On 24-1-2010, at 7.29 AM, David Bakin wrote:
> I have a copy of Coxeter's Introduction to Geometry but haven't opened it
> yet - I didn't much like his book Projective Geometry (much prefered Wylie's
> book on Projective Geometry) so would appreciate someone else's review of
Coxeter wrote at different levels. As you suggest, his "Projective Geometry" can be rather challenging. However, his "Introduction to Geometry" is more elementary and really beautiful, although he still doesn't waste words. You might like the way he surveys basic triangle geometry in the first chapter before moving on to other things.
An out-of-print book which you may be able to find is H.G. Forder, "Geometry", Hutchinson's University Library, 1950. It has some impressive insights from an elementary point of view.
A similar but bigger and much better known book is Hilbert & Cohn-Vossen, "Geometry and the Imagination". It's based on a series of public lectures given by Hilbert to a general audience.
And for light reading in odd moments, David Wells "The Penguin Dictionary of Curious and Interesting Geometry" is good fun.