic Number Theory

Undergraduate Texts in Mathematics ( continued from page ii ) Frazier : An Introduction to Wavelets Through Linear ... Hartshorne : Geometry : Euclid and Beyond . ... Martin : Transformation Geometry : An Introduction to Symmetry .

Author: Tom M. Apostol

Publisher: Springer Science & Business Media

ISBN: 0387901639

Category: Mathematics

Page: 340

View: 323


"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS