to Flatland: A Romance of Many Dimensions
by Dionys Burger. The full title of this book is Sphereland: A Fantasy About Curved Spaces and an Expanding Universe
In 1880, Flatland was published. While it was revolutionary at the time, it carried with it a great deal of Victorian concepts. Some of these may seem 'crude' or 'odd' to modern readers (such as the treatment of women and the social structure).
Sphereland: A Fantasy About Curved Spaces and an Expanding Universe
was published in 1962, updates the world of Flatland with a more enlightened social structure and the revised model of the universe. Furthermore, it deals much more with the nature of curved space and multiple spatial dimensions that come with the understanding relativity.
One of the difficulties in reading math books is that they are math books - no plot, no characters and incredibly dry. Sphereland (and its predecessor Flatland) introduce us to a world of two-dimensional creatures with some curiosity. The explanations of the world are readable and understandable by a 7 year old and yet still interesting and enlightening to a know-it-all twenty something.
In Sphereland, A. Hexagon (the grandson of A. Square) tells of his encounters with the Sphere and the Sphere's encounters with a fourth dimensional being. It deals with such things as the flipping of a object through a higher dimension and the curvature of the universe.
To any who are interested in understanding the nature of multiple spatial dimensions. By taking a step back to the second dimension, familiarizing ourselves with the world there and then looking at the third dimension that we are already familiar with, we can begin to have an understanding of what the fourth spatial dimension would mean to us.
While the original book is out of print, it can be found in the book:
Fatland : The Classic Speculation On Life In Four Dimensions/Sphereland : A Continuing Speculation On An Expanding Universe which contains both Sphereland and Flatland. The ISBN is 0062732765 and the publisher is HarperCollins.