The Colossal Book of Mathematics by Martin Gardner

This is a book of recreational mathematics. I could not finish this book as I had to return it to library. Some of the sections in the book that are of interest are (directly from my notebook):

1. Rep-n Polygons
2. Piet Heins Superellipse
Super Egg - Exponent 2-1/2 . Columbus experiment of making an egg stand
Interesting Fact: If Center of Curvature is above Center of Gravity the superegg will be stable -P69 -> Wiki

3. Planiverse - 2D universe - very interesting depiction of men and women

4. Helix and its importance - The shape is everywhere - shapes of nut & bolts , horns ,sea shells, snails shells, DNA molecules -> can be both right handed and left handed

5. Spheres & Hyperspheres
137 -> a2+b2+c2+d2=r2 is called hypersphere in 4 dimensions
surface of a n-sphere has a dimensionality of n-1. Does this mean that 3-space is actually the hypersurface of the vast 4-sphere.

If space is a hypersphere, then that hypersphere must sit in a four-dimensional Euclidean space, allowing us to view it from the outside. Nature, however, need not cling to this notion. It would be perfectly acceptable for the universe to be a hypersphere and not be embedded in any higher-dimensional space. Such an object may be difficult to visualize, because we are used to viewing shapes from the outside. But there need not be an "outside."

Good Explanation: Paradigm Shifts in Astronomy and Cosmology - More

6. The Church of Fourth Dimension

I had to stop here. I will provide some updates on more sections once I get the book back.

The Colossal Book of Mathematics>