Customer Reviews

The Four Pillars of Geometry (Undergraduate Texts in Mathematics)

5 star:		(4)
4 star:		(1)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

This nice book contains many things that every mathematics student should know (but don't). Chapters 1-2 are on Euclid. The main ideas are picked out very nicely, in welcome contrast to the usual "let ABCD..."-style books. Chapters 3-4 on linear algebra in geometry will probably be skimmed by most readers. This is perhaps just as well, since it consists of little more than the pearls from the usual linear algebra course and since the presentation feels somewhat forced (e.g., things like the inner product are cheerfully defined out of thin air) compared to how naturally the rest of the book flows. Chapters 5-6 on projective geometry are more interesting. Perspective in art sets the stage, but we quickly move to purer things. Stillwell is very fond of the mysterious and fascinating connection with hypercomplex number systems one obtains by building up an arithmetic from within a projective plane. Then in chapter 7 we learn that transformation groups are a clarifying and unifying idea, and we play around with them a bit, somewhat aimlessly it seems, until we finally get to hyperbolic geometry in chapter 8. This chapter crowns the whole book beautifully, showing how projective geometry explodes into hyperbolic geometry through transformation-group thinking. It ends with an excellent short survey of the history of non-Euclidean geometry.

This text makes the connections simply, readably among various interrelated branches of mathematics including geometry (four of them), trig, group theory, complex variables, and linear algebra. Recommended for every high school mathematics instructor.

While this book is a cheaper alternative to the hardcover, there are many mistakes in the printing. There are little dots where there should be parentheses, brackets and square root signs in the problem section. It makes the problems hard to understand if you do not know what symbols are supposed to be there. If you are using this for a class, make sure have someone else's book to compare it to. I know it is not just my book because everyone with the soft cover in my class has the same problem.

I found this text to be of excellent quality. Dr. Stillwell's writing is easy to read, yet very informative. He creates many examples that helps in uderstaning his main thesis. I found his reason why 'The Slope is consistent throughout a line' by using similar traingles quite interesting. I highly recommend this book for all who enjoy mathematics, regardless of your degree or interest. I am anxious to read and study more of his books.

This book has a nice balance of history and theorems. The author provides plenty of illustrations and the problems support the text well. One of my better math text books.

This is a fine book for learning Euclidean and non-Euclidean geometry. Fairly clear. I wish it had more examples.