Author: Gary L. Musser
Publisher: Prentice Hall
Release Date: 1994-01-01
This book exposes readers to many practical applications of geometry, especially those involving measurement. A three- part organization divides topics into Problem Solving, Geometric Shapes, and Measurement; Formal Synthetic Euclidean Geometry; and Alternate Approaches to Plane Geometry.
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
Release Date: 2011-06-24
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: I. Martin Isaacs
Publisher: American Mathematical Soc.
Release Date: 2009
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: Loren C. Larson
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.
Author: Gerard A. Venema
Release Date: 2013
This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincaré disk model for hyperbolic geometry. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry. The text consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. First the ideas are explored at the computer and then those ideas are assembled into a proof of the result under investigation. The goals are for the reader to experience the joy of discovering geometric relationships, to develop a deeper understanding of geometry, and to encourage an appreciation for the beauty of Euclidean geometry.
Note: You are purchasing a standalone product; MyMathLab does not come packaged with this content. If you would like to purchase both the physical text and MyMathLab, search for ISBN-10: 0321900340 /ISBN-13: 9780321900340 . That package includes ISBN-10: 0321431308/ISBN-13: 9780321431301, ISBN-10:0321654064 /ISBN-13: 9780321654069 and ISBN-10:0321923480 /ISBN-13: 9780321923486. MyMathLab is not a self-paced technology and should only be purchased when required by an instructor. With an emphasis on problem solving and critical thinking, Mark Dugopolski’s Trigonometry, Fourth Edition gives students the essential strategies to help them develop the comprehension and confidence they need to be successful in this course. Students will find carefully placed learning aids and review tools to help them do the math.
Author: Margaret L. Lial
Publisher: Addison-Wesley Longman
Release Date: 2003-10-01
Written for students who need a refresher on Plane Euclidean Geometry, Essentials of Geometry for College Students, Second Edition, incorporates the American Mathematical Association of Two-Year Colleges (AMATYC) and National Council of Teachers of Mathematics (NCTM) Standards on geometry, modeling, reasoning, communication, technology, and deductive proof. To make learning interactive and enjoyable, this new edition includes exciting new features such as Technology Connections and Hands-on Activities. Knowledge of beginning algebra and a scientific calculator are required for this text
Author: Alan S. Tussy
Publisher: Brooks/Cole Publishing Company
Release Date: 2002-09-01
Intended to address the need for a concise overview of fundamental geometry topics. Sections 1-7 introduce such topics as angles, polygons, perimeter, area, and circles. In the second part of the text, Sections 8-11 cover congruent and similar triangles, special triangles, volume, and surface area.
Facts101 is your complete guide to College Geometry, A Problem Solving Approach with Applications. In this book, you will learn topics such as Perimeter, Area, and Volume, Reasoning and Triangle Congruence, Parallel Lines and Quadrilaterals, and Similarity plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.
Author: Pierre von Meiss
Publisher: EPFL Press
Release Date: 2013-11-13
Genre: Architectural design
Modernity has opened the way to a greater pluralism of forms. But even if architecture is a cultural phenomenon, that does not mean it is a product of fashion.Its principles are enduring and its foundations less tangible than the novice who tried to shake them would realize. To start that stretch towards the foundations one must first acquire the basics: to know the permanence of the architectural field and appreciate the certainties tested by time. This book will act as a guide for the reaching hand. The first part explores the mediums of compositional architecture and the relationships between space, light, and place. Four or five thousand years of history demonstrate the persistence of certain fundamental principles intrinsic to a discipline that organizes, in three dimensions, the vital space of man. In the second part, the author provides certain keys to manage the relationship between shape, materials, and construction – recalling that the need to build, by itself, has never been enough to design the form of the house or the city. Neither encyclopedia nor dictionary, this book seeks to fill a gap in light of our time: it serves as a contemporary introduction to architectural design and criticism. Following the praise of critics, the first edition has been adopted as a reference text in numerous schools and translated into several languages. This new translation from the 3rd French edition offers revised and reworked content with an additional three chapters dedicated to tectonics.
Author: G. Polya
Publisher: Princeton University Press
Release Date: 2014-10-26
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out—from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft—indeed, brilliant—instructions on stripping away irrelevancies and going straight to the heart of the problem.