Author: Henry Africk
Publisher:
ISBN: 9780759341906
Category : Geometry
Languages : en
Pages : 369

View

Book Description

Author: David C. Kay
Publisher: CRC Press
ISBN: 1439819114
Category : Mathematics
Languages : en
Pages : 655

View

Book Description
Designed for mathematics majors and other students who intend to teach mathematics at the secondary school level, College Geometry: A Unified Development unifies the three classical geometries within an axiomatic framework. The author develops the axioms to include Euclidean, elliptic, and hyperbolic geometry, showing how geometry has real and far-reaching implications. He approaches every topic as a fresh, new concept and carefully defines and explains geometric principles. The book begins with elementary ideas about points, lines, and distance, gradually introducing more advanced concepts such as congruent triangles and geometric inequalities. At the core of the text, the author simultaneously develops the classical formulas for spherical and hyperbolic geometry within the axiomatic framework. He explains how the trigonometry of the right triangle, including the Pythagorean theorem, is developed for classical non-Euclidean geometries. Previously accessible only to advanced or graduate students, this material is presented at an elementary level. The book also explores other important concepts of modern geometry, including affine transformations and circular inversion. Through clear explanations and numerous examples and problems, this text shows step-by-step how fundamental geometric ideas are connected to advanced geometry. It represents the first step toward future study of Riemannian geometry, Einstein’s relativity, and theories of cosmology.

Author: Daniel C. Alexander
Publisher:
ISBN: 9780395870556
Category : Mathematics
Languages : en
Pages : 566

View

Book Description

Author: I. Martin Isaacs
Publisher: American Mathematical Soc.
ISBN: 0821847945
Category : Mathematics
Languages : en
Pages : 242

View

Book Description
One of the challenges many mathematics students face occurs after they complete their study of basic calculus and linear algebra, and they start taking courses where they are expected to write proofs. Historically, students have been learning to think mathematically and to write proofs by studying Euclidean geometry. In the author's opinion, geometry is still the best way to make the transition from elementary to advanced mathematics. The book begins with a thorough review of high school geometry, then goes on to discuss special points associated with triangles, circles and certain associated lines, Ceva's theorem, vector techniques of proof, and compass-and-straightedge constructions. There is also some emphasis on proving numerical formulas like the laws of sines, cosines, and tangents, Stewart's theorem, Ptolemy's theorem, and the area formula of Heron. An important difference of this book from the majority of modern college geometry texts is that it avoids axiomatics. The students using this book have had very little experience with formal mathematics. Instead, the focus of the course and the book is on interesting theorems and on the techniques that can be used to prove them. This makes the book suitable to second- or third-year mathematics majors and also to secondary mathematics education majors, allowing the students to learn how to write proofs of mathematical results and, at the end, showing them what mathematics is really all about.

Author: John Roe
Publisher: Clarendon Press
ISBN: 9780198534563
Category : Language Arts & Disciplines
Languages : en
Pages : 324

View

Book Description
This textbook provides an introduction to Euclidean geometry. While developing geometry for its own sake, the book also emphasizes the links between geometry and other branches of pure and applied mathematics.

Author: Daniel C. Alexander
Publisher: Cengage Learning
ISBN: 9781439047903
Category : Mathematics
Languages : en
Pages : 624

View

Book Description
Building on the success of its first four editions, the Fifth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with a new chapter on locus and concurrence and by adding 150-200 new problems including 90 designed to be more rigorous. Strongly influenced by both NCTM and AMATYC standards, the text takes an inductive approach that includes integrated activities and tools to promote hands-on application and discovery. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Author: Nathan Altshiller-Court
Publisher: Dover Publications
ISBN: 9780486788470
Category :
Languages : en
Pages : 336

View

Book Description
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

Author: A.N. Pressley
Publisher: Springer Science & Business Media
ISBN: 1447136969
Category : Mathematics
Languages : en
Pages : 336

View

Book Description
Pressley assumes the reader knows the main results of multivariate calculus and concentrates on the theory of the study of surfaces. Used for courses on surface geometry, it includes intersting and in-depth examples and goes into the subject in great detail and vigour. The book will cover three-dimensional Euclidean space only, and takes the whole book to cover the material and treat it as a subject in its own right.

Author: A.N. Pressley
Publisher: Springer Science & Business Media
ISBN: 1848828918
Category : Mathematics
Languages : en
Pages : 469

View

Book Description
Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com ul

Author: Henry Sinclair Hall
Publisher:
ISBN:
Category :
Languages : en
Pages : 286

View

Book Description