Shining Gems of Geometry... True Value
I am constantly amazed by authors and their ability to produce new insights. Some authors have the ability to take common ideas and display them in new clothes, to the extent that one wonders if they had actually understood the idea previously. I guess this is what "depth" in understanding means.
John Barnes, a nonmathematician, is such an author, offering a book based on a series of lectures he gave for adults at Reading University (UK). The text Gems of Geometry is a gem itself.
The ten basic lectures focus on these concepts:
 Phi: The Golden Ratio
 Polygons, Polyhedra, and Tilings
 The Fourth Dimension and Extensions
 Projective Geometry
 Topology: Coloring and OneSidedness
 Bubbles
 Harmony of the Spheres and Inversion
 Chaos and Fractals
 Relativity, Curvature, and Black Holes
 Misc. Geometric Ideas
The content is aimed at the general public and supposedly requires only a "basic understanding of mathematics." However, be forewarned that Reading University (and the author) must define "basic" different than the expected, as some of the mathematics is demanding (but worth the effort).
The author also includes problem sets and an interesting collection of Appendices. Usually the latter are meant to clarify previous content, but in this sense, the author seems to include Appendicies for presenting content of interest but not included in the ten lectures.
My suggestion: Get the book and browse. I expect that in every chapter, you will discover a new "gem" of an idea about content you already know well...or thought you knew.
