Modern Geometries (Contemporary Undergraduate Mathematics Series)

• Publisher:   Thomson Brooks/Cole
• Number Of Pages:   371
• Publication Date:   1973-01
• ISBN-10 / ASIN:   0818500514
• ISBN-13 / EAN:   9780818500510

This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics. References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems.

I was very pleased with this product. I received it very quickly, and it was in excellent condition.

This book was used in my modern geometry class at school and I purchased it only as a resource in the future. Is well organized and written. I also suggest a refresher book to review Euclidean Geometry before using this book.

this geometry book assumes the student knows traditional high school euclidean geometry, ans presents an advanced, modern survey of many interesting topics that are more fascinating than the plain old facts about isosceles triangles, parallel lines, and circles. Unfortunately most of todays students do not even know basic high school geometry, so the book's "review" in 2 pages, in an appendix, of the basic elementary theorems of high school geometry, is the material that they actually need to learn. Still, since learning the basic stuff is pretty boring to the average student, it might be possible, to just review that list of facts with them, since they are pretty intuitive, and go on as if they knew it. I.e. the problem of teaching euclidean geometry is that it is hard to give an intellectually honest and thorough treatment of even simple geometric facts that most kids think are obvious anyway. The good stabndard books that are out there for teachers (greenberg, millman and parker) mostly spend a huge amount of time filling in logical gaps that euclid omitted. but these gaps, being too subtle for mathematicians to notice for 2000 years, are also too subtle for students to appreciate. so the effort is kind of wasted, dwelling on niceties in a subject whose basics are big news to todays students. the present book does not do this, but presents interesting things even a seasoned mathematician may not know, like Pick's theorem for the area of a polygon in terms of the lattice points inside and on its border, and gives fun an d challenging exercises, like asking the student what the theorem of concurrence of altitudes for a triangle becomes after inverting the tringle with respect to a suitable circle. the question is, can you teach the more advanced and interesting stuff succesfully to people who do not know even the basic stuff. can you quickly give them enough of a feel for it to go on, or do you have to get down in the nitty gritty details? i.e. the problem with thsi book, is how long do you have to spend on the 2 page summary of high school geometry in appendix 5. oh, and the new higher price just made using it unfeasible to me, in the 5th editiion.

This book covers a broad range of geometries, including convexity and an introduction to topology. It presents revelent definitions followed by intuitive theorems (some with full proofs, others partial).
For a general study in geometry at the university level, this book is quite adequate. It's use of analytic methods and exploratory exercises, makes it an appropriate introduction for the undergraduate who is considering further studies in geometry or analysis.

This is the required text in my Eucliden Geometry class in college and while for the most part I find this book a useful tool, I often find terms and definitions either underexplained or introduced without definition, which can be frustrating to a student new to the dicipline. It has a very easy-to-follow introduction to non-Euclidean geometies, however, and I recommed the book especially on this level. Overall, however, I feel it could be written in more of a student-friendly manner.

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