All inhabitants of the novel's world, dubbed Flatland, are polygons, the narrator being a square. Flatland features a strict caste system, with a polygon's class being determined by his number of sides. A square is higher on the social order than a triangle, for example, yet lower than a pentagon. The rulers, or priests, are circles. Well, actually they are polygons with very many sides, approximating a circle. The lowest figures in Flatland are women, who are straight lines. One can interpret this fictional social order in a number of ways, including accusing Abbott of being classist and sexist. I happen to see this as a critique, even a satire, of our (spaceland's) social order, replete with classism and sexism. "Flatland" also spoofs eugenics and political short-sightedness, so there's plenty to choose from.
After introducing Flatland's social order, the narrator describes a journey he takes to lineland and spaceland, which offers a great way of looking at dimensionality, even for mathematics laypersons. I'd advise reading it slowly or even more than once to be sure your mind grasps all the interesting narrative and dialogue.
Mixing a clever introduction of mathematical concepts with an element of social satire, "Flatland" is well worth reading, even for those who are normally averse to anything that has to do with mathematics. While I still plan on using this novel to teach geometry, perhaps I'll also infuse some social justice issues into my lessons.
I question its value as a teaching tool, though. I fear the Victorian niceties employed in the exposition will seem stilted and nigh unbearable to today's younger audience, especially if assigned as schoolwork. But, I think those who already grasp the mathematics involved (basic geometry) will enjoy it. Also, A. Square's unabashed enthusiasm and thirst for knowledge are qualities one would happily encourage in students.
My favorite part of the whole book has got to be the visit to the King of Pointland. The way Abbot so succinctly portrays humanity's capacity to ignore evidence that does not conform to preconceived notions, then force the facts to fit long established beliefs is a stroke of genius. In Pointland, ignorance really is bliss.
This little tale definitely provided excellent entertainment for the price I paid here at Amazon. If it sounds interesting to you, I suggest putting it on your wish list, and then adding it to the next purchase you make (your wallet will barely feel it).
List price: $30.00 (that's 30% off!)
Used price: $10.51
Collectible price: $34.40
Buy one from zShops for: $9.75
The purpose of this novel is two-fold: to introduce the casual reader into the concepts of multi-dimensional spaces (i.e. what will become the concept of four dimensional space-time) and to provide social commentary on Victorian society. I cannot comment much on what he achieves in terms of opening the eyes of the Victorian reader to the ills of that society; however, I find his ability to illuminate the concepts of dimensionality extra-ordinary. As a math and physics teacher, I am always looking for ways to open my students' minds to visualizing what they are doing. Even after well over 100 years, few people have approached Abbott's clarity in helping people visualize the difference between different dimensions. One of the best examples: a square only "looks" like a square to someone who can see in three dimensions. A square itself, trapped in a plane, would see another square (or, indeed, any figure) only as a line. This leads to intriguing thoughts on what creatures who live in higher dimensions than our own see as they look at us.
Of course, the story of Flatland alone is wonderful but Stewart's annotation and commentary take the book to another level. On nearly every page, Stewart offers insight and background into the text. Unable to resist the pun: he added another dimension to the book. Having read Flatland many years ago and enjoyed it, I felt I understood the book much better this time around with Stewart's help. Anyone with an interest in math and physics should not pass up the opportunity to read this edition of Flatland.
Buy one from zShops for: $20.62
Used price: $10.00
List price: $18.95 (that's 30% off!)
Sphereland is entirely the opposite. Sphereland deals with ideas such as the expanding universe theory others. This it explains even clearer then flatland did. But Sphereland's focus was not on the story, but rather on the theories that it tried to convey. This may be a good thing in some people's minds, but I enjoyed the story of flatland and didn't like it pushed aside to explain the theories. I also didn't like the fixing of flatland to make it less backwards (Besides giving equality to women) since flatland to me was backwards.
So If you want to learn complex Ideas simply and with fun, these are the books for you.