Classical Geometry: Euclidean, Transformational, Inversive, and Projective 1st Edition by I. E. Leonard (PDF)

Description

Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and scienceAccessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout.The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which provides the foundation for the rest of the material covered throughout; Part Two discusses Euclidean transformations of the plane, as well as groups and their use in studying transformations; and Part Three covers inversive and projective geometry as natural extensions of Euclidean geometry. In addition to featuring real-world applications throughout, Classical Geometry: Euclidean, Transformational, Inversive, and Projective includes:Multiple entertaining and elegant geometry problems at the end of each section for every level of studyFully worked examples with exercises to facilitate comprehension and retentionUnique topical coverage, such as the theorems of Ceva and Menalaus and their applicationsAn approach that prepares readers for the art of logical reasoning, modeling, and proofsThe book is an excellent textbook for courses in introductory geometry, elementary geometry, modern geometry, and history of mathematics at the undergraduate level for mathematics majors, as well as for engineering and secondary education majors. The book is also ideal for anyone who would like to learn the various applications of elementary geometry.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Classical Geometry: Euclidean, Transformational, Inversive, and ProjectiveIE Leonard, JE Lewis, ACF Liu, GW TokarskyPublished by John Wylie and Son, Inc, Hoboken NJ, 2014, simultaneously in CanadaReviewed by Peter Taylor, Emeritus Professor, University of Canberra,Address: PO Box 6165, O’Connor ACT, 2602 AUSTRALIAEmail: pjt013@gmail.comGeometry has declined significantly as a component of high school mathematics syllabi over the last three decades. The reasons for this are maybe complex, but my feedback is that the powers that be often failed to see its relevance. It seems syllabus makers were looking at direct application, and failed to see the real use other than its contribution to understanding space around us, that is its role in developing disciplined thinking, which is of course a generic asset for any student.Possibly we as mathematicians were our worst enemies in publicising the subject. Those of us who loved and appreciated the subject were all too happy to accept a delivery which to many nonbelievers was an unattractive mystery. Text books were dry and there were not many of them anyway capable of exposing the subject, certainly in the English language. Of course there were some. The works by Coxeter (Introduction to Geometry and Projective Geometry) and by Coxeter with Greitzer (Geometry Revisited) were technical masterpieces, which took the role of references for many mathematicians and training manual for younger students building up an armoury of skills and knowledge as preparation for Olympiads. I also include the MAA books by Yaglom on Transformations in this category.Albeit, some of the more remote tools, such as the barycentric coordinates devised by Möbius, while generally discussed in books such as those of Coxeter, despite being revived in some quarters as valuable modern-day problem solving tools, often became lost.It is very refreshing to see this new book on the market, which not only gives a broad coverage on Euclidean Geometry, but also extends this into other related or derivative topics. This book is primarily directed at University students, assuming they have had limited exposure to Euclidean Geometry at school and filling the void. The authors have been teaching geometry at University, and this book is based on the materials they developed.The book does cover in its initial chapters the Euclidean topics of congruence and similarity, a general coverage of the interesting aspects of concurrence, area, the theorems of Ceva and Menelaus and a good number of miscellaneous topics such as the nine-point circle, Euler Line, polygon construction, the Circle of Apollonius, etc.It then moves on to transformations, with the Euclidean transformations, rotations, reflections and translations, moving on to isometries, symmetries, groups, homotheties and tessellations.Finally topics move on to inversive and projective geometries, with chapters on reciprocation and cross ratios.The book is well laid-out, written in a useful explanatory style. Topics challenging in other books are accessible here. A student who can master this book will be very well equipped indeed, not just for the knowledge in the book, but able self-explore deeper into the subject than what can be covered here.This book is designed as a text for a university course, however this is also a must for all mathematicians who train students for Olympiads, not only for their own reference, but also to help students in their training. If one needs only a small number of geometry books for reference this should at least be one of them.

⭐Anyone fortunate enough to have discovered the pleasures of geometric reasoning for themselves must surely agree that the reduction, and even elimination, of geometry in schools and universities in the last few decades is unfortunate, to say the least. Although the joys of geometry were perhaps not always delivered in an appropriate way in our institutions of learning, a whole academic generation has now been deprived of access to much of the beauty of the subject. While it is obviously too much to ask of a single book to reverse this trend, the joys of the subject are certainly quite obvious in its pages.The book is divided into three parts, titled Euclidean Geometry, Transformational Geometry and Inversive and Projective Geometries, and each section is presented in a clear and well structured manner. Perhaps most important, the fascination of each subtopic is made clear in a manner that will become obvious to anyone spending some time working through them. The book is obviously meant as a university course textbook, and as such it can wholeheartedly be recommended, but it is also well suited to anyone interested in discovering the subject on their own. High school students preparing for mathematical olympiads will be especially pleased to find their skills in this area increased substantially after study of this text.Anyone with any interest in geometry at all, or with a wish to develop such an interest, should definitely have this book on their bookshelf.

⭐Es un buen libro de geometría, muy actual y completo. Quizás sus dibujos son algo sencillos y requeriría en algunos casos (o todos!) diferenciación con trazos gruesos.

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⭐item received on time, the same as advertised,

⭐very good

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