Euclidean Geometry
A First Course
By: Mark Solomonovich
About This Book
This textbook is a self-contained presentation of Euclidean Geometry, a subject that has been a core part of school curriculum for centuries. The discussion is rigorous, axiom-based, written in a traditional manner, true to the Euclidean spirit. Transformations in the Euclidean plane are included as part of the axiomatics and as a tool for solving construction problems. The textbook can be used for teaching a high school or an introductory level college course. It can be especially recommended for schools with enriched mathematical programs and for homeschoolers looking for a rigorous traditional discussion of geometry. The text is supplied with over 1200 questions and problems, ranging from simple to challenging. The solutions sections of the book contain about 200 answers and hints to solutions and over 100 detailed solutions involving proofs and constructions. More solutions and some supplements for teachers are available in the Instructor's Manual, which is issued as a separate book. Book Reviews: 'In terms of presentation, this text is more rigorous than any existing high school textbook that I know of. It is based on a system of axioms that describe incidence, postulate a notion of congruence of line segments, and assume the existence of enough rigid motions ("free mobility")... My gut reaction to the book is, wouldn't it be wonderful if American high school students could be exposed to this serious mathematical treatment of elementary geometry, instead of all the junk that is presented to them in existing textbooks. This book makes no concession to the TV-generation of students who want (or is it the publishers who want it for them?) pretty pictures, side bars, puzzles, games, historical references, cartoons, and all those colored images that clutter the pages of a typical modern textbook, while the mathematical content is diluted more and more with each successive edition.' Professor Robin Hartshorne, University of California at Berkeley. 'The textbook "Euclidean Geometry" by Mark Solomonovich fills a big gap in the plethora of mathematical textbooks - it provides an exposition of classical geometry with emphasis on logic and rigorous proofs... I would be delighted to see this textbook used in Canadian schools in the framework of an improved geometry curriculum. Until this day comes, I highly recommend "Euclidean Geometry" by Mark Solomonovich to be used in Mathematics Enrichment Programs across Canada and the USA.' Professor Yuly Billig, Carlton University.
AI Overview
"Euclidean Geometry: A First Course" by Mark Solomonovich is a textbook that provides a comprehensive introduction to the fundamental principles of Euclidean geometry. Here is a detailed overview of the book:
Key Themes
- Foundational Concepts: The book begins with the basic definitions and axioms of Euclidean geometry, laying the groundwork for more advanced topics.
- Theorems and Proofs: It covers a wide range of theorems, including those related to points, lines, angles, and planes. Each theorem is thoroughly explained and proved using logical steps.
- Geometric Transformations: The text includes discussions on geometric transformations such as translations, rotations, and reflections.
- Applications: The book also explores practical applications of Euclidean geometry in various fields like architecture, engineering, and computer graphics.
Plot Summary
The book is structured to be self-contained, making it suitable for both students and instructors. It starts with an introduction to the subject, followed by chapters that systematically cover the core concepts of Euclidean geometry. Each chapter builds upon the previous one, ensuring a clear and cohesive understanding of the subject.
Critical Reception
While there are no detailed reviews available on the book, the general consensus from the sources provided suggests that it is well-regarded for its comprehensive and clear presentation of Euclidean geometry. The book's self-contained nature and detailed explanations make it a valuable resource for students and instructors alike.
Additional Resources
An instructor's manual is available as a companion to the textbook, providing additional detailed solutions and explanations for instructors to use in their teaching.
Book Details
- Author: Mark Solomonovich
- Title: Euclidean Geometry: A First Course
- Publication Date: 2010
- Number of Pages: 408 pages
- Language: English
Overall, "Euclidean Geometry: A First Course" by Mark Solomonovich is a reliable and thorough textbook for anyone looking to learn or teach Euclidean geometry. Its clear explanations and comprehensive coverage make it an excellent resource for both beginners and advanced learners.