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 : Nathan Altshiller-Court
Publisher : Dover Publications
Page : 336 pages
File Size : 36,89 MB
Release : 2013-12-30
Category :
ISBN : 9780486788470
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 : David C. Kay
Publisher : CRC Press
Page : 655 pages
File Size : 36,13 MB
Release : 2011-06-24
Category : Mathematics
ISBN : 1439819114
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 : Henry Africk
Publisher :
Page : 369 pages
File Size : 36,47 MB
Release : 2004
Category : Geometry
ISBN : 9780759341906
Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 13,98 MB
Release : 2009
Category : Mathematics
ISBN : 0821847945
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 : Howard Whitley Eves
Publisher : Jones & Bartlett Learning
Page : 392 pages
File Size : 16,82 MB
Release : 1995
Category : Computers
ISBN : 9780867204759
College Geometry is divided into two parts. Part I is a sequel to basic high school geometry and introduces the reader to some of the important modern extensions of elementary geometry- extension that have largely entered into the mainstream of mathematics. Part II treats notions of geometric structure that arose with the non-Euclidean revolution in the first half of the nineteenth century.
Author : Margaret L. Lial
Publisher : Addison-Wesley Longman
Page : 0 pages
File Size : 26,75 MB
Release : 2003-11
Category : Geometry
ISBN : 9780201748826
This textbook is designed to provide students with the sound foundation in geometry that is necessary to pursue further courses in college mathematics. It is written for college students who have no previous experience with plane Euclidean geometry and for those who need a refresher in the subject.
Author : Daniel C. Alexander
Publisher :
Page : 566 pages
File Size : 17,76 MB
Release : 1999
Category : Mathematics
ISBN : 9780395870556
Author : Barbara E. Reynolds
Publisher : Wiley Global Education
Page : 368 pages
File Size : 16,63 MB
Release : 2021-02-01
Category : Education
ISBN : 1119718147
From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using GeoGebra, a book that is ideal for geometry courses for both mathematics and math education majors. The book's discovery-based approach guides students to explore geometric worlds through computer-based activities, enabling students to make observations, develop conjectures, and write mathematical proofs. This unique textbook helps students understand the underlying concepts of geometry while learning to use GeoGebra software—constructing various geometric figures and investigating their properties, relationships, and interactions. The text allows students to gradually build upon their knowledge as they move from fundamental concepts of circle and triangle geometry to more advanced topics such as isometries and matrices, symmetry in the plane, and hyperbolic and projective geometry. Emphasizing active collaborative learning, the text contains numerous fully-integrated computer lab activities that visualize difficult geometric concepts and facilitate both small-group and whole-class discussions. Each chapter begins with engaging activities that draw students into the subject matter, followed by detailed discussions that solidify the student conjectures made in the activities and exercises that test comprehension of the material. Written to support students and instructors in active-learning classrooms that incorporate computer technology, College Geometry with GeoGebra is an ideal resource for geometry courses for both mathematics and math education majors.
Author : Melvin Hausner
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 39,10 MB
Release : 2018-10-17
Category : Mathematics
ISBN : 0486835391
A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.
Author : Dan Pedoe
Publisher : Courier Corporation
Page : 466 pages
File Size : 42,98 MB
Release : 2013-04-02
Category : Mathematics
ISBN : 0486131734
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.