Flatland

Home | Download | Purchase | Contact

Call Center Software:

Freeware for Call Center:

Free Internet Tools:

Net Picker

Call Center Solution:

Resources:

Flatland

List Price: $21.99

Our Price: $17.59

You Save: $4.40 (20%)

Product Description

I call our world Flatland- not because we call it so- but to make its nature clearer to you my happy readers- who are privileged to live in Space.' (Excerpt from Section 1)

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:

A Multi-Demensional Story of Two Dimensions!

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!...more info

Not a math book!

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....more info

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

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).

Excellent. ...more info

A fine example of early science fiction.

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....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

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 look into other dimensions

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. ...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 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."

+++++
...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

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

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

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

Flatland: A Romance of Many Dimensions

"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. ...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

A Classic

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....more info

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

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.
...more info

A glimpse into 4D

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. ...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!!

Highly recommended!...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

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.

...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

Ok, so we glimpse the 4thD, is this the Spirit World?

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....more info

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

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

An all-time favorite!

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!...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.

...more info

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

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

A fun read for those who enjoy math, politics, and puzzles

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

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

A sci-fi classic about life in two dimensions

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....more info

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