Book Description

Customer Reviews (13)

Good Geometry Proofs Textbook
This is a good text book.It has lots of clear worked out proofs of propostitions.Many of the exercises at the end of each lesson require that you find proofs of propostions mentioned in the text but were not proven.This book also has good drawings of shapes that explain what the propositions, theorems,and axioms mean.Since I am a student, I personally think the exercises at the end of the chapters are somewhat difficulty to figure out, but for others they might not be.If your professor doesn't explain the material well, you can at least try to understand by yourself using this text.Overall, this is a good textbook.

Thanks!
Thank you for the book.It came on time and the condition of the book was very good, which the sender had promised.

A wealth of knowledge of geometry
This text provides a wealth of knowledge about geometry. For me, with only a minimum of college level geometry previously studied, it was my first meeting with a rigorous development of any type of geometry, euclidean or noneuclidean. It was very exciting to see how this subject can be so carefully developed. Even though I was exposed to a meticulous construction of real analysis and algebra ,there is quite a difference in the techniques used to develop geometry, which you might anticipate.

Each time I have reviewed Dr.Greenberg's text, I am not only able to retain the material easier, but also to achieve a new level of understanding, which is kind of surprising.

This text is a treasure of knowledge of geometry, but the reader, if not much better prepared than me, needs to understand that digesting this text requires a bit of a committment , but it is well worth the effort.If you are a prior football player, like me, you will probably remember the coach mentioning it will take a 110% effort to win. This is a different way of indicating how tenacious, I feel, you will need to be.

I am really looking forward to reading Dr. Greenberg's most recent edition of this text, which is now available.

Hard to get into without a math professor on hand
First of all, I must point out that i am reviewing the second edition of this book. I'm sure the third edition is different, but i think the main points of my review will still hold.

I bought this book because i needed to brush up on my geometry for the California Subject Examination for Teachers (CSET) in mathematics. While it is certainly a well written book (I found the historical aspects of it particularly interesting), its major flaw is that there are no answers to the end-of-chapter excercises! This makes the book virtually useless to anyone not in school wanting to learn geometry in their own time (i.e. not for a class). Whilst i managed to do most of the exercises at the end of the first chapter (at least i think i did), it seemed pointless to attempt subsequent problems as they were quite in depth and there would be no way for me to know whether they were right or not! A big improvement would be if the number of problems were cut down (seriously, it would take years for someone to finish all of the end-of-chapter problems!) and something resembling answers was in the back of the book.

Excellent Condition
I received the textbook within just a few days after placing my order online. The book came new, as was promised. The promptness of the delivery and the quality of the product would definitely persuade me to buy from this seller again. ... Read more

Book Description
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic. The primary purpose is to acquaint the reader with the classical results of plane Euclidean and nonEuclidean geometry, congruence theorems, concurrence theorems, classification of isometries, angle addition and trigonometrical formulae. However, the book not only provides students with facts about and an understanding of the structure of the classical geometries, but also with an arsenal of computational techniques for geometrical investigations. The aim is to link classical and modern geometry to prepare students for further study and research in group theory, Lie groups, differential geometry, topology, and mathematical physics. The book is intended primarily for undergraduate mathematics students who have acquired the ability to formulate mathematical propositions precisely and to construct and understand mathematical arguments. Some familiarity with linear algebra and basic mathematical functions is assumed, though all the necessary background material is included in the appendices. ... Read more

Customer Reviews (1)

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

Book Description
This is a reissue of Professor Coxeter's classic text on non-Euclidean geometry. It begins with a historical introductory chapter, and then devotes three chapters to surveying real projective geometry, and three to elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases of a more general 'descriptive geometry'. This is essential reading for anybody with an interest in geometry. ... Read more

Customer Reviews (1)

The beauty of geometry is captured
Originally published in 1942, this book has lost none of its power in the last half century.It is a commentary on the recent demise of geometry in many curricula that 33 yearselapsed between the publication of the fifthand sixth editions. Fortunately, like so manythings in the world, trendsin mathematics are cyclic, and one can hope that the geometriccycle is onthe rise. We in mathematics owe so much to geometry. It is generally conceded that much of the origins of mathematics is due to the simplenecessity ofmaintaining accurate plots in settlements. The only book fromthe ancient history of mathematics that all mathematicians have heard of isthe Elements by Euclid. It is one of the most read books of all time,arguably the only book without a religious theme still inwidespread useover 2000 years after the publication of the first edition. The geometry taught in high schools today is with only minor modifications found in theEuclidean classic.
There are other reasons why geometry should occupya special place in our hearts. Most of the principles ofthe axiomaticmethod, the concept of the theorem and many of the techniques used inproofs were born and nurtured in the cradle of geometry. For manycenturies, it was nearly anact of faith that all of geometry wasEuclidean. That annoying fifth postulate seemed so out ofplace and yet itcould not be made to go away. Many tried to remove it, but finally theHolmseandictum of ,"once you have eliminated the impossible, what isleft, not matter how improbable,must be true", had to be admitted. Therewere in fact three geometries, all of which are of equalvalidity. Theother two, elliptic and hyperbolic, are the main topics of this wonderfulbook.
Coxeter is arguably the best geometer of this century but therecan be no argument that he is thebest explainer of geometry of thiscentury. While fifty years is a mere spasm compared to thetime sinceEuclid, it is certainly possible that students will be reading Coxeter farinto the futurewith the same appreciation that we have when wereadEuclid. His explanations of thenon-Euclidean geometries is so clear thatone cannot help but absorb the essentials. In so manyways, Euclideangeometry is but the middle way between the two other geometries. A pointwellmade and in great detail by Coxeter.
Geometry is a jewel thatwas born on the banks of the Nile river and we should treasure and respectit as the seed from which so much of our basic reasoning processessprouted. For thisreason, you should buy this book and keep a copy onyour shelf.

Published in Smarandache Notions Journal, reprintedwith permission. ... Read more

Book Description

Customer Reviews (1)

A Classic on Euclidean geometry
Recently Dover has reissued two classics on Euclidean geometry, College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics)and this book by Johnson. Both books were originally issued in the first half of the 20th century and both were aimed at a college level audience. Both of them also have a considerable amount of so called triangle geometry. As triangle geometry has seen a large upsurge the last years there is certainly a need for an English book that gives an overview of the subject. These books are useful in this respect but are out of date. Until a modern treatment of the subject (The Triangle Book by Conway and Sigur for instance, but when when ... ?) will be available, these two books and the resources on the www will have to do. Altshiller Courts' book has a great set of exercises that can be used as a training ground for geometric problem solving. The problems in Johnsons' book mostly ask for proofs of theorems that are ommited in the text (that's why I give 4 stars). If you are interested in the subject, buy both, its certainly value for money.

The book assumes that you are familiar with simple geometrical concepts like congruence of triangles, parallelograms, circles and the most elementary theorems and constructions as can be found in Kiselev's book Kiselev's Geometry / Book I. Planimetry. ... Read more

Book Description

Book Description

Advanced Euclidean Geometry provides a thorough review of the essentials of high school geometryand then expands those concepts to advanced Euclidean geometry, to give teachers more confidence in guiding student explorations and questions.

Customer Reviews (3)

Book Good but CD Has no Program - Just Prog Help
I purchased this book that came with "Geometry Sketchpad" CD except CD contained no program file, only help files.

Just a scam to purchase program?

Instructions and program purchase made unclear on website and within book itself.

This book just made teaching the course so much easier!
What an invaluable supplemental resource to have at my side while teaching a course in College Geometry! Although the class text is excellent (Geometry for College Students, by Isaacs), having this as a back-up made all the difference. The explanations are detailed and pitched at a level that students can easily follow, and the (Geometer's Sketchpad) diagrams show all the required information. Having the CD saved me from recreating the diagrams myself for class use. I highly recommend this book to anyone teaching high school or college geometry, or anyone who just wants to advance their knowledge of Euclidean and synthetic geometry.

A must-have book for every geometry teacher
As a high-school geometry teacher, I have often wished for a book like this. Sadly, the typical one-year geometry course comes to an end just as students are within reach of some truly beautiful and intriguing theorems. Dr. Posamentier's book begins where most high-school geometry textbooks end, and presents many wonderful results that lie just beyond their purview: the nine-
point circle; the golden rectangle; the theorems of Ceva, Menelaus, Ptolemy, Pascal, Desargues, and Brianchon; excircles and incircles; cyclic quadrilaterals; and much more. This book provides a rich geometric feast.

There are several books that cover much of the same ground that Dr. Posamentier surveys: GEOMETRY REVISITED, by Coxeter and Greitzer, and EPISODES IN NINETEENTH AND TWENTIETH CENTURY EUCLIDEAN GEOMETRY, by Honsberger, are two of the best. What makes Dr. Posamentier's book stand out is its usefulness as a textbook. Theorems are fully proved, and arranged in a logically coherent sequence. (The book is Euclidean in format as well as in subject matter.)

The book is thoughtfully designed. The pages are large, the type is easy to read, the diagrams are clear, and the book lies flat when opened.

EVERY HIGH-SCHOOL GEOMETRY TEACHER SHOULD HAVE THIS BOOK. It's a rich source of supplementary material for regular sections, and an ideal textbook for the second semester of an honors-level class, or for a student who wants to pursue the study of geometry on an independent-study basis.

I know that I'll be turning to this book again and again next year, and for as long as I teach geometry. In fact, I plan to buy another copy so that I'll have one at home and one in my classroom.

Bravo, Dr. Posamentier, and thank you! ... Read more

Book Description

Book Description
The Foundations of Geometry and the Non-Euclidean Plane is a self-contained text for junior, senior, and first-year graduate courses. Historical material is interwoven with a rigorous ruler- and protractor axiomatic development of the Euclidean and hyperbolic planes. Additional topics include the classical axiomatic systems of Euclid and Hilbert, axiom systems for three and four dimensional absolute geometry, and Pieri's system based on rigid motions. Models, such as Taxicab Geometry, are used extensively to illustrate theory. ... Read more

Customer Reviews (1)

Wonderfully clear and complete
Though perfectly clear to the mathematician, Non-Euclidean geometry is surronded by an aura of mystery and mistrust among the general public, and even a good many mathematicians would be hard pressed to explain exactly how the negation of the parallel postulate leads to all those strange formulas teeming with hyperbolic functions and other exotica. G.E. Martin explains everything beautifully, with exemplary clarity and just the right amount of detail. The reader also gets a complete construction of Euclidean geometry starting with the Birkhoff-Halsted axiom system, as well as a wealth of historical information into the bargain. Every serious math major or amateur ought to read this book, and many a professional could well benefit from it. ... Read more

Book Description
Introduction to NON-EUCLIDEAN GEOMETRY by HAROLD E. WOLFE . PREFACE This book has been written in an attempt to provide a satisfactory textbook to be used as a basis for elementary courses in Non-Euclid ean Geometry. The need for such a volume, definitely intended for classroom use and containing substantial lists of exercises, has been evident for some time. It is hoped that this one will meet the re quirements of those instructors who have been teaching the subject tegularly, and also that its appearance will encourage others to institute such courses. x The benefits and amenities of a formal study of Non-Euclidean Geometry are generally recognized. Not only is the subject matter itself valuable and intensely fascinating, well worth the time of any student of mathematics, but there is probably no elementary course which exhibits so clearly the nature and significance of geometry and, indeed, of mathematics in general. However, a mere cursory acquaintance with the subject will not do. One must follow its development at least a little way to see how things come out, and try his hand at demonstrating propositions under circumstances such that intuition no longer serves as a guide. For teachers and prospective teachers of geometry in the secondary schools the study of Non-Euclidean Geometry is invaluable. With out it there is strong likelihood that they will not understand the real nature of the subject they are teaching and the import of its applications to the interpretation of physical space. Among the first books on Non-Euclidean Geometry to appear in English was one, scarcely more than a pamphlet, written in 1880 by G. Chrystal. Even at that early date the value of this study for those preparing to teach was recognized. In the preface to this little brochure, Chrystal expressed his desire to bring pangeometrical speculations under the notice of those engaged in the teaching of geometry He wrote It will not be supposed that I advocate the introduction of pan geometry as a school subject it is for the teacher that I advocate vi PREFACE such a study. It is a great mistake to suppose that it is sufficient for the teacher of an elementary subject to be just ahead of his pupils. No one can be a good elementary teacher who cannot handle his subject with the grasp of a master. Geometrical insight and wealth of geometrical ideas, either natural or acquired, are essential to a good teacher of geometry and I know of no better way of cultivat ing them than by studying pan geometry. Within recent years the number of American colleges and uni versities which offer courses in advanced Euclidean Geometry has increased rapidly. There is evidence that the quality of the teaching of geometry in our secondary schools has, accordingly, greatly improved. But advanced study in Euclidean Geometry is not the only requisite for the good teaching of Euclid. The study of Non-Euclidean Geometry takes its place beside it as an indispensable part of the training of a well-prepared teacher of high school geometry. This book has been prepared primarily for students who have completed a course in calculus. However, although some mathe matical maturity will be found helpful, much of it can be read profitably and with understanding by one who has completed a secondary school course in Euclidean Geometry. He need only omit Chapters V and VI, which make use of trigonometry and calcu lus, and the latter part of Chapter VII. In Chapters II and III, the historical background of the subject has been treated quite fully. It has been said that no subject, when separated from its history, loses more than mathematics. This is particularly true of Non-Euclidean Geometry... ... Read more

Book Description

Customer Reviews (5)

Excellent for high school teachers and students
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.

Disappointing
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.

Excellent for what it is
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 atable top book, but is a book for mathemeticians and those interested inmathematics.Others need not apply (regardless of how interesting thetopic is).This is an excellent introduction to non-euclidean geometrybecause it strips away common misconceptions about the nature ofnon-euclidean geometries.This text is excellent for grade school childrenand those who would like to branch into more advanced non-euclideangeometries like hyperbolic.

This is a book for a math student only.
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, itturned out to be a lethally boring book, full of math problems, that wasLESS interesting than my geometry book in high school!

A simple, real-world example of non-Euclidean geometry
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 followingonly roads. This form of travel is similar to the taxicab geometry in thatmovement is restricted to lines. The only difference is that roads can beplaced at any location or angle whereas the lines in taxicab geometry areequidistant and perpendicular. Think of it as the geometry of graph paper.As I constructed the program, I was struck by how so much of classicalEuclidean geometry does not apply. Yet, the geometry is generally easier tounderstand because it is almost always how we move from place to place.
The phrase non-Euclidean geometry generally conjures up thoughts ofcurved space and Riemannian geometry. However, in this delightfully simplebook, a natural non-Euclidean geometry is developed in great detail. Verylittle mathematics is needed to understand the geometry, if you can markand understand the points on a grid of graph paper, nearly all of thetopics will make sense. A large number of problems are included at the endof each chapter and solutions to many appear in an appendix.
Theproblems cover topics such as finding the point(s) of minimum distancebetween two or more points and what the taxicab analogues of circles andellipses are. Determining the point of minimum distance between three ormore points is a hard problem in standard geometry, but fairly simple inthe taxicab geometry.
Geometry is the godfather of abstractmathematics, being first used to codify the parceling of land and theconstruction of cities. In this book, you will learn how to minimizefunctions based on the restrictions of traveling through cities, a taskwith many applications in the world. ... Read more

Book Description
"Non-Euclidean Geometry is a history of the alternate geometries that have emerged since the rejection of Euclidostulate. Italian mathematician ROBERTO BONOLA (1874¿1911) begins by surveying efforts by Greek, Arab, and Renaissance mathematicians to close the gap in Euclidhen, starting with the 17th century, as mathematicians began to question whether it was actually possible to prove Euclid he examines non-Euclidean predecessors Saccheri, Lambert, Legendre, W. Bolyai, Wachter, and Thibaut, and non-Euclidean ¿founders¿ Gauss, Schweikart, Taurinus, Lobachevski, and J. Bolyai. He concludes with a look at later developments in non-Euclidean geometry. Including five appendices and an index of authors, Bonolaean Geometry is a useful reference guide for students of mathematical history." ... Read more

Customer Reviews (1)

A very old classic
In Einstein's day this might have been a very good read! It is very well written. It is like reading a Spanish concurrent to Russell. A little reading finds it is a translation of a 1912 text. With general Relativity being a product of the understanding of the velocity based non Euclidean geometry of Lorentz who based his work on Poincare who based his work on Klein who based his work on... you see that history is important in an axiomaticdevelopment like this has been! But for a modern student of geometry, this book is much like buying a copy of Euclid's book on geometry: a reference that might help with understanding, but is so far out of date that it can be very little help in current problem! ... Read more

Book Description

The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.

Customer Reviews (3)

Excellent book
This is an excellent introduction to hyperbolic geometry. It assumes knowledge of euclidean geometry, trigonometry, basic complex analysis, basic abstract algebra, and basic point set topology. That material is very well presented, and the exercises shed more light on what is being discussed. Plus, solutions to all the exercises are at the end of the book.

Very good introduction
I used this text along with Tristan Needham's "Visual Complex Analysis" to get a full dose of the geometric beauty inherent in studying complex variables. I found it to be a nice complement to the second year course in geometry at Cambridge University. Anderson does a wonderful job of working out in detail lots of examples so that you can get the algorithmic practice of solving problems. However this is not merely a cookbook. Rather, core elements of the theory are presented from the ground up, with plenty of time spent on understanding the group structure of Mobius transformations in various settings. Disc and upper-half plane models are treated as well as more general models. I recommend you buy both this book and Needham's if you want to appreciate the world of complex numbers.

great book
this is a really great introduction to hyperbolic geometry.especially if you want to study gammas acting on the upper half plane.it starts at a much lower level then any other text. ... Read more

Book Description
Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation.Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems.For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists. ... Read more

Customer Reviews (1)

This book is not great.
First of all, there are numerous minor errors in the printing; they get to be annoying at best, and extremely confusing at their worst.

The book also is too much of an overview--it makes a good introduction but a poor reference text.It is also very poorly indexed, which can make it hard to find things.The exercises are also poor--many new concepts are introduced in the exercises at the end of the chapters.

The writing is actually pretty good, for the most part.I think that the stuff that is explained in the book is explained well in most places, and the author does a very good job of tieing things together and bringing in historical background and significance of the topics being discussed.

I lastly might add that the name is very misleading--the geometries described in this book were mostly discovered over 100 years ago--there is nothing drastically "modern" about them.

Overall, this book was not prepared for being published--it needs a new edition to correct errors and tie up loose ends. ... Read more

Book Description
This introduction to the geometry of lines and conics in the Euclidean plane is example-based and self-contained, assuming only a basic grounding in linear algebra. Including numerous illustrations and several hundred worked examples and exercises, the book is ideal for use as a course text for undergraduates in mathematics, or for postgraduates in the engineering and physical sciences. ... Read more

Customer Reviews (1)

Geometry of lines and planes in the Euclidean plane
The content of this book is not what I expected from the title. My thoughts were that it would be a book of traditional geometry, based on the Euclidean set of axioms. Instead, the book covers the geometry of lines and conics in the Euclidean plane.
It begins with the representation of points and lines as vectors and how length and distance are computed in the Euclidean plane. From this, the equations of the three standard categories of conics, as well as all of the associated figures such as the asymptotes are examined. Understanding the material requires knowledge of the basics of linear algebra, in particular how to work with matrices and determinants.
The presentation is well done, based on a large number of worked examples and many figures. If your interest is in learning the formulaic representations of conics in 2-space, then this book is right for you. However, I do consider the title misleading, the book is not about geometry as we usually consider it in the Euclidean sense. It deals with an application of geometry as applied to a specific class of figures and equations.

Published in Journal of Recreational Mathematics, reprinted with permission.
... Read more

Book Description

Customer Reviews (1)

What does this mean?
I quote from page 10.

"12. Theorem. If the two angles C and D are equal, the perpendiculars are equal, and if the angles are unequal, the perpendiculars are unequal, and the larger perpendicular makes the smaller angle."

There is no accomapanying diagram and no proof provided. I choose this particular theorem because it is used in distinguishing Euclidean, hyperbolic and elliptic geometries, where it is needed for the theorem to hold when comparing a perpendicular to either an acute or an obtuse angle.

After reading this gobbledygook, I gave up in despair.
... Read more

Book Description
Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michèle Audin, professor at the University of Strasbourg, has written a book allowing them to remedy this situation and, starting from linear algebra, extend their knowledge of affine, Euclidean and projective geometry, conic sections and quadrics, curves and surfaces.
It includes many nice theorems like the nine-point circle, Feuerbach's theorem, and so on. Everything is presented clearly and rigourously. Each property is proved, examples and exercises illustrate the course content perfectly. Precise hints for most of the exercises are provided at the end of the book. This very comprehensive text is addressed to students at upper undergraduate and Master's level to discover geometry and deepen their knowledge and understanding. ... Read more

Customer Reviews (1)

Math
Un libro con un contenido propicio para lo que buscaba, el lenguaje se entiende claramente y no deja espacio a dudas ... Read more

Book Description
The book conveys a distinctive approach, stimulating readers to develop a broader, deeper understanding of mathematics through active participation—including discovery, discussion, and writing about fundamental ideas.It provides a series of interesting,challenging problems, then encourages readers to gather their reasoningsand understandings of each problem. ... Read more

Customer Reviews (2)

First-principle arguments: a great intro to theoretical geo.
Geometry has always come as a difficult subject for me.For some reason, it's hard for me to "see" the answers and proofs like some people can.But, that's where a book like this came in handy.

Basically, this book is good for two things:first-principle arguments and model building.The problems in here almost require you to make models and draw pictures to see for sure what's going on.So, for a person raised on the calculator like myself, having to make models is a good thing (although very challenging!).Also, the first principle arguments are good for thought and frustration:Almost every problem in this book takes a very long time to solve, with combined thinking time, study time with your notes, and actually writing out your solution.Only on a couple of the problems that my class worked on was I able to get away with using less than one sheet of paper to write out my answer.Basically, you start from the very beginning and look at concepts you know already, like straight lines, and try to explain them as clearly and concisely as you can, which isn't always easy.But, Henderson gives hints for almost every problem, gives background on each problem, and sometimes provides solutions to the problems (but rarely!); he also provides motivation for studying the concepts rather than to pass a math course, which is very good.He also does an excellent job of introducing the concept of hyperbolic geometry by first discussing what properties stay the same or differ between the sphere and plane, which is excellent because hyperbolic geometry is not as easy to grasp as the other two; this instructional method is actually carried out through the book, an excellent way to introduce two types of geometry that many people (including myself) may have never seen before.

Honestly, my only gripe is that the book is SO based on first principle arguments that, while it provides excellent framework for prospective elementary and high-school teachers, it won't do much for the applied mathematician who wants to see some computational examples because there are barely any!It forces a student to be held accountable for abstract thought and proof, but there are many aspects of geometry that can be handled with computations like arclength, areas of polygons, etc., which are not discussed in the book.

Basically, here's the short version:It's a great book for the student who wants to work through arguments based on first principles, but be prepared to work hard!Because almost none of the exercises come with answers, I don't find this book suitable for independent study, so I hope you have a good teacher!Also, get a ball, some rubberbands, and plenty of paper with some good erasers; you'll need them!

Geometry Teacher Likes It!!
I found this book caused me to rethink much of how I approach Geometry personally and in my classroom.From the first problem, "What is Straight?" which had me thinking about my own assumptions straight lines, I have been thinking of ways to approach Geometry differently with my students.

I enjoy the problem-centered exposition, but at times, I wish I had a little more direction.The emphasis on INTUITIVELY understanding what is going on in these different spaces, and on working with physical models (the hyperbolic models are cool), is a refreshing change from an algebraic/matrix approach.This book is all about DOING geometry, and formulating convincing arguements to your "Why?" questions. ... Read more

Book Description
Geometry and Its Applications combines traditional geometry with ideas of recent decades to present a new approach for the 21st century. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidian geometry, non-Euclidian geometry, and transformational geometry. The text integrates realistic applications throughout, includes historical notes in many chapters, and contains student and instructor's guides that support Geometer's Sketchpad. Includes a free instructor's manual to professors of adopting universities.

* A unique blend of modern applications and theory
* Excellent balance of mathematical rigor and informal style
* CD-ROM (included) offers courseware for use with The Geometer's Sketchpad
* Covers polyhedra and planar maps
* Offers balance between deductive geometry and coordinate geometry using vectors
* Contains over 700 exercises with complete solutions available
* Includes Student and Instructor Guides which support the software ... Read more

Customer Reviews (2)

Good practical book
This book is a good college level textbook, with a lot of practical applications for geometry.Good for a college text to prepare geometry teachers to deal with questions from students like, "What will I ever need to use geometry for?"I really liked that the book has solutions to the odd numbered problems and the sections in each chapter on how geometry applies to everyday problems faced in physics and engineering.The CD was a nice supplement to use with geometers sketchpad.

THE BOOK OF IDEAS
I got this book as a second hand and shortly its very very nice book.
The applications are very smart and clear ,
Its contexts and illustrations are adequate ,precise and really easy to read and understand.
I realy loved this book ,and i guess this is how the geometry Should be taught as rich ideas with apps not in abstract form.
You will find a nice proof for fermat's least time principle,
and lots lots more intersting ideas good for physics and computer
graphics programming.
This book really worth any price. ... Read more