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!!

Highly recommended!

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

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

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.

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).

Excellent.

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.

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, or pair of books, beacause it is good for you. That sort of praise is the kiss of death as far as most readers are concerned. But sometimes you just can't avoid 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.

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.

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.

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!

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.

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.

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.

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

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!

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!"

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.

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.

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.

Great book great exchange!

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.

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!

I read Flatland (which, I believe, in the US was published without post colon, as it was in the UK) when I was a teenager in the 1970s studying geometry and many other things (girls, art, girls, movies, girls...) without understanding much of any of it. The book fascinated me, and I went on (probably not because of it, but certainly in appreciation of it) to study Mathematics at University. I even sometimes bring it up in my consulting engagements as a way to explain how different types think of their world and learn. While there are different dimensions represented in the book, there are different learning styles, different socioeconomic exposures, different interests, different *people* we all have to deal with. I'd recommend Flatland to anyone who wants to take a different slant on why we are all different.

This little book(and subsequent sequels by other authors) is guaranteed to cause the non-mathematically inclined reader to think in new ways and new directions.

As one of the classics in this (very limited) genre, this book is well-worth the brief time it takes to read..

This book in its semplicity is very smart. It's like a comic fairytale but in the end the author's message is very deep. Everybody should read it..

While the concept was certainly revolutionary at the time this book was written, I found the story itself uninteresting and sexist. I would not recommend this book.

This is an excelent primer on line, plane and spactial geomerty. no math just the ideas put in a way that anyone can understand. If you read it as fantasy to small children they will grasp the concepts and it will give them a great leg up in there later life. P.S. It is also a great story

P. P. S. I know the spelling sucks ;)

This book was written by a theologian, not a math professor, and it's not about geometry. The author uses geometry to create a parable that was intented to help open the mind of the reader to spiritual reality.

What happens when a lowly square receives a revelation of a higher dimension of reality from a sphere, and then tells the other flat shapes what happened to him? He gets presecuted and thrown in prison. Does that sound vaguely like something that might happen in our world and has happened over and over again in history?

Anyway, it seems our Westen Civilization is getting flatter all the time. Read this book, and gain some insight into our human condition, and some funny insights into the culture of Victorian England. How can you miss at this price? This book really is a classic.

Flatland is a unique and brilliant treatise on a trifurcated level. It is a sociological statement, a mathematical statement and a religious statement all rolled into an incredibly astute 82 pages. The book centers mostly on the differences between a two dimensional world and a three dimensional world; but comments on society, law, prejudice, religion, and proselytizing.

The book especially points out the difficulty in envisioning a greater reality and a greater vision than is commonly observed by any individual in any dimension or society. The author's premise relates to things existing in a "plane geometry" world as opposed to a "Euclidian Geometric" three dimensional figure universe. The book carefully illustrates to one denizen of Flatland how the three dimensional world of space works and/or exists. Upon finally understanding the "Gospel of Three Dimensions" our protagonist goes on to try and apply the same arithmetic logic and geometric analogs to a fourth dimensional universe. Shouldn't there exist a fourth dimensional universe that allows an entity to look down upon the three dimensional universe with as much transparency as one can from three dimensions to two?

Alas, things become different in dimensions other than the first, a world of lines, the second, a world of shapes and the third, a world of objects. In the zero dimension, all things are a point. Mathematically we know that any number raised to the "0" power equals 1 and therefore, all things in the zero dimension resolve into one single omnipotent point. This condition would also exist in the fourth dimension; as those of us in the third dimension have no model to compare it to. Envisioning a fourth dimension, even with time as the fourth dimension is truly difficult or impossible for us in the third dimension.

Interspersed with this witty and intellectual dialogue are comments on society and its structure. He specifically comments multiple times of the degradation of women in society to the lowest social status. Only men are educated in Flatland. Interestingly, he paints a picture of an authoritarian society in which people are judged by their shapes and angles. This reflecting the Victorian societal values around him at the time of his writing.

Flatland is recommended to all those who seek to enlighten their view of the universe and of potential universes. It is especially recommended to those seeking higher knowledge of any type. Flatland is truly a multi-dimensional experience and worth every minute.

I purchased this book as part of a required reading for my high school honors geometry course. It is perhaps the most utterly boring and fanatical piece of fiction I have ever read. Not only is the book completely devoid of plot, it is lacking in all aspects of what a true work of fiction should include.
This book has not educated me further on geometric concepts, nor has it enlightened me of any time period of which this book is said to be mirroring. Instead, it has wasted my time, which is precious to me now, and has completely confused me. Do not purchase this book. Do not assign it as required reading and most definitely do not read it for pleasure. There are other 80 page books that you can spend your time on.
Read anything else before you read Flatland.

this book was written a century ago - yet is embodies the principles, the mind skills which are currently developing our outstanding dot com industries. Read it - you will be fascinated!

This book is a cure for insomnia. If I ever have trouble falling to sleep, I'll just dig out my old "Flatland" book, and I'll probably be fast asleep a few minutes later! Listening to the A. Square character telling us about his flat, two dimensional world is not thought provoking, its just confusing! Trying to imagine life in two dimensions is truely mind numbing. I mean I understand what Flatland would be like, but only after I carefully think out what Mr. Square is saying. I spent more time trying to comprehend the two dimensional reality of Flatland than I do enjoying the story. Not very interesting at all, even two stars is being generous!

Edwin Abbott's "Flatland" is a story that can be read as many things: as an Orwellian satire on The State, as a contemplation of dimensions (even ones we do not know yet), as a philosophical variation of Plato's Cave, or simply as a delightful sci-fi story.

Flatland is broken up into two parts. The first sees our main character (a square who is a mathemetician - how cute!) telling us - those who live in "spaceland" - about the ins and outs of flatland. He teaches us both about how life is lived as a two dimensional object, explaining such things as how one can recognize by sight a squre from a hexagon without being able to see the angles. Also, the square explains how flatland's class and government system works: how women, for instance, are inferior to men and do not attend school, how polygons are superior to lowly squares and triangles, and how the circles make the laws.

It is this first section that is both a savy critique on government and the then prevailing social mores. Also, this seciton is fascinating from a mathematical point of view, answering questions that the astute reader is bound to have. (How, for instance, is sight possible in two dimensions?)

The second section of the book is where stuff gets even more intersting. This is the section where our square mathemetician both finds himself (in a dream) having to explain the concept of a second dimension to a "linelander", and is visited by a "spacelander" who must try to convince our "flatlander" that a third dimension is possible.

This section is most interesting from a philosophical perspective. How, for instance, is it possible to explain a third dimension to one who only knows two dimensions? To the flatlander, terms like "up," "down," "above," "below," "vertical," (etc.) have no meaning as they presuppose knowledge of a third dimension. That is, can a spacelander use "two diemsional language" (language presupposing no familiarity with any but two dimensions) to explain a third dimension? (Edwin Abbot thinks he can, but the astute reader will notice Abbott's linguistic fallacy in how he brought this about!)

At any rate, it is this part of the book that can also be seen as a variation on Plato's Cave. (Plato's Cave analogizes us to people looking at the back wall of a cave open at the other end, who see only shadows of objects outside the cave, but who are convinced that what they see is the real things.) That is, "Flatland" very beautifully articulates the idea of someone realizing that what they assumed was a complete view of reality was only a partial view of reality. And now, the flatlander bears the burden of trying to convince other flatlanders that the reality they take for granted as "all there is," is, in fact, not a complete view of reality at all.

Can he do it? Will he run into the same linguistic stumbling block already spoken of? More interestingly, if the "linelander" was wrong in assuming only one dimension, and the "flatlander" was wrong in assuming only two dimensions, might the "spacelander" be wrong in assuming only three dimensions, and so on? And how, if possible, could we find out?

These questions and more are artfully and skillfully broached in Edwin Abbott's mathematical classic "Flatland." Even if all you want is an intersting science fiction book, "Flatland" will do the trick. But for those who want a great "thinking" novel, "Flatland" is an outstanding choice!

A fascinating geometric tale. An easy and short (<100 pages) read. It is an interesting read for anyone (not just mathematicians). It's amazing to think this was written over 100 years ago - Abbott was way ahead of his time.

Imagine if you were an ultra-flat two-dimensional being, as flat as atoms say, and that you inhabited a universe as flat as you are. Then imagine a non-flat three dimensional being poking its finger into your universe. First you would see a point, and then a circle as the finger dug into your flat universe. This appearance, since you and your senses are confined to a two-dimensional world, would seem like inexplicable magic to you. This is the satirical, oft hard-humored, raw, religiously conflicted, war-torn world of Flatland.

Now imagine that, so-to-speak, Flatland may be real. We, living in three dimensions, might, by seeing violations of the conservation of (four) energy through experiments at the world's most powerful atom smashers, might be able to prove the existence of higher dimensions than the four-space of relativity! (Look up Large Hadron Collider and Extra Dimensions.) Might other higher-dimensional beings then, in past, present or future, "mess" with us Flatlanders?

Alex Alaniz

PS--The inclusion of Sphereland is quite nice.

1. Please see the reviews of my own strong science fiction book: Beyond Future Shock about the near-terms perils and promise of advanced bio/nano technology in a world still roiled with Middle Age religious conflict and ever growing extreme wealth gradients.

2. I have REVIEWED many books from undergraduate to graduate in: PHYSICS, MATH, ECONOMETRICS, and HISTORY among other areas.

"Flatland" isn't like any other book I've ever read. There's not a complicated plot. It won't make you cry. You really don't care about the characters at all, and it's a book you can read in a couple sittings. However, what you can take away from the book is just as much, or more than a 500 page novel.
The entire book illudes to Victorian Society and how strict their lives were lead. "Flatland" is narrated by A. Square, a two dimensional square. He lives in Flatland, a completely two dimensional world. From here he narrates how he came to learn about the third dimension.
The laws within flatland are extremely strict. A. Sqaure tells of their geometric heirchy: Irregular peasants, Triangular tradesman, square and polygonal politicians, and spherical priests. The inhabitants are classified according to their shape. Their shape determines how well off they are in society.
Anyway, after learning how life is lived in Flatland, A. Square begins to tell of his encounter with a Sphere and the reactions of his own world. After he is exposed to the wonders of the "third dimension" he comes eagerly back to the second dimension in hopes of enlightening his peers of his experiences. The government immediately sends A. Square to jail after hearing his story. No one belives him and they deem him insane.
The most interesting part of the book is learning how life functions within Flatland. It really makes you think. From a two dimensional perspective, it's really interesting to imagine how they would recognize one another. From that perspective everything would look like a straight line. According to A. Square, they use "feeling" in order to distinguish the degrees of one angle, thus be able to figure out how many angles are on that shape. A. Square also continues to describe their homes, weather, writing, families, etc.
"Flatland" is one of the most interesting books I have ever read. It was a lot of fun trying to picture a world in just two dimensions. The witty illusions to Victorian society and incredibly creative aspects of life within Flatland make this book a must read for anyone. It's just a good book to make you think.

This book "flatland" is one of my favorite books of all time. Even though it was written along time ago, it still introduces new theories that most people would not think about everyday. The details on geometry and polygons and the other dimension are well. Also the diagrams included also help a lot. The trips to Lineland, Pointland, and Spaceland portray the stubbornness of people to adapt to new customs that our introduced to them. The questions I have after reading this book is their other dimensions like 5th and 6th. My favorite character in the book is the square because; he is very curious and smart. A thing I liked in this book is that it was written in third person. I would strongly recommend this book because it takes an idea that is rarely used, and makes it understandable to the general public.

I just finished the book, and let me say this: just because it is talking about polygons and n dimensions does not make this book a math book! This book is first and foremost a book on philosophy and a social satire, and secondarily a book on religion.

Why?

Well, the long running theme is the socio-economic class system of Flatland, which is not simply unjust, but more accurately elitist, and misogynist. Polygons are just metaphors; well-off people get better off more quickly for every successive generation, and low poor working class people are stuck in a perpetual circle of poverty but always wishful to achieve higher status in the next generation.

The trips to Lineland, Pointland, and Spaceland illustrate the stubbornness of mankind and the irony of that stubbornness. After his dream that Lineland people and Pointland person are too stupid to accept Flatland, Square himself was regarded as too stupid to accept a higher form, i.e. the Spaceland. The Sphere, in turn, refused to accept an even higher form just after he admonished the Square for refusing to accept a higher form to him.

Granted, the details on geometry and polygons and the line on 4th dimension are pretty well-written, but such focuses are brief in this 81 pager, and briefer still when their metaphorical powers are accounted for. Don't just read the words. For a classic like this, one must read between the lines.

Although the decidedly Victorian language may sound a bit strange to the 21st Century ear, Abbott's approach is classic: assume a set of social rules that is driven by an alien environment. In this case, assume the constraints (and freedoms) offered by living in two dimensions. Further, imagine encounters with life in one or three dimensions. Do you mock those living in one dimension? Do you gape in awe at the three dimension world? You might read Flatland to appreciate the historical foundations of modern sci-fi. You might contemplate the themes for personal reflection. You might share it with others to sponsor interesting conversations. No matter how you use it, it's worth the read.

This is one of my favorite books of all time. Even though it was written so long ago, it still comes across as timely, innovative, creative, and pertinent. A real mind-opener. Abbott is a genius!

I read this book over 20 years ago for extra credit in 10th grade geometry. It has the effect of compressing your mind like a spring, (into 2D) then releasing it. What I got was a different meaning than most. And that is...this could explain "where" Heaven and Hell are. If our 3D existance is a subset of 4D or higher as the book suggests, then it "fits" for an answer to a rather basic question of faith in God.

Flatland is a two-dimensional unvierse, inhabited not by people as we know them, but by shapes - triangles, polygons, circles, etc. The narrator, A. Square, introduces the readers to the customs, class distinctions (based on geometric shape), male and female roles, how to tell one another apart, and on general life living in a world of only two dimensions. Square's life is turned upside down when, on the eve of the new millenium, a strange visitor literally drops into his home. This visitor - a Sphere - has chosen Square as his apostle to teach the two-dimensional masses about how more to life there is beyond their flat world view.

At first glance, this comes across as a novel about higher math: geometry, 2- and 3-dimensions, the possiblity of higher cimensions after the third, etc. Author Edwin Abbott examines and illustrates what life would be like living in such flat world, in which everyone resembles a straight line - whether the "person" is a circle, a triangle, or a square - because only one side of them can be seen. On a deeper level, though, Abbott offers a scathing parody of Victorian society. (After all, the book was first published in the late 1880s.) Class distinction based on birth is rampant. The "lower" beings, such as isocoles triangles and irregular shapes, live in shame and are looked down upon by society. They will never attain the good paying jobs or respectability that those shapes with more sides have. Women are seen as merely lines, very dangerous to society, though, so they must be kept uneducated. Their main purpose is to help their male counterparts achieve higher and higher status through breeding.

Quite a remarkable book for its time.

This is an absolutely fascinating book. It's also a classic, written in 1880, that has definitely stood the test of time. I am mildly interested in math and fascinated by science, and the concept of multiple dimensions (or fewer dimensions) is one of great interest to me. The notion of Pointland, Lineland, Flatland, and above and beyond into 4-D, 5-D, 6-D, and more is, to allow my geek side to show, exciting. The book also has some interesting social statements to make. I can't recommend this book enough to anyone at least mildly interested in math or science.

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).

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.

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!

Okay honestly I felt the book was a bit drab to read through, such that, how excited can one get about little triangles & polygons, moving here & there on a two-dimensional plane? And yet, the personalities the author invokes onto these geometric figures indeed livens up the story-line substantially. And near the end things come together in not exactly a nail-biter, but somewhat of a page-turner nevertheless. I had found myself pretty emotionally invested in this little geometrical society.

What I came away with after finishing the book was a renewed sense of humility for this multi-dimensional world we live in, the multi-dimensional lives we lead. In the story, the geometrical or linear figures who insist that their world of one or two dimensions is all there is, and who scoff at the possibilities of any superceding possibilities (like a two or three-dimensional world) occasionally reminded me of my own limited view, evidenced by my pride. Today we can look back on great thinkers who shook up our complacent intellectual views of our world (Freud & Einstein are the first two which come to mind), who indeed added extra dimensions to our world, to our thought about our lives. And in a less dramatic fashion perhaps, this book caused me to think of new, undiscovered dimensions awaiting me in existing relationships, in new pursuits, career changes, etc. - through trying to see things in an entirely new way.

With that said, the book has done me good. Thank you, Mr. Abbott!

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.

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.

+++++

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."

+++++

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.