A Romance of Many Dimensions
Edwin A Abbott
Flatland is not only one of the very first science fiction books ever written (1884), but it is such an enjoyable and excellent introduction to the concept of dimensions and their effect on our perceptions, that it remains high on the list of books recommended for curious students of mathematics. I would personally recommend it for precocious 7th or 8th graders as well as high school and college students. Every mathematician I’ve ever met has read it, remembered it fondly and recommended passing it along to the younger generation.
Here’s the story line:
A. Square is a mathematician and resident of two-dimensional Flatland, where women — thin, straight lines — are the lowliest of shapes, and where men may have any number of sides, depending on their social status. [n.b.: the sexism alone can be guaranteed to spark hours of lively discussion!]
Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions — a revolutionary idea for which he is returned to his two-dimensional world.
There are charming illustrations by the author throughout. Who says mathematics can’t be fun?