Euclidean Geometry: A First Course by Mark Solomonovich (PDF)

Description

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 pretty pictures, side bars, puzzles, games, historical references, cartoons, and all those colored images that clutter the pages of a typical modern textbook, while the mathematical content is diluted more and more with each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.

User’s Reviews

Editorial Reviews: From the Publisher “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.

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

⭐This book fills an important gap among geometry textbooks.

⭐Solomonovich attempts to bridge the logical gaps in Euclid through an early introduction of what are called rigid transformations (or isometries) – functions that translate, rotate, and reflect geometric figures in the plane in a way that preserves their size and shape. Whereas rigid transformations are the modern approach to Euclidean geometry, they’re usually only introduced after students have been exposed to elementary linear algebra, set theory notation, and a bit of group theory. Solomonovich postulates rigid transformations without setting up any of the algebraic foundations that make them clear and precise. The way he employs them in proofs is really no better than Euclid talking about picking up a triangle and laying it atop another.As another review noted, there are also major organizational problems with the book. One example: Solomonovich first proves the existence of perpendicular lines using reflection and then, in a later chapter, without referring to the first proof, proceeds to construct a perpendicular line in a way similar to Euclid. Alternate proofs can be interesting, but here Solomonovich treats construction as separate from proof of existence. The first four chapters seem to lack any progress or organizing principles.I also found that the exercises were exceedingly trivial, although I must admit that I stopped reading the text after the fifth chapter. This might also be nitpicking, but I found the presentation of some exercises rather childish; I know I’m older than the targeted audience, but I doubt many teenagers will take kindly to exercises that ask them to match clown faces.Finally, some better alternatives: after reading a small library of elementary geometry texts, I’ve concluded that there’s really no substitute for Euclid’s Elements as a first course in geometry and mathematical reasoning. There are issues with Euclid’s Elements, but solving these issues requires more of an extended preface to the Elements than a revision of the core text . For those who find Euclid’s language obscure, or want to learn a bit of classical geometry after Euclid, I recommend Saul Stahl’s “Geometry From Euclid To Knots”. Stahl follows Euclid while recasting his proofs in modern language and discussing where Euclid strays. Stahl includes answers and hints for most exercises.For those interested in a more rigorous introduction to geometry, I advise completing a course in linear algebra and abstract algebra and picking up one of the numerous texts that approach geometry from a more “analytic” perspective – Brannan and Esplen’s “Geometry”, John Roe’s “Elementary Geometry”, Melvin Hausner’s “A Vector Space Approach To Geometry”, and John R. Silvester’s “Geometry Ancient and Modern” are all excellent books for self-study.

⭐A nice combination of intuition, rigor, and interesting problems. Solomonovich isn’t trying to be a 21st century Euclid, and that is a good thing. At the same time, there are solid proofs in the book, but the proofs tend to shed light on the geometry, rather than obscure it. I think this book is particularly appealing for future HS teachers, and the price is right for use as a textbook.

⭐I agree that the rigor is good – will push the envelope for even the brightest high school student. Poorly written text, no index, no summary of topics GREATLY detract from the presentation. Gets an “A” for content, “F” for presentation/format – almost as though the author assumes the reader knows as much about the subject as he does.

⭐A bit hard going, not for the curios looking for an understanding

⭐Excellent

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