We are preparing a new book on Mathematical Discovery. It is intended for students with just the usual high school background in mathematics (algebra and geometry) who wish to learn how mathematicians discover new methods to attack problems. It is based on a course Andy Bruckner gave to students at UC Santa Barbara for non math majors, covering interesting topics that require less background preparation than the usual university-level courses would need.
There will be (as usual) FREE PDF FILES as well as a trade paperback version. The first chapter on Tilings discusses the famous problem of "squaring the rectangle," i.e., tiling a rectangle with a number of unequal sized squares. You can download this one now.
