Modern Geometries

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.