Euclidean-Geometry Books

I am currently teaching my trig. class out of this book. It has been an extremely frustrating experience.

Many of the introductory sections serve as a complete waste of time- with many topics introduced in very non-intuitive ways. Case in point: Section 3.3 (p 131) introduces "definition III" for trigonometric functions using the arc length of the unit circle. WHO DOES THAT? Even if the students understand what the book is trying to get at, the text fails miserably in justify why we even care to do that.

My second gripe about this book is pointed to the section I am currently covering, Chapter 4, which introduces graphs, amplitude, period, etc. It is SOOOOO BORING!!! This is coming from the teacher, not the student! I'm not a textbook writer, but come on! There's got to be better ways of introducing this section!

Lastly (for now), why in the world would you publish a trigonometry textbook and charge more than $150? It's not as if the author is introducing cutting-edge theories that are introduced in the form of published works for the very first time. Is this really fair market value? Even with the discounted price that Amazon charges (about $128) this book is a complete rip-off. It makes me wonder how much of this money is going to the authors and how much of it is going to Cengage. I hope in the following semesters I will be teaching out of a textbook that doesn't charge my students an arm and a leg for a 15 week course.

Okay- I'm done complaining about this book for now. I'm sure I'll think of many other things later.

This Book was too simple. Nothing in this book is rationalized. The notation is designed for people who have trouble with algebra2. I consider this book too simple. I gave it 4 stars because trig should not be taught in this notation.

It explains things well enough that I had a basic understanding of the material before going to my professor's lectures. It made it really easy to find the topics in the book to help me solve problems too.

Well laid out book, taking you a step at a time through trigonometry. Frequent reviews of material from previous chapters enables you to stay in touch with the full subject so you can be ready for the cumulative final. Author does a good job of trying to find real world examples, which is not easy. (Hardcover edition)

This book is great. It is well organized, but best of all, it comes with a CD-Rom that ROCKS!! The actual author, Chuck McKeague, teaches each concept on a markerboard, then you can practice as much as you want with different problems every time. Plus, if you just can't get it, the CD will guide you step-by-step through every problem if you want. If your teacher requires another book for Trig. you can still benefit from this one's excellent CD-Rom.

I buy this Trigonometry Book to tutor my son. It's great. It's easy for me to keep track of what my son is studying at school. Thanks to the key on each odd number in the practice part and the illustration in the model part,I can step by step show my son how to study Trigonometry.
Phu Pham
Garden Grove, California

This text was required for my university Trig class. Other reviewers have argued that math text books are only supplemental to the material covered in class - that it's the teacher that makes the difference. If that's the case, without a good teacher, this book is nearly useless. Whether the authors are covering fundamentals or advanced concepts/calculations, most everything gets a very cursory, succinct treatment. Should you not understand something covered in class, this text likely will not help to clarify. If you are at all unfamiliar with Trigonometry (as I was going in to this class), this text is not intended to enhance your understanding.

I first learned trigonometry 26 years ago, and am currently a tutor in a Tutoring Center where math and English are the primary calls for our assistance. We started using this book on Trigonometry by Lial, Hornsby and Schneider last year, and it has been a real aid to all of us.

The chapters are designed with brief overviews, 'Chapter Openers', at the beginning of each. There are sample exercises in the explanations, as well as exercises in the problem sets keyed to specific application of examples. There are summary exercises that give review of mixed concepts, pull-quote boxes (here called 'Function Boxes') to highlight the reference aspect of the text, and useful chapter reviews to the same.

One thing that stands out about this text from the one I used so many years ago is the colour aspect. There are pictures, multi-coloured graphs and illustrations, and a general feel to the book that makes it visually worthwhile to look at. This book also takes advantage of the increasing sophistication of calculators - again, back when I took trigonometry, there were tables of data in the back for looking things up, since calculators (such as they were) had only add/subtract/multiply/divide functions.

The chapters go in a fairly standard pattern for trigonometry. Chaptes progress from basic Trigonometric Functions, defining triangular and angular ideas. This continues more in depth with Acute Angles and Right Angles, then proceeds to Circular Functions, introducing Radian Measures in for good measure. The fourth chapter introduces graphing ideas for the circular functions (sine, cosine, etc.), while the sixth chapter introduces the idea of the inverse circular and trigonometric functions. Other chapters include trigonometric identities (this always seemed to me to be like geometry or logic using trig functions), vectors, complex numbers, polar equations, exponential and logarithmic functions. Many of these concepts have direct application in engineering and other sciences.

This book is also geared for students who will be advancing on to calculus, and gives marginal notes on how trigonometry is used in calculus (so as to pre-empt the question, 'when am I ever going to use this?').

Actually, I found trigonometry to be among the more enjoyable math courses I ever took; together with geometry, it confirmed an early love of the discovery of patterns and symmetry in the very fabric of existence. This book reminds me of those early days of exploring ideas, and it is a pleasure to share these same ideas with new students via this text.

This trig book I used in college in Spring 2005 was GREAT. When I'm stuck with difficult math problems, I looked at the examples in the book and then i got it figured it out and got right answers. This book made homework easier for me. The examples are very clear. This book was so much better than other book (I dont remember the title of the book and name of publisher and author's name) I used in high school trigonometry. The high school trig book was terrible and confusing and caused me to fail the class. Great job, Lial because this book made me to aced the trig final and pass the class with a B in college!

I used this book in a semester trigonometry course (covering Chapters 1 through 8), and the book was not the best. First of all, some lessons contained too much information and some too little. In addition, although the exercises are worthwhile, their difficulty levels differ from question to question, so there is no gradual increase in skill and difficulty. The book only provided good explanations on a couple of topics (for example, inverse trig. functions). All in all, the book is "okay"; if you have a good instructor, you'll still learn trigonometry.

I was very surprised that the book I ordered was in such good shape and in hardback(thoughgt it would be in paperback). I saved about $112 buying it from Amazon!!

Trigonometry hasn't changed in centuries. I compare this book with those I had as a student in high school. It does have far more colourful material. The visuals here are spectacular if set against the plain black and white of my texts. But those were from the 70s. The book also has many worked out examples and scads of exercises.

However, if you need many exercises to work through, this old fashioned offering from Schaum's has those, at a far cheaper price, Schaum's Outline of Trigonometry.

The apparently innovative stuff of the new book is its Eduspace website. Where the reader can go to get more material. The publisher and authors seem to have put a lot of effort here. Maybe this gets you value for $130. Or maybe not.

A FOURTH EDITION IS NOW OUT COPYRIGHT 1997 NEW ADDITION HAS MANY WHITLES AND BELLS

Only shows every other odd answer and doesn't go into much detail about how to do the problems. It is useful to some extent, but i was a bit disappointed.

I did appreciate the applications approach, but I felt like with almost every lesson that there were not nearly enough practice problems. A formula would be introduced with only two practice problems, only one of which is in the back of the book (of course). In my study groups, we would work those same two problems a few times and feel confident, then bomb the exam. If I remember correctly, I believe you can order an extra workbook in this series. I would recommend this text IN ADDITION to a workbook.

The biggest problem that I saw with my department adopting this textbook is that the instructors really do not teach the applications approach. I would go home to study and find that the text did not follow at all what we were covering in class. The innovative approach of the textbook was thereby lost as we flipped back and forth between the chapters trying to cobble together problems to match lectures.

I really have difficulties to understand some reviewers given one star for such a wonderfull book. If you read this book before Uni, you will have a stable ground for calculus.

All frequently used functions and their practical usage as modelling tools are lucidly explained. I finally know what hyperbolic functions are, I finally know how the path from given data to an appropriate model works. I finally know how can I practically sketch seemingly complex but simple functions.

It's strength based on model oriented approach to functions. This has pratical value for all candidate engineers...

Without any doubt I'll give five stars to acknowledge the authors.

I am currently taking pre-cac in summer school and I fear I will have to drop the class! This book is ABSOLUTELY HORRIBLE in presenting concepts and helping to guide you through the process on figuring things out. There is no reason why I should read a book, be confused, read it again, be more confused, ask friends to read it and have them be confused. I don't know how educators get away with writting books of such low quality-- and I have even less of an idea how a school chooses to use such a book. Minimally, instructors should be looking here to see the absolutely horrible feedback on this book and CHOOSE A DIFFERENT TEXT! It seems the only reason why my summer school is using this book is due to the fact that it was written by some professors here. For such a prestigous university that surely strikes of a highly unintelligent decision.

This is probably the most incoplete, inarticulate book I've ever used so far in my 3 years in college. It fails to COMPLETELY explain ALL THE MANY concepts you will ,sort-of ummmm, need to pass the class,tests or even complete the problems within the book. Expect to buy at least one other pre-calc text to clearly explain EVERYTHING this book consistently DOESN'T. This book is not a student-friendly one, its more of an EXPERT MATHEMETICIAN-FRIENDLY text book, written for people who already have lots of experience with pre-calculous. First time precalculous students should not actually expect to learn from this book or be able to count on this book as a reliable source to turn to during homework assignments or study sessions... As this book consistently fails to articulate even the most simple of precalculous concepts. If you don't beleive mine along with most other negative ratings of this book, go ahead and compare this book to almost any other precalc text book for yourself. You'll quickly see that EVEN THOUGH YOU'VE PAID A GENEROUS AMOUNT OF MONEY FOR THIS BOOK TO TEACH YOU, this book FAILS TO PERFORM EVERY SINGLE STEP OF THE WAY, PARTICULARLY when you need it to CLEARLY EXPLAIN SOMETHING TO YOU most. REALLY THIS BOOK ONLY MAKES IT HARDER TO UNDERSTAND ANYTHING IT ATTEMPTS TO EXPLAIN. My recommendation is that you buy "THE COMPLETE IDIOTS GUIDE TO PRECALCULOUS" by W. Michael Kelly, an author who thouroughly prooves his TEACHING SKILLS, COMPETENCE and ABILITY TO SUCCESFULLY ARTICULATE concepts so students can actually get some learning out of the time they spend reading his CLEAR, HELPFULL EXPLENATIONS that will actually help you in precalculous.

I use the ideas in this book in my mathematics teaching in high school. Students learn to think of the world as Euclidean through most of their instruction; Taxicab Geoemetry gives teachers a very straghtforward way to introduce non-Eucliean Geometry. Admittedly, this book is not thorough, and it is very open ended (which I consider to be positive). Nevertheless, for its intended audience it is outstanding.

Before purchasing this book, realize what it is. This is a book about non-euclidean geometry. Specifically, a specialized form of non-euclidian geometry affectionately referred to as taxi-cab geometry. This is not a table top book, but is a book for mathemeticians and those interested in mathematics. Others need not apply (regardless of how interesting the topic is). This is an excellent introduction to non-euclidean geometry because it strips away common misconceptions about the nature of non-euclidean geometries. This text is excellent for grade school children and those who would like to branch into more advanced non-euclidean geometries like hyperbolic.

Some years ago, I was employed by a company that built mapping software. One of the projects I worked on was the design of features that allowed for the computation of the shortest path from one position to another following only roads. This form of travel is similar to the taxicab geometry in that movement is restricted to lines. The only difference is that roads can be placed at any location or angle whereas the lines in taxicab geometry are equidistant and perpendicular. Think of it as the geometry of graph paper. As I constructed the program, I was struck by how so much of classical Euclidean geometry does not apply. Yet, the geometry is generally easier to understand because it is almost always how we move from place to place.
The phrase non-Euclidean geometry generally conjures up thoughts of curved space and Riemannian geometry. However, in this delightfully simple book, a natural non-Euclidean geometry is developed in great detail. Very little mathematics is needed to understand the geometry, if you can mark and understand the points on a grid of graph paper, nearly all of the topics will make sense. A large number of problems are included at the end of each chapter and solutions to many appear in an appendix.
The problems cover topics such as finding the point(s) of minimum distance between two or more points and what the taxicab analogues of circles and ellipses are. Determining the point of minimum distance between three or more points is a hard problem in standard geometry, but fairly simple in the taxicab geometry.
Geometry is the godfather of abstract mathematics, being first used to codify the parceling of land and the construction of cities. In this book, you will learn how to minimize functions based on the restrictions of traveling through cities, a task with many applications in the world.

I thought that this book would be about geometry of exotic (but real) places in outer space (such as a black hole, for example). Instead, it turned out to be a lethally boring book, full of math problems, that was LESS interesting than my geometry book in high school!

Very simplistic treatment, with some results left for the reader to work through exercises. The chapters are almost non-existent, with all the book being mainly exercises.

An excellent book such as this one deserves praise. I read it, I got it, and I can teach it.

This book was the text for a class I took. Everyone, including the teacher, found it almost impossible to learn from the book. We used it for exercises and examples, but that was about it.

I studied Dr. Cederberg's text a while ago while I was at St. Olaf College. Being an ambitious youth, I was always trying to seek out the "best" book in a field to study. However, it's certainly difficult to learn from the masters if one doesn't have a solid background in the basic materials. I learned Calculus from G. Hardy's "Pure Math" but found it extremely difficult to comprehend (though it was a rewarding try). Then I turned to Spivak for a more modern treatment. In geometry, I went the opposite way: studying Cederberg's book first before moving to the more advanced one. I like her clear presentation and especially the part on matrix representations of groups of transformations. This book would be a valuable source for teachers of geometry.

I chose this book to replace the official textbook for a course where we had been using Blau's Foundations in Geometry (which I was not entirely satisfied with.)

From Amazon, I was able to look at some excerpts from the first chapter which impressed me, so I ordered the text for the class.

The first chapter is well written and talks about the importance of models in showing consistency and independence of axioms. it contains some nice examples.

After that the book more or less falls apart. Chapter 2 talks about the inadequacies of Euclids original axiomatic system and then refers to some possible other axiomatic systems in appendices. In the second section of Chapter 2 while Euclid's problems are being discussed, there is an exercise to show that Pasch's Axiom 1 and 2 are equivalent. The exercise is impossible because the author has not defined what it means to be interior to a triangle, or even remotely addressed the issue.

For the remainder of Chapter 2, the author abandons any axiomatic framework at all and just proves various theorems about Eucilidean and hyperbolic geometry. Since axioms are not stated and terms are not adequately defined, I am not sure what the author is doing in this Chapter. To be honest, I think she is doing nothing at all. The chapter ends with an intuitive discussion of elliptic geometry.

Chapter 3 talks about geometric transformations of the Euclidean plane. It is also full of imprecise definitions, impossible exercises, and other issues. For example, in Definition 3.10 the author states "A group of transformations that keep a given line c invariant and whose translations form an infinite cyclic subgroup is known as a _frieze group_ with axis c. A point set that remains invariant under a frieze group with axis c is called a _frieze pattern_ with axis c anf denoted F_c. (Note: A frieze group is the symmetry group of the associated frieze pattern.)"

Well, which is a frieze pattern then? In the exercises, exercise 4 asks the student to explain why a frieze pattern cannot have rotational symmetry for theta other than 0 degrees or 180 degrees. Of course, under the definition given, the set of all points in the plane with integer coordinates is a frieze pattern and it does have 90 degree rotational symmetry. Yes, the *full* group of translations of the points in the plane with integer coordinates is not infinite cyclic, but it is a point set which remains invariant under a translational action by the integers and is thus a frieze pattern by the authors definition.

As another example, in section 3.7 the author defines congruence and line segments. Then as an exercise readers are asked to show that if segment PQ is congruent to segment P'Q', then the measures of the line segments d(P,Q) and d(P',Q') are equal. Nowhere is it mentioned that this is somewhat tricky given how the author has defined things. I believe readers are "supposed" to give a proof that follows something like this: Since segment PQ is congruent to segment P'Q', there is an isometry T from one set to the other. So either T(P)=P', T(Q)=Q' or T(P)=Q', T(Q)=P'. In either case, since T is an isometry d(P,Q)=d(T(P),T(Q)), and the result follows after a little work. But this of course is completely inadequate and we do not know that T(P) is also an endpoint of segment P'Q' without more work. In fact, the quickest proof of the exercise would probably not end out following this approach at all.

These are just some small examples, but the book is full of issues like this. It seems to employ very sloppy reasoning, very sloppy definitions, and either ridiculously complicated or ridiculously simple exercises. I am not sure what audience the author is trying to aim the book at. The back of the book says "[It] is designed for a junior- to senior-level course for mathematics majors." I think it would be horrible as such a text. I was trying to use it for a class aimed at mathematics education majors, and found it horrible for that use. I strongly encourage you not to adopt this textbook.

This is so rigorous it is only for the advanced mathematician. I was looking for something much more accessible. I'll have to keep looking.

This book about euclidean and non-euclidean geometry is great! A must for researh or math class!

More drawings should have been included, the rest of the book was clearly worked out. It is also suitable for new competitors in Noneuclidean Geometry. Only minus the few drawings.

I found this book to be quite helpful. It is a nice compliment to either Thurston's or Ratcliffe's book. Results are generally proved in a somewhat more restricted setting than in Thurston (making results like Margulis lemma easier to understand on first meeting). The proofs in Ratcliffe seem very dry in comparison with the present work (the authors here tend to be more geometric in their arguments). As a matter of fact, I would put this book somewhere about the midpoint of the geometric intuition spectrum between Ratcliffe and Thurston.

Although the author, as to be expected, is knowledgeable about his subject matter, my concern is again the perpetuation of mistaken thinking in the fields concerned.

The author sees instead as mistaken the contrary thinking of the past, in which he often could indeed be right, in view of the undeniable progress in the sciences. But this progress can make associated practitioners overconfident in the rightness of their ideas.

To be more specific, the author paints the rosiest picture he can of non-Euclidean geometry, while deprecating classical geometry as "deadening" (p.86). And like much of the mathematical community, he does not for a moment pause and wonder if there could be any mentioned mistakes in its accepted proposals, as current thinkers themselves submit finding mistakes in understandings held for centuries.

One of present-day contentions, as I brought up elsewhere, is that the parallel postulate, central to the rise of non-Euclidean geometry, is unprovable, and an entire system of arguments was built around this and in support of the newer geometries.

In these I find fundamental fallacies, a main one being, as I noted, a redefinition of critical concepts like straightness. In trying to by this means disprove something about Euclidean geometry, one commits the fallacy of equivocation, of speaking about something else, about, for instance, what happens on a sphere rather than in a plane.

Yet the author, for example, says (p.160) "it cannot be the case" that a line "equidistant from a straight line [be] itself straight" (for an equivalence to the parallel postulate), because in e.g. elliptic geometry (dealing with surface curvatures, not the originally meant plane) "the equidistant [line] is a circle". Or, he speaks (p.107) of the "mistaken belief" "that the parallel postulate must hold", although it is under fallaciously changed definitions of such as "line" or "infinity" that it was determined not to hold.