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Summary: It should be required reading in math and social studies
Review: This book should be required reading for students in both mathematics and social studies. The explanations by Abbott of how three dimensional beings would appear to a two dimensional creature have never been improved upon. I have seen them reproduced in nearly every book that I have read about space with dimensions more than three. Since we cannot visualize objects in four dimensions, the best that can be done is to describe them mathematically or by using an analogy to the dimensions that we can visualize.
However, the book is also a satire about the English social structure of the nineteenth century. Abbott was a champion of the rights of women, so his caricature of females must be read with that fact foremost in mind. His description of the society of Flatland is meant to be a critique of what he saw in an enormously class-conscious England with a distinct privileged class. Read with that foremost in mind, his caricatures of the inhabitants are quite amusing.
This is one of the very few books that I have read over three times. It has never failed to keep my interest, containing some of the best teaching analogies ever created. I even read it when it appears paraphrased in books written to describe the principles of space with more than three dimensions. I have no doubt that this is a book that will still be interesting to people thousands of years in the future.
Rating: 
Summary: A wonderful book containing hitherto unexpected insights
Review: The justly famous Flatland by Abbott stands out for several reasons1. Its old Victorian style writing which is written from the somewhat "distant observer" viewpoint with the accompanying Englishness to go with it. It is full of social mores of the time (1884) such as the role of women in society or the very specific roles of the "lower classes" and those of the higher levels of society. Included also in this is the social graces themselves where his "feeling" inserted into the book as a means of differentiating various shapes is really a metaphor for the almost repugnant consequences of a meeting between a peasant and a member of the Aristocracy. As such the book is a superb example of he Victorian Age. 2. Another aspect, maybe not so much mentioned, is the fact that the book presents a fine example of the fact that people are trapped by their own culture/upbringing, this time dealt with through the idea of a 2 dimensional being not being able to comprehend 3 dimensions. Apart from the fact that the mind is not able to get around the concept of dimensions higher than the usual 3 I believe the book was intended maybe even accidently to support the idea of a prison of your own culture. However Abbott goes on to show that people are infinitely adaptable and there are ways to meet these seemingly insurmountable challenges. Again a path breaking book when looked at from this angle, who before Abbott would have considered such a view. 3. Finally the book presents many wonderful examples of the illumination of strange concepts not even considered in ordinary life through the vessel of the trek of the square who attempts to grasp his new world with the aid of a sphere. A wonderful little book containing hitherto unexpected insights.
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Summary: How I Vainly Tried to Explain the Nature of Flatland
Review: Flatland is an interesting piece of fiction. On the one hand the ideas it presents are endlessly intriguing, and trying to percieve what they speak of is much like running in a dream (at least for me). On the other hand, the book is too short, a thinly veiled lecture, in which the societal patterns in Lineland aren't explored to their full extent. One main problem I had in the novel was the main character's view of women (despite the cryptic apology in the Preface). Women are seen as unskilled "lines", the simplest of figures, dominated by their emotions, ignorant, and dangerous. While this might seem like a commentary on the ways women are treated today, I threw this idea aside: the fact remains that many of the harmful descriptions are proven true by the narrative. Should not they be contradicted to make such a point? But I digress. I understand the novels purpose is not to improve the role of women in society, but rather to convince the reader of the existence of a fourth dimension. At this is surely succeeds. I still am wondering is whether the added dimension might be spacial, temporal, mental, or something entirely different. It truly elicits thought. To continue, I enjoyed the book. However, it isn't for everyone, and at times I simply wished to hurry through it to finish and get on with things. But at a slim 80 pages, it is decidedly worth it. I would have given a four star rating because of this, but length seems like a poor measure of quality. Also, allow me to commend Dover for their Thrift editions of books. While most of these are free on the internet, it's great to get something to hold in my hands for only a pittance.
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Summary: I am become as God
Review: You have to follow geometry and be able to read with your index finger to follow this book. That is its greatest fault. It presents an interesting satire on Victorian social structure, but the main purpose, mathematics, is mind boggling. I am not an inept reader, but I found myself having to reread several parts just to make sure I go the jist of them. I will say that the most interesting part is how Abbott decides to describe the social structure and how it changes certain aspects of their existence. For example, although it was a bit convoluted for the aforementioned reasons, the way that the shapes reproduce was one of the more interesting parts of the book. I also enjoyed the way that each succeeding generation had more sides, thus making them higher on the social ladder. Then, once Abbott begins to go into the other dimensions, it become even more fascinating. His imagination is the most redeemable quality of the whole experience. Also, I commend Abbott on his introduction to the system of dimensions.
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Summary: Intersecting Planes
Review: This ingenious approach to science and mathematics relates the higher forms of each to the graduate educated as well as the proverbial layman. But disguised amidst the ideas of another dimension of reality for these complacent Flatlanders, lies a social and religious commentary on our own society. The roots of ignorance, or rather self-perpetuated blindness, toward several social and religious truths are discussed, and each hold as true today as when Abbot first wrote. This triumph of penmanship is of multiple dimensions; where the planes of scientific inquiry, dimensional mathematics, social forces, Christian ethics, women's rights and aristocratic roots all meet--to name a few. Don't let its small size disguise you; there is more in these few pages than in many full length novels. A must read!
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Summary: Great Introduction to Other Dimensions
Review: Flatland is an excellent pseudo-fiction written to enlighten the reader as to the interactions between the dimensions. The escapades of the squares, lines, circles and triangles as they live their lives in only two dimensions and encounter both 'lower' and 'higher' dimensions is very illuminating as to how different dimensions work together, and how it is not possible for someone of a lower dimension to perceive the higher dimensions. I especially enjoyed Sphereland (which is at the other end of the book, flipped over in a somewhat corny configuration) because of the added thought and depth it brought to the interactions between the sphere and the squares that were being observed in flatland. It is the original introduction of the sphere that leads the enhabitants of the two-dimensional world to ponder the third dimension, and it is this further discussion of the three dimensional world that allows us to ponder what lies out in the fourth dimension. The second book does a very good job of answering a lot of the questions raised in Flatland, as well as bringing up many other curious items (such as the 'flipping' of the dogs and what flipping would entail in a three dimensional world). Sphereland does a good job of walking the reader through the initial set up of Flatland, so if one is reading them back to back there is a lot of initial material that can be skimmed or skipped. I would recommend that you can go straight to sphereland and not miss a beat. I did think that the emphasis placed on the 'backwardness' of the Victorian thinking two dimensional universe was a little much, but understand it was part of the times. It would have been nicer had the author of Sphereland merely skipped over its presence, rather than trying to set things straight through some kind of cultural revolution. All in all, this is a very good book that leads to some very serious thinking - I would recommend it to everyone, regardless of their interest in science and math.
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Summary: A beginning for illumination
Review: I'm still not sure to this day if Abbott's geometry students grappled how fantastic a book it was that their teacher had written for them. First off, my geometry skills improved two-fold after reading this. Second of all, the book was a masterful satire of the times society. Women being regarded as witless beings, and soldiers portrayed as violent louts. Finally, it practically started the entire religion of modern illuminism. First, Abbott shows that even he who is regarded as the wisest in the land can be ignorant, and some "priests", or government officials, may not tell all of the facts. Lower planes may be ignorant, but with the help of a being in the higher dimension anyone can be guided. Further more, it suggests that there are limitless multitudes of higher dimensions.
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Summary: Classic romance and satire
Review: Besides being a "Romance" about higher and lower dimensions, and the ingenious way in which Abbott uses geometry to show us the limitations imposed by our own limited world view, this is also a very pointed social satire about Victorian England. For example, in the main character's flatlander universe of two dimensions, one's intellect and social class are determined by the number of sides you have as a polygon. If I recall correctly (it being 35 years since I read it--someone please correct me if I err in the details) workers have three sides and are triangles, the middle class consists of squares, and the professionals and the nobility have five sides or more. But basically the principle is, the more sides you have, the higher up the social scale you are. Therefore, the king of this odd dimension has so many sides he is basically a circle. Then there are the women, who are virtually straight lines, pointed at each end, which basically means they have no intelligence at all! Furthermore, if a woman bumps into a "higher" polygon she will puncture their side and instantly kill them. This means women are both the dumbest and most dangerous creatures in this strange dimension. If a woman is coming at you straight on, she is essentially invisible, and you can bump into her without knowing she is even there and accidently kill yourself. Hence, there is a law requiring women, when they are out and about, to make a lot of noise so that other polygons will be able to avoid impaling themselves. Anyway, as you can see, there is a lot of vicious social satire in this short work. The author's satirical portrayal of social class issues and especially of women is even more prescient in view of social developments over the next 100 years, at least in the west.
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Summary: Makes you think about perspective...
Review: In this book, Abbott uses the best tool available to those of us who try to understand the incomprehensible: analogy. "Mr. A. Square" is a man that lives in the two-dimensional world "Flatland," and through strange phenominon that leave him branded as a heretic, he visits the 1- and 3-dimensional worlds. He sees that many things are just about perspective. Flatland was written in a time before computers, and when "higher dimensions" were still about space and perception and analogy rather than some strange physics notion that this mathematette doesn't understand. It was also written in a time when it was appropriate for the author to have one-dimensional women in a two-dimensional world (or, alternatively, women as points in the one-dimensional world). This difference between the author's perspective and ours certainly adds a... "new dimension" to reading it! I first read this book when I was 12 years old, and it was not at all above my head at that age. I'm no a professional mathematician, and I still enjoy reading the novel. I recommend it to anyone.
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Summary: A Summer Reading No-No
Review: As a future sophomore high school student that was forced to read this book over summer vacation, I would like to voice my opinion. Flatland, by Edwin Abbott was absolutely horrible. This man should have been locked up when the book was written in 1895 or '96 (whenever it was written). I had to read Flatland for my Geometry class and let me tell you, just by reading the description online sent me into a fury. I had no interest in reading about a two-dimensional world with shapes that move about in a society based on how many sides they have. But I did try to keep an open mind - but that (as you can see) didn't work. You have to be truly TRULY interested in that sci fi dimension hogwash to completely understand and fully enjoy this book. Maybe I disliked it so because I had to read it over my 90 days of summer vacation as well as 4 other non intersting and unentertaining "books of literature" (I think summer reading really makes students dislike reading even more). I personally enjoy reading the newspapaer, National Geographic magazines, and some books that may grab my attention at BARNES AND NOBLE (just for those who believe me to be some hot headed teenager who dislikes a good book). Please! Save your $4.45 and put it toward saving hungry and dehydrated children in Ethiopia instead of buying this ridiculous "satire".
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