Flatland: A Romance of Many Dimensions by Edwin A. Abbott. Published by MobileReference (mobi).

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This is an electronic edition of the complete book complemented by author's illustrations. This book features the table of contents linked to every chapter and subchapter. The book was designed for optimal navigation on the Kindle, PDA, Smartphone, and other electronic readers. It is formatted to display on all electronic devices including the Kindle, Smartphones and other Mobile Devices with a small display.

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Flatland: A Romance of Many Dimensions is an 1884 novella by Edwin A. Abbott, still popular among mathematics and computer science students, and considered useful reading for people studying topics such as the concept of other dimensions. As a piece of literature, Flatland is respected for its satire on the social hierarchy of Victorian society. Isaac Asimov, in a foreword to one of the many publications of the novella, wrote that it is "The best introduction one can find into the manner of perceiving dimensions."

Several films have been made from the story, including a feature film in 2007 called Flatland. Other efforts have been short or experimental films, including one narrated by Dudley Moore and another with Martin Sheen.

- Excerpted from Wikipedia, the free encyclopedia.

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Unless you're a mathematician, the chances of you reading any novels about geometry are probably slender. But if you read only two in your life, these are the ones. Taken together, they form a couple of accessible and charming explanations of geometry and physics for the curious non-mathematician. Flatland, which is also available under separate cover, was published in 1880 and imagines a two-dimensional world inhabited by sentient geometric shapes who think their planar world is all there is. But one Flatlander, a Square, discovers the existence of a third dimension and the limits of his world's assumptions about reality and comes to understand the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England. The further mathematical fantasy, Sphereland, published 60 years later, revisits the world of Flatland in time to explore the mind-bending theories created by Albert Einstein, whose work so completely altered the scientific understanding of space, time, and matter. Among Einstein's many challenges to common sense were the ideas of curved space, an expanding universe and the fact that light does not travel in a straight line. Without use of the mathematical formulae that bar most non-scientists from an understanding of Einstein's theories, Sphereland gives lay readers ways to start comprehending these confusing but fundamental questions of our reality.

Customer Reviews:

Wisdom for pennies It's nice in this economy that you can still buy this much idea for this little money.

Here is the book that tells what it means to be a prophet....more info

Ok, but no story I was assigned to read this book as part of my online geometry course, and it was ok, except there is absolutly no story line to the book....more info

A classic I have read this book at least a dozen times. It's a must read for anyone, a satire of many dimensions. While the aspects of dimensionality apply to the math geeks, the pun on straight-laced Victorian society actually mirrors many of the things we face in our society today, but with a different twist. This is a great way for a lay person to understand the concept of dimensionality. If you like this book, I also highly recommend reading Rudy Rucker's Spaceland and Ian Stewart's Flatterland. Both are great sequels to this original classic and absolutely hilarious!...more info

Absolutely worth it The first contact I ever had with this book was in fourth grade when my teacher read a couple of passages as a lead-in to geometry.
That being said, I need to tell you that I hated my freshman geometry course. My teacher didn't speak English; there were all these formulas, theorems, and postulates that we had to memorize; and we spent all our time doing useless proofs. But this is getting into my high school career, and away from a review of this book.
Even though I didn't enjoy geometry, I found this book fascinating. Don't be deceived by the subtitle; it's not a love story. Abbott uses the word "romance" in the sense of "epic." I guarantee that you will stop at least once while you're reading this book to try to wrap your mind around what the fourth dimension must look like.
The only criticisms I have are about the misogyny and the pacing. In Flatland, women are treated as second-class citizens, but this is not a major theme. A few times, particularly during A Square's conversation with the King of Lineland, I got bored. But overall the book was paced well, and I'm impressed that the 19TH century churned-out any book less than two hundred pages.
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A Gateway Book I read this book when I was 13 because my math teacher recommended it. This book is great. It was first published in 1952 and is still used and taught by schools, mathematicians, physicists, and others. I have always had an interest in math and since reading this book I have been reading other math/science related books nonstop. Anyone who likes math should read this book....more info

A Great Read-Even If Your Not Into Math It's hard to believe that this book was published in 1880. Abbot, the author, was in my eyes, a genius. I read this book and was amazed by several things:
1-All the amazing concepts in this book were incredibly easy to understand-even for a high school student. The diagrams included also help a lot. I did not know or understand much about dimensional theory before reading this book, but after, I'm amazed at how much I learned from an amusing book written in the late 1800's.
2-This book should not be taken just for its mathematical simpleness and genius, but also for it's amusing writing. The story was funny, often satirical of the Victorian world which Abbot lived in. This is one of the reasons the book was so easy and quick to read-it is interesting in a literary as well as a mathematical sense.
3-The book contains no complex math equations involving numbers what-so-ever. It only explains theory in an easy to understand way that does not limit the concept that the author is teaching.

These and other details make Flatland one of the best books I have ever read. If you liked Flatland after reading it, also read Sphereland. I have written a review for it, also (you may see it by pressing the link)....more info

Expand your mind! Flatland is a great book for those who have the ability to think in an abstract way. If you appreciate mathematical puzzles, physics, or programming, you'll probably love Flatland. Although I liked it, I expect Flatland would be more popular among men than women.

The book is relatively short and an easy read. It doesn't have much of a plot; instead, the narrator spends time explaining the nature of a two-dimensional universe, and compares it to three-dimensional "Spaceland".

The book opens your mind - if two-dimensional characters can't see or imagine a three-dimensional universe, who is to say we can't see or imagine a four- or five-dimensional one?...more info

Excellent mathematical analogy! This book is a great piece of very clear, very convicting prose, using well-explained mathematical analogies for classism, sexism, and close-mindedness. I think it's a great analogy for people's willingness to accept paradoxes and the possibility of a spiritual realm. It was written by a minister, so that's not so much of a surprise. I highly recommend this book! The mathematics are simple and not intimidating. Mind-opening....more info

Flatland visited Flatland: A Romance Of Many DimensionsThis is not the version I bougt, because that one was nott in the list. This is the same title and author and about the same price, so it is about the same book. It's an entertaining story about analogies between two and three dimensions mainly, to come to an idea to percieve four and more dimensions, although for me some ideas were new, I can't say that I can imagine 4 spacial dimensins now, a two dimensional square with four one dimensional line borders leeds via a three dimensional cube with six two dimensional square sides to a fourth dimensional "supercube", with eight cubes as borders and twelve cornerpoints, how I must imagine that is not clear. But the ideas and the story are original considering the time in which the book was written....more info

A Book that Introduces the Reader to Strange, New Lands +++++

In order to understand this twenty-two chapter book (first published in the mid-1880s) by Edwin A. Abbot (1838 to 1926), you have to understand what is meant by the word "dimension," a word in the book's subtitle "A Romance of Many Dimensions." A dimension is any measureable distance such as length or width. So something that has one dimension has only one measurable distance, something that has two dimensions has two measurable distances, and so on. You also have to realize that there are geometrical forms that can be drawn in these dimensions. Thus a line is such a form that only has one dimension, a triangle is such a form that has two dimensions that appears flat and non-solid, and a sphere is such a form in three dimensions that appears solid. (Another name for three dimensions is space.)

Part one (twelve chapters) of this book gives us a glimpse of the two-dimensional land where the narrator, Mr. "A. Square," comes from. This place, called "Flatland," is inhabitated by two-dimensional beings of which Square is one. These beings no nothing of "up" and "down." Square tells us details of Flatland society such as its resident's domestic life and its political turmoil. It is a place dominated by such things as a rigid social hierarchy, sexism, and closed-mindedness.

Abbot was a Victorian and his description of Flatland is meant to be a parody (using wry humor and biting satire) of English Victorian society. Abbot seems to have fun mocking the upper classes of the 1880s in his book. I found that much of what Abbot says can be applied to modern society.

As an example, Square tells us of the social hierarchy that exists: "Our women are straight lines. Our soldiers and lowest classes of workmen are Triangles with two equal sides [called an Isosceles triangle]...Our middle class consists of Equilateral or equal sided triangles...Our professional men...are Squares...and five-sided figures, or Hexagons, and thence rising in the number of their sides till they receive the honorable title of Polygonal, or many-sided...Finally when the number of sides becomes so numerous...that the figure cannot be distinguished from a Circle, he is included in the Circular or Priestly order; and this is the highest class of all."

Part two (ten chapters) of this book is very interesting since Square tells us of his visits to "Lineland" (a land of one dimension), "Spaceland" (a land of three dimensions, a land Earthlings are used too), and "Pointland" (a land of no dimensions). Readers will find that they will have to adjust their thinking every time the two-dimensional Square visits a world of different dimensions. For example, when Square meets "Sphere" (of Spaceland), the reader will have to "see" Sphere as Square does--in two dimensions. The end of this part has Square realizing that three (and perhaps more) dimensions exist and trying to tell his fellow close-minded Flatlanders this.

My favorite sentence in part two occurs when Sphere makes an unexpected visit to Square's home (and Square doesn't know who Sphere is, fearing that he is a burglar). Square says, "The thought flashed across me that I might have before me a burglar or cut-throat, some monstrous irregular Isoceles, who by feigning the voice of a Circle, had obtained admission somehow into the house, and was now preparing to stab me with his acute angle."

Abbot, besides being a writer and educator, was also a theologian. So are their any spiritual or metaphysical aspects to this book? The answer is yes but this is not always obvious. For example, when Sphere makes his first unexpected visit to Square's home, he slowly seems to materialize in front of Square. Thus Sphere seems to be a supernatural, supreme being and Square refers to him as "your Lordship." Another example is Sphere sees Square as "a fit apostle for the Gospel of the Three Dimensions."

This book is written in Victorian English that may be difficult (for some) to comprehend at first. But I found that as I progressed further into the book and got used to this type of English, it becomes much easier to comprehend. The sketches found throughout the book also help immensely in getting across what Abbot was attempting to convey.

This book raises a number of questions, some of which are as follows:

(1) Why does our universe have three dimensions and not two or four?
(2) In what ways does our three-dimensional universe affect its physical, chemical, and biological properties?
(3) Do universes that have two, four, five, or more dimensions exist?
(4) If other universes of different dimensions do exist, then are there beings in these other dimensions?

Finally, for those who want a good non-fiction account of possible other dimensions, I recommend Dr. Michio Kaku's book "Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the 10TH Dimension" (1994).

In conclusion, this is a unique book that sparks your imagination and raises certain questions. Be warned though! By reading this book, you may become one in "a race of rebels who...refuse to be confined to [a] limited dimensionality."

Wisdom for pennies It's nice in this economy that you can still buy this much idea for this little money.

Here is the book that tells what it means to be a prophet....more info

very nice ebook One-click transaction. Couldn't ask for a more wonderful buying experience. Thank you very much!...more info

My favorite book to teach This book is such a great tool. I've used it for 10 years and it still gets my students excited about dimensions. They can't believe it was written over one hundred years ago and still, as they say, "blows their minds!"...more info

An amazing look at the perceptions of the world in an old-fashioned style Flatland is quite an interested and at times, mindblowing piece of writing. The novella length story can be seen as an expansive, yet fictitious look a a unique and possible world or can be perceived as an interesting look at our world from a vantage unlike any other and in this, there are many strong implications. This is a must read for any math lover or sci-fi fan....more info

Some of my best friends are square The persecution of individuals is an abhorrent way of life in some lands. To be repressed simply for preaching a new view of things. To be imprisoned for your beliefs. I am thinking, at this moment, of one individual in particular who has had to suffer the humiliation of life without parole simply because he chooses to see things in a different way. Should the fact that this person is merely a square (four equal sides and corners) be any kind of an impediment towards our full understanding of him? As a recent convert to three-dimensional worlds, the author of "Flatland" (given, originally, as merely A. Square) describes his own two-dimensional existence as best as he is able. It is hoped that perhaps by publishing this petite memoir of his world and experiences he may shed new light on his predicament and perhaps even win a follower or two.

The world of Flatland (as opposed to our own multi-dimensional Spaceland) is a simple one. In it, the more sides an individual has, the (supposedly) greater intelligence and influence. Therefore it stands to reason that circles (which is to say, many sided polygons) rule as priests and all hexagons, squares, triangles, etc. hope to someday ascend or let their children ascend to that most worthy class. Women, sadly, are given short shift. They appear as lines (though the narrator does concede later on that they are perhaps more accurately described as very thin Parallelograms. The narrator goes on to describes how shapes in Flatland recognize one another, what their lives are like, and even gives a bit of brief historical background regarding the great Chromatic Sedition that almost made all shapes equal under the eyes of the law and society. The square then recounts the adventures he had when, in a dream, he approached Lineland and then was visited by a sphere preaching the gospel of the Spaceland. With the discovery of a third dimension the square is given to preaching about this new place to his fellows and, for his efforts, is summarily arrested and cast into prison from whence he writes this book.

"Flatland" was originally published in 1884, a fact that places some of its odder elements into (ha ha) perspective. Appended with a Preface that accompanied its second revised addition, the "author" (A. Square) responds to those critics that accuse him of classism and sexism. The square admits that years in prison may have, since the publication of the book, given him greater insight into both women AND his "betters". Just the same, it's difficult for a reader today to hear that women are "consequently wholly devoid of brain-power, and have neither reflection, judgement nor forethought, and hardly any memory" and not feel a little put out. On the other hand, we're dealing with some serious satire here, and we should treat the book accordingly. In general, it's a delight. Paving the way for such modern classics as "The Phantom Tollbooth" or even "A Wrinkle In Time" (the latter making at least one direct reference to "Flatland"), the book is a satire in the finest sense of the word. The narrator is, undoubtedly, unreliable which makes the entire book just that much more enjoyable. Author Edwin A. Abbott put an extraordinary amount of effort into this story. As is often the case with authors that slum in fiction, children's literature, or works of humor (right off the top of my head I'm thinking of Gilbert & Sullivan and Sir Arthur Conan Doyle), "Flatland" was written as a bit of fluff and ended up (whether Abbott liked it or not) as the author's best known work.

Though a lovely concept, this book is perhaps best read by teens and adults rather that kids. I'm not saying that there won't be the spectacularly brainy ten year old who's a fan of both Math AND English and speeds through this book like butter. I'm just saying that such a child is in the minority and that you probably shouldn't foist a tale that contains such sentences as "Now, all our lines are equally and infinitesimally thick (or high, whichever you like): consequently, there is nothing in them to lead our minds to the conception of that Dimension". You get the picture. One fact I discovered to my own delight was that this book does not, in fact, require a firm grasp on geometry. It couldn't hurt, and I'm sure you'll get quite a lot more out of it than if you've heard of angles or circumferences, but it's not a prerequisite for enjoying this tale. As long as you've a certain amount of imagination and a will to suspend disbelief, you should be in the clear.

The Saturday Review of Literature once said that Flatland was, "One of the best things of its kind ever written". This seems to me to be somewhat backhanded praise since very few "things of its kind" HAVE ever been written. And shouldn't it be unequivocally be pronounced the best by default alone? To my mind, the book's well worth the reading. It deserves its praise and should be remembered amongst the best of the fantastical satires ("Gulliver's Travels" for example). It's a short book too, so you've really no excuse for not reading it. A delightful dip into the unknown.

Neither a good math nor fiction book, but a passable hybrid What is there to say about Flatland? It is certainly a creative attempt at trying to familiarize people with the concepts of dimensionality. It is not nearly as enlightening as some reviewers have made it out to be, though there are a couple of great endearing ideas that will stick with you.

Unfortunately, what starts off as a great book quickly becomes mired in tedium. Part of the tedium stems from the vast difference between 19th and 21st century cultures. Abbott works hard to describe a society for one-dimensional or two-dimensional beings based on his own Victorian era. Unfortunately it is written in such a way that the difference in values between our two eras adds confusion rather than enlightenment to the message of the book. We can't identify with the society, and that identification is crucial to the usefulness of the story. Second, there is entertaining fiction, and then there is ad-nauseum details which detract from the plot. His penchant for tangents (pun intended) reminded me of how boring the Iliad could be at points.

The book receives an A for originality. As for simplifying weighty concepts and making the matter entertaining, it receives only a passing grade. It is so far entangled in a social scheme that is outdated as to detract from the overall enjoyment....more info

A book of its time. This book was written in an attempt to prepare the minds of the Victorians to the concept of a fourth dimension, as a side story it is a commentary on the sexist and stratified society in which the clergyman, mathematician and head master Mr. Abbott found himself in. Abbott draws our attention to the lowly status of the "irregulars", triangles and in particular female "lines" not because he agrees with their plight but to highlight the inequity and absurdity that the majority can be lorded over by the minority. But I digress. The main story is about enlightening a people accustomed to 2 or 3 dimensions to the prospect of 3 or 4 dimensions respectively. I only gave it three stars as I dislike the first half of the book in that it doesn't have a coherent story - rather a series of chapters each on a different area of 2D society. A story is developed in the second half of the book and this is where it really picked up for me. While I would have liked to know how lines "give birth" to polygons I understand that this is a minor technicality and the concept is still sound without that detail being included.

A note to teachers: Don't set this as required reading, your students won't like it, they already know all about the 3D world and the 4D concept isn't alien to them like it was to the Victorian society it was written for. Instead read them Planiverse by A.K. Dewdney it will blow their minds.
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Flatland This book is a great reminder that what lies outside of our understanding does not necessarily lie outside the realm of possibility. You don't have to enjoy mathematics to enjoy this book - I'd recommend it to anyone!...more info

Wonderful experience Smooth transaction, careful and fast shipping, very nice product, couldn't ask for a more wonderful buying experience. Thank you very much! A+++...more info

Beware the USE of this story In Flatland, we are reminded that it is hard to convince people of something, when they have no terms of reference with which to make sense of what we're saying. It is a great reminder to us that, when we are talking to people from other religions or belief systems, it will be very hard for them to understand us. We have to really bend over backwards to translate our message into something that they can latch onto and understand. Fine. But here is the problem: Today, people are using this film to convey a very different message. They try to leave the impression that anyone who disagrees with their agenda (political, environmental, gender, whatever) is (1) wrong, (2) too poorly armed to ever understand them, and (3) therefore not worth trying to reason with. The result of this line of "thought" is that they will simply have to impose their wisdom on the Others. This leads to having government health care, whether you want it or not; using politically correct language, whether your want to or not; for your own good! So, the only problem with the Flatland story is that it fails to remind us that most people who go against the crowd are simply wrong. Sure, everyone laughed at Einstein and he turned out to be right. But everyone also laughed at millions of clowns who were simply nuts. The idea that anyone who is different is therefore right, is wrong. The idea that there is no point in reasoning with your adversaries, is also wrong. Please read or watch this story and enjoy it, but when your boss says, "I want us all to see this film so that we have a common language ..." RUN!...more info

A fun read for those who enjoy math, politics, and puzzles If you're obsessed with math but need a break from equations and formulas, pick up a copy of Edwin Abbott's Flatland and go to town. Published over a century ago, this book illustrates the faults of politics and nobility as it explores the delicate relations between the inhabitants of Flatland. As the book progresses it diligently explains the factors of the known dimensions, and the obstacles that separate them. This book is a great read for anyone who loves history, math, and a good laugh.

This book follows a square that is set in his ways about the world. As an inhabitant of Flatland, this square ranks as a "Professional" or "Gentleman". He is joined by every other imaginable regular figure, and all have their place in the world according to their shape. The chain of nobility begins with women, who are, as Abbott repeatedly mentions, "straight lines". Following the women are Isosceles Triangles, who make up the army and servant class. Next come Equilateral Triangles, followed by Squares, Pentagons, Hexagons, and the rest of the regular Polygons follow suit. At the top of the pyramid rests the Priestly Circles, along with Polygons made up of so many thousands of sides they appear to be circles. Each level is smarter than the previous, starting with women who are like goldfish in their mentality, and ending with the Circles who occupy the highest roles of society. The second way Abbott connects the generations is highly entertaining for me, so I'll just leave that treasure for you to discover on your own.

Abbott has a lot of fun in creating the geometric figures' way of life. For instance, he has made recognition of another figure possible by sound, sight, and touch. The women have to take special precaution due to their dangerous shape. Abbott goes to the extreme when describing their circumstances, which I believe to be rather humorous.

The second part of the book follows the Square as he is shown dimensions that are unimaginable as well as down right silly in his perspective. He's shown Lineland, the world of one dimension, in a dream. Later a figure appearing to be a magical circle shows him the way to Sphereland, the world of three dimensions. Lastly, the Square is shown the world of Pointland, a place of no dimensions consisting of simple dots. Each world evokes a different response from the Square as his mind is opened to the various spaces surrounding him.

All in all, the book was a fun read. The best part to me was Abbott's many explanatory diagrams. However, being a female I was severely disgruntled by the low intelligence and mockery of women. I did find peace in knowing that our sharp points could be the weapon of ultimate destruction, as ironic as that may be. The line of nobility definitely revealed the books age, and also evoked several strong feelings I have towards equal rights. I love how I was connected to the troubles and controversy of an older era while learning about present day mathematics. Honestly, if you are a person with strong opinions who loves to argue, this book will give you and your book club things to talk about! One factor that kept me zoned in throughout the story was the reoccurring mention of the phrase "straight line". This redundant fault of Abbott's was a rather comical feature for me, and I have to say it was interesting to see how many times it popped up.

This book is a fun way to view the world as it exists in two dimensions. The flashbacks to historical ideals make for a highly political and controversial read that will surely keep the reader interested. Once Abbott starts explaining the multiple dimensions and their connections, the book becomes a whirlwind of that "I know what I mean but I just can't explain it" feeling of frustration and determination. If you or anyone you know enjoys geometry, controversial issues, and puzzles, this book is sure to be a hit.

For hundreds of great reviews of young adult books by young adults themselves, be sure to check out notrequiredreading.com. ...more info

Written for all Flatlanders...like us This book is a must have for all bonafide Flatlands fans.

First off, it has the original Flatlands classic by Edwin Abbott Abbott, the mathematician/clergyman would first took us to the world of A Square. And it also has the 1967 followup Sphereland.

It bears noting that Sphereland is but one of many follow up so Abbott's classic and because they're all good and worthy in their own right, I'll repeat them here:

Spaceland...the Rudy Rucker classic which focuses more on following up the story than the science of Abbott's original book;

Plainiverse...the Dewdney work which actually endeavors to thoroughly flesh out the physics and biological issues of what life actually would be like in 2D (for what it's worth philosopher Dan Dennett says that this is favorite take on the Flatlands theme); and

Flatland Annotated and Flatterlands...both by mathematician Ian Stewart. If I wasn't as a big of a fan of this book I probably admittedly would've stopped my collection at just these entries because the annotated version has the original Flatland in it and also because in my opinion at least Flatterlands does the best and most recent job of updating the mathematics of Flatland.

But that being said, Sphereland is a serviceable entry and does faithfully follow the A Square story...albeit two generations later...and like the original Flatland serves as a great metaphor for the desireability of open mindedness and looking past your limitations....more info

Everything A OK! This book has to be read by every mathematician and why not everyone! It can help you get a better view of higher dimension, in a very strict mathematical way, without having difficult terms. It is also a deep book with implications even to relegion and the way we see the world! Plus the whole story is very funny! As for the transaction it was excellent. The book came to me within the appropriate dates.

A quite curious book I bought this book on a whim because it was so cheap, and I rather enjoyed it, despite it being a very short book. At the minute, it is circulating among my friends.

The first part deals with the social structure and mores of the flatland society. I've heard that it's a critique of the way life was set up when the book was written, but I can't confirm that. It describes a world where women are seen as worthless nobodies who are dangerous without really noticing, and where people are judged and placed in social classes based merely on their appearance (more specifically, how many sides they have).

The second part is why you should buy this book. It is the tale of what happens when one of the members of this two-dimensional society is taken and shown how life is lived in worlds of one, zero, and three dimensions. It is this part of the book which is absolutely fascinating, and convinced me that I will never be able to envision a fourth spatial dimension.

I highly recommend this book as a singular novelty, and a very good read....more info

A 2D and 4D Classic Text Originally written with a Victorian theme, it is now a must-read classic for anyone who enjoys reading about the fourth dimension. The story is about a two-dimensional being (called A Square) living in a two-dimensional world (hence the title, Flatland). As a three-dimensional being imagining this two-dimensional world, you come to realize that you can understand higher-dimensional space through lower-dimensional analogies. In fact, A Square meets a three-dimensional being (A Sphere), and takes a journey beyond the second dimension. Although some readers may enjoy the book for its historical and Victorian period merits, math lovers can enjoy the book for its geometric insight.

If you are curious about the fourth dimension, you should also read:

- Spaceland: A Novel of the Fourth Dimension, Rudy Rucker's novel of the fourth dimension
- Flatterland: Like Flatland, Only More So, a continuation of the geometric idea from Flatland
- The 4th Dimension: Toward a Geometry of Higher Reality, Rudy Rucker's classic introduction to the fourth dimension
- The Visual Guide to Extra Dimensions: Volume 1: Visualizing the Fourth Dimension, Higher-Dimensional Polytopes, and Curved Hypersurfaces, a modern geometric introduction to the fourth dimension...more info

Excellent book! Incredibly easy and direct way to give a new perspective into a 1D, 2D and 3D "space"!

Flatland is written in 1800's English, so it might be a little bit tricky to get it straight, if you aren't a native English speaker. Sphereland is straight forward!!

Understand Multi-Dimensional Worlds This book is often recommend by theoretical physicists and mathematicians (most often mathematicians involved in hyperdimensional topology) to their students.

It was written by a Shakespeare scholar in Britain more than 100 years ago. The reason it is recommended by theoretical physicists, etc., is it provides the reader with a framework for understanding and trying to visualize dimensions above or beyond our ordinary four-dimensional world (length, width, heighth, space-time).

It deals with a two dimensional world with two dimensional beings and what happens when a third dimensional being interacts with a two dimensional world and what the two dimensional beings would see. It also does this in terms of a one dimensional being and one dimensional world interacting with a two dimensional world and two dimensional beings (or structures).

This book written with apparently some intent on commenting on Victorian England and its values (with what appeared to me to have some misogynistic comments within it), was otherwise an enjoyable book and really does provide a good analysis on multi-dimensional view points and visualizing or imagining hyper-dimensions.

If you are interested in advanced theoretical physics, hyperdimensional geometry or topology or mathematics, this is a very interesting book and may be useful. If you are just interested in a good unique science fiction story, I would highly recommend this. This is not an (explicit) math or science book - so you won't find any explicit mathematics (i.e., no math is required).

Thinking W A Y Outside the Box Yes, many young people have been required to read Flatland against their wills. Yes, many people have missed the real point of the book. This book stretched the mind and imagination in ways that are fun and challenging. The author might not have been entirely serious in writing the book, but nonetheless provided serious food for thought.

I believe Flatland is an excellent (and quick) reading experience for minds in the formative stage, a stage I recommend maintaining throughout life. The book's theological implications were the most important to me. I had always wondered where heaven might be, how God can see inside us, and what the spirit is made of. I do not know if extrapolating the Flatland concepts into a fourth (or fifth) physical dimension reflects ultimate reality, but it provides a sufficiently possible and plausible explanation to remove rationalist objections.

The 3-D sphere that intersects the plane of reality provided the "Aha" moment. The sphere embodied perfection and could mysteriously appear and disappear. Explaining the view from above the plane to a flat square is as difficult as explaining the spiritual realm to a person unable to envision beyond the world seen with the eye. A greater-dimensional being floating above the plane can see inside the geometric shapes, reach inside their skins without intersecting their boundaries, think far more complex thoughts, and take them out of their limited reality to a better place they could not have imagined. If a Flatland person had no thickness, he would have no volume by our reckoning, and therefore no real existence. If there is a spiritual dimension and a person has no thickness in that direction at all, then he may not really exist either.

We have learned to adjust to modern concepts of reality that are no longer Euclidean and Newtonian. Perhaps we need a view of creation that is not limited by unfounded presumptions of limited dimensionality. After you ponder the concepts of Flatland and extrapolate them to your life, I wonder what new thought may form....more info

ahead of its time This is a must read for anyone. Its written simply for anyone to understand yet the underlying principles can inspire thought and contemplation on the ideas of relativity and perspective. On the surface this book explores dimensions but it provokes thought about perspective and encourages you to evaluate your own perspectives. You can get anywhere from mild amusement from this book to philosophical life changing perspectives.

In detail, Flatland is a classic story about a two dimensional square that discovers the world of a line, a point, a sphere and beyond. The square contemplates his role in society as a square and realizes that there is something else out there when a sphere comes to visit....more info

Upward, not Northward A. Square is a rather exceptional member of Flatland, a world that only has two dimensions. He not only dreams about a one-dimensional world, but also dares to question the limitation of having only two dimensions. Being a polygon himself, he will never truly understand the magic of Spaceland, but his unbound imagination lets him travel beyond what others call their `space'. When he finally succeeds in going "Upward, not Northward" he gets convinced that he has a message to give to the other members of Flatland. But will the others accept his prophecy?

Flatland is a truly remarkable piece of literature. Not only makes is philosophy and mathematics accessible for the common reader, it also gives evidence of Abbott's visionary mind. Written in 1884 this book introduces the readers to concepts that will prove to become very `hot' more than 100 years later. Mathematicians of today who have no theory about the number of dimensions are almost considered to be unfaithful to their science.

This is simply a must-read for everybody who likes to fantasize about dimensions and what the world would look like if we could see beyond our known dimensions....more info

Incredible and amazingly provocative. A page turner! Abbott's imagination is just fantastic. And I say fantastic in the most realistic sense. He has so many amazing ideas and makes everything so believable, but also makes you consider the possibility of something, some world completely beyond your conception; completely beyond your reality. It's entertaining and interesting and left me turning page after page, not putting the book down. Anyone who would like a good, interesting book should check this out. It's great for everyone because not only is it a fabulously well-written imaginitave piece of literature, it's very short. Short enough to finish in a day as I did....more info

There's more to life than meets the eye (...). The obvious is that it is a math-ish book, just as any book written in English is also an English language book. To me, using an imaginary world of 2 dimensions and a journey into 0,1,3 dimensional worlds the author is revealing to us a potentailly new way in which to look at our own life, the universe etc. Its less a mathematical book and more a philosophical/spiritual book. The author's background should be an additional pointer towards this conclusion.

The message is that there is more to us and our life on earth than is commonly understood. That our perception of the universe need not limit it to just that in reality. The story itself is a highly interesting illustration of this fact using mathematical concepts. And the best part -- the author commendably stays away from actually expounding any theories or belief systems. For anyone interested in spirituality, this book will be mighty enjoyable....more info

It will stretch your imagination I just finished reading "Flatland" by Edwin A. Abbott and I'm not entirely sure what to think. While this book challenges the imagination of the reader with the possibilities of any number of dimensions, I found the language of the book a bit harder to wade through. While only around 100 pages, I feel it took me a longer time to read it than a longer, modern fiction, as the language is a bit older, complete with whence, thou shalts, and so forth.

However, I still think this is a worthwhile read, as the ideas are still applicable, especially with modern physics and with string theory claiming that more dimensions do indeed exist. I encourage you to pick it up if you're at all interested in mathematical curiousities and having your knowledge of 3 dimensions pulled and twisted a bit. Also, the social structure of a two-dimensional society is extremely interesting.

The first part of the book describes the world of Flatland, a world restricted to two dimensions and the society contained therein. In this world, each human is a shape, and irregularity is highly condemned. Women are straight lines and the highest class of society is filled with circles, or many sided polygons. Our author is a square, who describes to us the ways of life in Flatland, from how to recognize each other (as every shape would appear as a straight line seen edge-on), to how the laws of nature grant that successive generations may gain a side, thus rising on the social ladder. Also, he tells of the history of Flatland, during the trying times of the "Universal Colour Bill" and the "Suppression of the Chromatic Sedition."

In the latter part of the book, our square friend tells us of his vision of Lineland, whose inhabitants are confined to one dimension. Sadly, he cannot convince the Lineland monarch of the existance of another dimension. The next day, however, he is visited by a sphere from Spaceland. Through much demonstration and persuasion, the Sphere finally convinces the square of the existence of a third dimension, by bringing him into it. Sadly, after the sphere departs, and the square is again restricted by Flatland, he is unable to convince his Flatland companions of this miraculous third dimension. He is sentenced to a life in prison, taunted by a knowledge of an extra spatial dimension, yet forbidden by his two-dimensional world from ever entering it again....more info

a mind-expanding exercise of a book to the person who said "there ARE three dimmensions and we are NOT shapes"....the book is an allegory, and nowhere does it state that there isn't a third dimension. The book uses an IMAGINARY, multi-dimensional universe inhabited by shapes to convey the idea of higher and lower dimensions to us, who live in a three-dimensional world. the shapes aren't the point. the point is, (in my opinion) that we can use the same argument presented by A Square to A Sphere concerning higher dimensions, and apply it to our universe, and our dimension. I had to read this book over the summer as well, for freshman math, and i think it is great. It teaches you to think in entirely different ways, and i realize that a lot of people my age simply aren't up to that....more info

A valuable read culturally, but a literary mediocrity Sometimes you look at a book and shake your head. From what I've heard, they did that when this book came out in the late 19th century.

This book isn't science fiction in the classical sense; compared to A. K. Dewdney's Planiverse, the science in it is actually quite bad. It's more valuable as a cultural benchmark describing the class strictures of Victorian Britain in an unusual setting than anything else. Its overriding message of being open to different thinking, while admirable, is lost in the portrayal of a society whose strictures are not merely cultural but biological, rendering the point of the book somewhat vague at best.

It's interesting, yes. For the price of a Dover Thrift Classic edition, it's worth getting. But it's heavy-handed and lacking in any real sense of wonder such as you'd expect from a Jules Verne or Arthur Conan Doyle....more info

Flatland If you are looking for a book that makes you think this is the one. Written in 1867, its amazing that we are still having the problems that are embellished in this lovely book. This book helped me remember I need to be more empathic to others when they are limited in thier perception. And for me to never stop dreaming. ...more info

fun thought experiment this is a great book to help you put your mind around other dimensions. It was cleverly written and an enjoyable read....more info

Have always loved this book... This has always been a favorite of mine, so I wanted to christen my kindle with it. I imagine most people who will buy it for the kindle have probably already read it. If you like a mixture of Gulliver's Travels, Geometry and social commentary, it is worth the small amount of money. Of course you can get it for free since it was written in the late 1800's, but the Gutenberg version doesn't have good diagrams - they are all ASCII. I couldn't find diagrams in the versions available on AMAZON except the Oxford World's Classics edition, so that is the one I recommend. The diagrams are important for the geometry aspect and are excellent in this version....more info

Aamzing book - high school freshmen literature student I started reading this book thinking it would not work well for analysis in a literature class but I was suprised. While explaining geometric concepts, it has all the elements of any other story. The book was easy and fast to read and comprehend. After finishing this book as an assignment, I quickly bought Flatterland for independant reading. I haven't found the time to start Flatterland but by the blurb on the jacket and other reviews, I am looking forward to it. I recommend this book to any high school student or slightly younger students interested in math or science. Of course, I recommend this to adults as well....more info

Sends the imagination soaring I have just finished reading this little book for probably the third time. As I tend to read in bed at night just before turning out the light to go to sleep, I would lie in bed after putting the book down trying to imagine the fourth dimension. The spiritual implications throughout the book are undeniable. Once one has been touched by a higher dimension, life will never be the same. However, trying to communicate to others what one has experienced proves near impossible, as our square friend in Flatland so aptly relates....more info

i'd rather read a 2 thousand page book about cheese okay, i was forced to read this book for summer reading. it was awful. i only have one thing to say about this book-there ARE three dimmensions and we are NOT shapes. stop forcing children to read this book!...more info

A fun read for those who enjoy math, politics, and puzzles If you're obsessed with math but need a break from equations and formulas, pick up a copy of Edwin Abbott's Flatland and go to town. Published over a century ago, this book illustrates the faults of politics and nobility as it explores the delicate relations between the inhabitants of Flatland. As the book progresses it diligently explains the factors of the known dimensions, and the obstacles that separate them. This book is a great read for anyone who loves history, math, and a good laugh.

This book follows a square that is set in his ways about the world. As an inhabitant of Flatland, this square ranks as a "Professional" or "Gentleman". He is joined by every other imaginable regular figure, and all have their place in the world according to their shape. The chain of nobility begins with women, who are, as Abbott repeatedly mentions, "straight lines". Following the women are Isosceles Triangles, who make up the army and servant class. Next come Equilateral Triangles, followed by Squares, Pentagons, Hexagons, and the rest of the regular Polygons follow suit. At the top of the pyramid rests the Priestly Circles, along with Polygons made up of so many thousands of sides they appear to be circles. Each level is smarter than the previous, starting with women who are like goldfish in their mentality, and ending with the Circles who occupy the highest roles of society. The second way Abbott connects the generations is highly entertaining for me, so I'll just leave that treasure for you to discover on your own.

Abbott has a lot of fun in creating the geometric figures' way of life. For instance, he has made recognition of another figure possible by sound, sight, and touch. The women have to take special precaution due to their dangerous shape. Abbott goes to the extreme when describing their circumstances, which I believe to be rather humorous.

The second part of the book follows the Square as he is shown dimensions that are unimaginable as well as down right silly in his perspective. He's shown Lineland, the world of one dimension, in a dream. Later a figure appearing to be a magical circle shows him the way to Sphereland, the world of three dimensions. Lastly, the Square is shown the world of Pointland, a place of no dimensions consisting of simple dots. Each world evokes a different response from the Square as his mind is opened to the various spaces surrounding him.

All in all, the book was a fun read. The best part to me was Abbott's many explanatory diagrams. However, being a female I was severely disgruntled by the low intelligence and mockery of women. I did find peace in knowing that our sharp points could be the weapon of ultimate destruction, as ironic as that may be. The line of nobility definitely revealed the books age, and also evoked several strong feelings I have towards equal rights. I love how I was connected to the troubles and controversy of an older era while learning about present day mathematics. Honestly, if you are a person with strong opinions who loves to argue, this book will give you and your book club things to talk about! One factor that kept me zoned in throughout the story was the reoccurring mention of the phrase "straight line". This redundant fault of Abbott's was a rather comical feature for me, and I have to say it was interesting to see how many times it popped up.

This book is a fun way to view the world as it exists in two dimensions. The flashbacks to historical ideals make for a highly political and controversial read that will surely keep the reader interested. Once Abbott starts explaining the multiple dimensions and their connections, the book becomes a whirlwind of that "I know what I mean but I just can't explain it" feeling of frustration and determination. If you or anyone you know enjoys geometry, controversial issues, and puzzles, this book is sure to be a hit.

For hundreds of great reviews of young adult books by young adults themselves, be sure to check out notrequiredreading.com. ...more info

No depth The fantastical setting of Edwin A. Abbott's "Flatland" is one of the most curious in literature: a two-dimensional world in which all the inhabitants are sentient flat shapes which slide around on a plane with no knowledge or conception of a third dimension. However, the book's theme -- the importance of unimpeded scientific inquiry and the danger of denying the possibilities of infinity in all its forms -- is treated with the didacticism of a tendentious theological tract, leaving the reader, who probably was already well aware of the book's implications long before he even heard of the book, gasping for breath.

We are introduced to the nature of Flatland by the narrator, a nameless Square, who describes his world as being populated primarily by regular polygons. A citizen's social and occupational status is in direct proportion to his number of sides, so those with so many sides that they approximate circles achieve the highest ranks. These circular elite are dubbed "priests" and rule Flatland apparently on a parliamentary model. At the other end of the spectrum are the Triangles, who constitute the working class. Even lower than the Triangles, however, are the simpleminded Lines -- and these are Flatland's women, useful only for procreation. It takes little imagination to guess what the irregular polygons represent.

The Square's purpose in writing this report is to rejoice in his discovery of the (previously unimagined) third dimension, revealed to him by a helpful Sphere who visits from Spaceland. The Square, now in possession of arcane knowledge and an intuitive conviction of the existence of higher dimensions, assumes an evangelical role and ultimately emerges as a Promethean figure when he is imprisoned for the heretical act of preaching a third dimension.

"Flatland" has been compared to "Alice in Wonderland" and "Gulliver's Travels," but I'd say there are clearer parallels to Huxley's "Brave New World" (in the classist regimentation of the Flatlanders' society) and Samuel Butler's "Erewhon" (in the Flatlanders' strange and limited belief system). The difference is that the aforementioned novels employ both irony to qualify as allegorical satires and narrative integrity to endure as pure fiction, whereas "Flatland" is so earnest in its delivery and so ineffectual in its impact, it feels like a pebble in an avalanche. Too obvious and elementary to be a scientific or mathematical essay, too obtuse to be a philosophical treatise, too moralistic to be a good example of a novel, "Flatland" misses its mark and slips silently through the cracks....more info

Terrific! This may be the greatest science fiction story of all time. I have read this story at least ten times and I never tire of it. An all time classic that makes a wonderful conversation topic....more info

A creative story for math As a math teacher, I believe Flatland should be required reading. It is a geometric view in 2-dimensions that is challenging and funny. Can you imagine a world of 2-dimensions? The way of identifying characters, class and intelligence is intriguing. I believe this book is a classic....more info

A Good Book for Looking at the World Differently This book at first is very dense. But once you get used to the writing style it becomes a great tool for thinking about perception. I especially like the section on shading and how that can determine what it is you are looking at. It is a short book but it does take a little a time to get through. Overall, it is a very good book....more info

A fascinating book in which the characters are shapes Flatland is one of the most interesting books I have ever read. The characters of the book are lines and geometric shapes. The main character lives in a two dimensional world, then is exposed to the third dimension. Returning to the second dimension, his heightened knowledge is marginalized. Overall, the book reminds me of Plato's allegory of the cave....more info

The Limits of Perception My appreciation of mathematics came late in life, but it finally came. I have neither the aptitude nor the training to be a professional mathematician, but I like to spend a fair amount of time reading books on mathematics. A handful that I recommend are: Darrell Huff's _How to Lie With Statistics_ (1954); David Salsburg's _The Lady Tasting Tea_ (2001); Simon Singh's _The Code Book_ (1999); Robert Osserman's _Poetry of the Universe_ (1995); Reuben Hersh's _What is Mathematics, Really?_ (1997); Bryan Bunch's _The Kingdom of Infinite Number_ (2000); James Gleick's _Chaos: Making a New Science_ (1987); and Douglas R. Hofstater's _Godel, Escher, Bach: An Eternal Golden Braid_ (1979). The last is fairly stiff reading. But it is beautifully written; and if you read only a fraction of it, your perception of the world is likely to change.

All of which brings us to a Victorian gentleman who gave some attention to the nature of and the limits of our perceptions of the world. Edwin A. Abbott (1836--1926) was a Shakespearean scholar who also took honors in mathematics and theology. In 1884, he published a mathematical fantasy called _Flatland_. It is set largely in a two-dimensional world, populated by sentient lines and shapes. Most denizens appear as lines to one another, though the relative faintness of lines gives a clue to the nature of different shapes. There is a class system built on the relative complexity of shapes: women (Straight Lines), workers and laborers (Isosceles Triangles), the middle class (Equilateral Triangles), professional men and gentlemen (Squares and Pentagons), and the nobility (Hexagons and Many-sided Figures). There is some movement from class to class, but "a woman is always a woman". The houses are also two-dimensional, mostly pentagonal in shape. There is a kind of gravitational pull to the south so that the base of various shapes turn toward the south and their apex angles toward the north. The narrator, "A. Square," has accepted his world at face value. But one day, he encounters a shape that _seems_ to be circular but who _says_ that it is a sphere... And nothing is ever quite the same.

_Flatland_ quickly became a classic. Several sequels and companion stories to the novel were written over the years by other hands, but one of the best is that of Dionys Burger, a Dutch physicist. It was originally published in 1957 as _Bolland_ and was translated as _Sphereland_ in 1965. Burger's novel relates how the natives of Flatland discover that their land is really curved. They then discover the Einsteinian properties that it contains. Burger relates how triangles can become greater than 180 degrees, how mongrel dogs can become pedegreed through three-dimensional trickery, how a brave Line explorer defied the courts to reveal new truths about the nature of space, and what geometric fairy tales can reveal about the nature of the world.

I hear the dry thunder of voices of the Mathematically Challenged rolling across the Waste Land: "We could _never_ understand!" And I say unto you: "Oh, yes you can." You don't need advanced training in math to grasp the concepts-- and they are presented in a painless, charming, and entertaining manner. So read these books and be refreshed by the rain.

Burger's book modernizes _Flatland's_ portrayal of women (Straight Lines). Here is Abbot's treatment in his novel:

Nor must it be for a moment supposed that our Women are destitute of affection. But unfortunately the passion of the moment predominates, in the Frail Sex, over every other consideration. This is, of course, a necessity arising from their unfortunate conformation. For as they have no pretensions to an angle, being inferior in this respect to the very lowest of the Isosceles, they are consequently wholly devoid of brainpower, and have neither reflection, judgement nor forethought, and hardly any memory. (15)

In a foreward to the novel, Isaac Asimov asserts that Abbott "may have participated in these now-antiquated social views" (ix). Perhaps. But I think that Asimov misses an ironic bite in this passage. I suspect that Abbott was less blinded by the prejudices of his day than his narrator, A. Square. In Burger's book, women still are the bottom social class. But they are better educated, more responsible, and less hysterically emotional. The social classes in Burger's novel (which takes place some time after the action in _Flatland_) have become a bit more fluid.

I hesitate to recommend a book because it is good for other people. That sort of praise is the kiss of death as far as most readers are concerned. But sometimes you just can't avoid mentioning that characteristic. These two fantasies are good for you. But they are also great fun. There is not a stuffy bone in either one of these beasts.

"Something-which-you-do-not-as-yet-know" Do not miscast this wonderful little book as being merely "sci-fi". Two-dimensional "worlds" exist within ours, if only in a somewhat pragmatic sense. If we imagine some "thing" intellective within such a world, then we have little difficulty seeing that our humble narrator, Mr. A. Square, might be such a world's most insightful oddball. The book is a classic exposition in basic geometry, but it is more than this. Abbott uses mathematics to make some very telling observations about human minds and psychologies. Edwin Abbott (1838-1926) was a clergyman and a math geek. He was an educator, an expositor of English literature and New Testament studies, a notable headmaster, and the author of something like 40 books on widely varied themes. Today you will probably have a difficult time finding any of his other volumes, but Flatland is said to have never been out of print since it was first published in 1884. No need to retell A. Square's big adventures here, other than this bit of dialog between our two-dimensional thinker and his three-dimensional visitor/teacher (Square is given to thoughts of still higher-dimensional worlds):

"SPHERE. But where is this land of Four Dimensions? [A. Square]. I know not: but doubtless my Teacher knows. SPHERE. Not I. There is no such land. The very idea of it is utterly inconceivable."

Abbott offers his allegory of physical and conceptual limits with an economy of word and thought that is nothing less than extraordinary. A great many volumes, five to ten times as large, conclude having said far less than this little parable. Read it. You will take from it what you are willing to take. If you find little or nothing here, you are indeed a citizen of Flatland....more info

Exponentially entertaining! Keep in mind that this book was written over a hundred years ago, and consider the incredible ground it covers with this little tale: geometry (obviously), physics, government, politics, the clash between the sexes, class structures, manners, human nature, psychology, philosophy and even neuroscience (consciousness)! At first reading, it's deceptively simple, but explain it out loud to someone else and you'll find yourself noticing new things. If something doesn't seem to make sense, ask yourself "why?" This story is an allegory, a metaphor for so many things that fall into disjunct categories. There's a reason for the weird; the "bump" is there to make you take notice. Read it, think about it, give it some time and you'll be on your way to understanding the incredible range of this tiny work. ...more info

A Valuable Idea for Science and Math Teachers Abbott, the author, has the reader imagine three-dimensional structures from a distant horizontal perspective. The third dimension becomes unimportant, and can be dispensed with completely. Taking this further, we are left with a "society" of circles, triangles, and other 2-D geometric figures, all living in Flatland.

As a science and math teacher, I found this book an inspiration for thought-provoking questions, such as: How would you describe the sphere to someone living in Lineland or Flatland? How, for that matter, would you communicate the very concept of thickness to someone living in Flatland? Or volume?

Visualize a sphere crossing Flatland. It starts as a point, then a circle of expanding diameter, then a circle of decreasing diameter, then a point, and then finally nothing. Other 3-D figures can be visualized in comparable manner. The possibilities are endless!
...more info

Free SF Reader Flat is an exercise in science fiction geometry, if you like. It shows a denizen of a 2 dimensional world seeing what it would be like to exist in higher dimensions. An interesting mathematical and philosophical exercise. Some will definitely find this very odd, and rather quirky. If you don't know what a dimension means in this sense, give it a miss.

fun thought experiment this is a great book to help you put your mind around other dimensions. It was cleverly written and an enjoyable read....more info

A delightful sci-fi classic "Flatland: A Romance of Many Dimensions," by Edwin A. Abbott, is a marvelous tale that I regard as a pioneering piece of science fiction. According to the introductory note in the Dover edition, Abbott was an English scholar and clergyman, and the book was first published under a pseudonym in 1884. The book is enhanced by the author's own delightful illustrations.

"Flatland" is told in the first person by an intelligent square who lives in a fantastic two-dimensional world. He describes in fascinating detail his own world of Flatland, going into such topics as architecture, war, genetics, medical arts, law, and family values. Particularly fascinating is his account of his society's rigid stratification by class and gender. The square tells of his visions of zero- and one-dimensional worlds, and of his life-changing contact with the three-dimensional world.

Abbott succeeds in a task attempted with varying success by generations of science fiction writers since him: he creates an alternate world which is utterly alien, yet disturbingly familiar--a world that is complete and consistently compelling. "Flatland" could certainly be read as a satire of Abbott's own world; parts of it are laugh-out-loud hilarious. Whimsical yet possessing a biting edge, this is a brilliantly conceived and wonderfully written book. For a companion text, try A.K. Dewdney's "The Planiverse" (also about contact between two- and three-dimensional worlds); also try Aldous Huxley's "Brave New World" (an equally intriguing view of a stratified sci-fi culture)....more info

Relatively Little Mathematical Heft A whimsical introduction to the concepts of multidimensional mathematics, this book is very much the product of the 1880's Victorian era in which it was written. In a preface to the book entitled ``Limitations'', Isaac Asimov writes, ``This book, then, should lead us to question the limitations we set to our Universe generally, not only those that are mathematical and physical, but those that are sociological as well.''

Indeed, this book taught me more about the backward attitudes of Victorian society than it did about mathematics. It does a nice job of illustrating what it means to project, say, 4-dimensional space into 3 dimensions, by starting from physical concepts we can grasp, namely, the projection of 3-space into 2 dimensions. However, if you're already familiar with such concepts, there's not much else here to recommend this one. The anachronistic references are just too distracting....more info