Flatland: A Romance of Many Dimensions

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Overview

With wry humor and penetrating satire, Flatland takes us on a mind-expanding journey into a different world to give us a new vision of our own. A. Square, the slightly befuddled narrator, is born into a place which is limited to two dimensions—irrevocably flat—and peopled by a hierarchy of geometrical forms. In a Gulliver-like tour of his bizarre homeland, A. Square spins a fascinating tale of domestic drama and political turmoil, from sex among consenting triangles to the intentional subjugation of Flatland's ...
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Flatland: A Romance of Many Dimensions

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Overview

With wry humor and penetrating satire, Flatland takes us on a mind-expanding journey into a different world to give us a new vision of our own. A. Square, the slightly befuddled narrator, is born into a place which is limited to two dimensions—irrevocably flat—and peopled by a hierarchy of geometrical forms. In a Gulliver-like tour of his bizarre homeland, A. Square spins a fascinating tale of domestic drama and political turmoil, from sex among consenting triangles to the intentional subjugation of Flatland's females. He tells of visits to Lineland, the world of one dimension, and Pointland, the world of no dimension. But when A. Square dares to speak openly of a third, even a fourth dimension, his tragic fate climaxes a brilliant parody of Victorian society.

An underground favorite since its publication in England in 1884, Flatland is as prophetic a science-fiction classic as the works of H.G. Wells, introducing aspects of relativity and hyperspace years before Einstein's famous theories, and it does so with a wonderful, enduring enchantment.

Century-old classic of British letters that charmed and fascinated generations of readers; witty satire of Victorian society and unique insights into the fourth dimension.

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Editorial Reviews

Asimov
The best introduction one can find into the manner of perceiving dimensions.
The Forward
Saturday Review
"This pre-Einstein geometrical fantasy is one of the best things of its kind that has ever been written, for it is more than an ingeniously sustained fantasy: it is a social satire, with wit as sharp as the sub-lutrous end of a Flatland woman; it is an easy philosophical introduction to the Fourth Dimension; and it is a rebuke to everyone who holds that there is no reality beyond what is perceptible by human senses."
Isaac Asimov
The best introduction one can find into the manner of perceiving dimensions.
The Forward
Victorian Studies
Flatland has remained of interest for over a century precisely because of its ability to engage its readers on so many different planes in so many different dimensions.
The Washington Post Book World
One of the most imaginative, delightful and, yes, touching works of mathematics, this slender 1884 book purports to be the memoir of A. Square, a citizen of an entirely two-dimensional world.
Zentralblatt MATH Database
This reprint of Abbott's Flatland adventures contains an Introduction by Thomas Banchoff which is worth reading on its own. So if you don't have yet this book at home, go ahead and buy this edition.
Zentralblatt MATH

This reprint of Abbott's Flatland adventures contains an Introduction by Thomas Banchoff which is worth reading on its own. So if you don't have yet this book at home, go ahead and buy this edition.
Saturday Review
This pre-Einstein geometrical fantasy is one of the best things of its kind that has ever been written, for it is more than an ingeniously sustained fantasy: it is a social satire, with wit as sharp as the sub-lutrous end of a Flatland woman; it is an easy philosophical introduction to the Fourth Dimension; and it is a rebuke to everyone who holds that there is no reality beyond what is perceptible by human senses.
From the Publisher
"One of the most imaginative, delightful and, yes, touching works of mathematics, this slender 1884 book purports to be the memoir of A. Square, a citizen of an entirely two-dimensional world."The Washington Post Book World

"Flatland has remained of interest for over a century precisely because of its ability to engage its readers on so many different planes in so many different dimensions."Victorian Studies

"This reprint of Abbott's Flatland adventures contains an Introduction by Thomas Banchoff which is worth reading on its own. So if you don't have yet this book at home, go ahead and buy this edition."Zentralblatt MATH

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Product Details

  • ISBN-13: 9780064800051
  • Publisher: Barnes & Noble
  • Publication date: 1/1/1963
  • Pages: 108

Meet the Author

Fifty Years in the Flatland
2012 will mark the 50th anniversary in print with Dover of one of the most significant and influential books of the past century and a half. The mathematical, satirical, and religious allegory Flatland by a little-known but immensely prolific Victorian English schoolmaster and theologian Edwin Abbott Abbott, was first published anonymously in England in 1884 — Abbott wrote it under the name "A Square." The unique geometrical romance which is Flatland posited a world and its inhabitants that exist in only two dimensions and forces the reader captivated by the originality of this central idea to think deeply about the meaning of such a world. Generations of readers and students swept into the romance and fascination of geometry and other branches of mathematics and philosophy owe their introduction to this world to Flatland, which continues to entertain and stimulate new readers today, still going strong 126 years after the first edition was launched. Abbott revised the text somewhat for a second edition published just a few months after the first. Dover's 1952 edition was the first American reprinting of the amended second English edition and was published with a new Introduction by physicist Banesh Hoffmann.

From the Book:
"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. Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows — only hard and with luminous edges — and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said 'my universe': but now my mind has been opened to higher views of things."

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Read an Excerpt

Part One This World

"Be patient, for the world is broad and wide."

1 Of the Nature of Flatland

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.

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising, above or sinking below it, very much like shadows-only hard and with luminous edges-and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe": but now my mind has been opened to higher views of things.

In such a country, you will perceive at once that it is impossible that there should be anything of what you call a " solid" kind; but I dare say you will suppose that you could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines; and the necessity of this I will speedily demonstrate.

Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view; and at lastwhen you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.

The same thing would happen if you were to treat in the same way a Triangle, or Square, or any other figure cut out of pasteboard. As soon as you look at it with your eye on the edge of the table, you will find that it ceases to appear to you a figure, and that it becomes in appearance a straight line. Take for example an equilateral Triangle-who represents with us a Tradesman of the respectable class. Fig. I represents the Tradesman as you would see him while you were bending over him from above; figs. 2 and 3 represent the Tradesman, as you would see him if your eye were close to the level, or all but on the level of the table; and if your eye were quite on the level of the table (and that is how we see him in Flatland) you would see nothing but a straight line.

When I was in Spaceland I heard that your sailors have very similar experiences while they traverse your seas and discern some distant island or coast lying on the horizon. The far-off land may have bays, forelands, angles in and out to any number and extent; yet at a distance you see none of these (unless indeed your sun shines bright upon them revealing the projections and retirements by means of light and shade), nothing but a grey unbroken line upon the water.

Well, that is just what we see when one of our triangular or other acquaintances comes towards us in Flatland. As there is neither sun with us, nor any light of such a kind as to make shadows, we have none of the helps to the sight that you have in Spaceland. If our friend comes closer to us we see his line becomes larger; if he leaves us it becomes smaller: but still he looks like a straight line; be he a Triangle, Square, Pentagon, Hexagon, Circle, what you will -- a straight Line he looks and nothing else.

You may perhaps ask how under these disadvantageous circumstances we are able to distinguish our friends from one another: but the answer to this very natural question will be more fitly and easily given when I come to describe the inhabitants of Flatland. For the present let me defer this subject, and say a word or two about the climate and houses in our country.

2 Of the Climate and Houses in Flatland

As with you, so also with us, there are four points of the compass North, South, East, and West.

There being no sun nor other heavenly bodies, it is impossible for us to determine the North in the usual way; but we have a method of our own. By a Law of Nature with us, there is a constant attraction to the South; and, although in temperate climates this is very slight-so that even a Woman in reasonable health can journey several furlongs northward without much difficulty-yet the hampering effect of the southward attraction is quite sufficient to serve as a compass in most parts of our earth. Moreover, the rain (which falls at stated intervals) coming always from the North, is an additional assistance; and in the towns we have the guidance of the houses, which of course have their side-walls running for the most part North and South, so that the roofs may keep off the rain from the North. In the country, where there are no houses, the trunks of the trees serve as some sort of guide. Altogether, we have not so much difficulty as might be expected in determining our bearings.

Yet in our more temperate regions, in which the southward, attraction is hardly felt, walking sometimes in a perfectly desolate plain where there have been no houses nor trees to guide me, I have been occasionally compelled to remain stationary for hours together, waiting till the rain came before continuing my journey.

Flatland. Copyright © by Edwin Abbott. Reprinted by permission of HarperCollins Publishers, Inc. All rights reserved. Available now wherever books are sold.
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Table of Contents

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Customer Reviews

Average Rating 3.5
( 130 )
Rating Distribution

5 Star

(53)

4 Star

(27)

3 Star

(26)

2 Star

(10)

1 Star

(14)

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See All Sort by: Showing 1 – 20 of 131 Customer Reviews
  • Anonymous

    Posted July 1, 2010

    Excellent book, available as free Epub elsewhere

    Good read, don't buy it though. You can get it for free in public domain.

    6 out of 6 people found this review helpful.

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  • Posted March 17, 2012

    I Also Recommend:

    Not so flat after all

    My friends in the literature department will tell you that this is a clever novel about Victorian England. If that's all it were, I couldn't recommend it to anyone. In point of fact, this book is a kind of bare bones look at culture itself (not merely Victorian Culture). By reducing everything to shapes, the author manages to show how cultures evolve—or perhaps better put: how nature influences the development of culture.

    Plus, if you don't know much about geometry (I don't), you may learn a little about that as well.

    3 out of 4 people found this review helpful.

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  • Anonymous

    Posted September 26, 2004

    Prepare to be amazed.

    I recommend this as required reading for any geometry student and/or anyone who has ever given the slightest thought to dimensions other than our lovely 3rd dimension.

    3 out of 3 people found this review helpful.

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted March 30, 2013

    A Timeless Classic

    This is going to be really corny, but it's true. This book influenced my decision to pursue mathematics and science as a career. Parts of it are a little dry, but these are the social commentary sections. I credit the rest of this book with equipping me to visualize higher dimensions. Definitely worth a read.

    2 out of 2 people found this review helpful.

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  • Anonymous

    Posted January 30, 2003

    A Great Book for the Open Mind

    This must be the best book I have read in years! It helped me understand mathematically and logically understand other dimensions as well as our own. This book will give you a glimpse of what living in a two dimensional world might look like, and also an Idea of what the fourth dimension might have in store in a logical manner. It also has a fantastic story and description of a two-dimensional culture, government and relationships. I strongly recommend it for geometry or advanced algebra students or anybody who wants a better understanding of multiple dimensions!

    2 out of 2 people found this review helpful.

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  • Anonymous

    Posted December 30, 2000

    Excellent Choice for Student Teachers

    This book is an excellent choice for future math teachers. I am a junior in college getting my BA in Middle Level Math Education. This is an excellent book that will help understand demensions beyond our own.

    2 out of 2 people found this review helpful.

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  • Anonymous

    Posted December 20, 2013

    Edwin A. Abbott wrote the "FLATLAND: A Romance of Many Dime

    Edwin A. Abbott wrote the "FLATLAND: A Romance of Many Dimensions" in 1884. He created a fictional world called Flatland for readers and introduced this two-dimensional world by depicting a journey of Mr. Square. Abbott used picturesque language, vigorous examples and his fabulous logical thinking to lead readers to enter the world he made. In this magic world, the Flatland is filled with Points, Lines, Triangles, Squares, Pentagons, Polygons, and Circles. The Law of Nature in Flatland is different from the three-dimension world that readers live in, and women in Flatland are compared to needles. The narrator of this book is A. Square. He is a humorous and wise square. The society he lives in always emphasizes the social hierarchy, and the mind of government is narrow. After visiting Spaceland, where is also called three-dimension world, with a sphere, Mr. Square finally unhesitatingly believed there is a real world, which is not allowed by the government. He even thinks there are maybe more dimensions in the universe, which just are still not realized by people. 
    Many people discussed why Abbott wrote the "Flatland". Maybe he wanted to satirize the ugliness of government and society at that time by using an imaginary world, or maybe he wanted to eulogize the people who tried to break through hardship for revealing deeper cognitive about the world, we do not know. However, no matter what his purpose was, the book was regarded as the first book which presented the idea of a multi-dimensional world and discussed the relationship between every dimension scientifically. It is totally worthy to be read by people because in this childlike world, people not only can enjoy traveling the creative and amusing two-dimension world with the narrator, but also can learn many things, like what the society is look like in the late 19th century. Go read it! I bet you will get more fun!    --- By May 

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  • Anonymous

    Posted January 26, 2013

    Great quick read

    Really fun nerdy read. The narrators formal tone is a easy to adapt to snd its written to the reader. Nice quick read and fun world to envision.

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  • Anonymous

    Posted December 28, 2012

    Worth it!

    Typing errors are frequent but not hard to understand, and the story is definitely worth it.

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  • Anonymous

    Posted October 23, 2012

    Horible

    Horible ebook a giant typo and to many big words!

    0 out of 2 people found this review helpful.

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  • Anonymous

    Posted May 19, 2012

    TYPO BAD

    Give me a free typo free book anyday but dont give me a google pasted mess-up and call it a great free book

    0 out of 2 people found this review helpful.

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  • Anonymous

    Posted May 9, 2012

    flatland, one of the best

    Great! if flatland was real, i would gladly live there

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  • Anonymous

    Posted February 29, 2012

    Student

    In class we have read this book it helps to have it explained by a teacher, it is very complex and dispite what the book says Abbott is not sexist, he is making fun of the time of whiched he lived in which many others were sexist. So his character A. Square acts as others. You might have to have a teachers guide to fully understand it because, if you are like me and my age it will help explain it in a way that really helps, WARNING: Many big words, lol

    0 out of 1 people found this review helpful.

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  • Anonymous

    Posted January 20, 2012

    An Amazing look into dimensions.

    This was easily the most entertaining math text I have read so far! I would recommend this text to anyone inrerested at all in reading it.

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  • Anonymous

    Posted December 26, 2011

    Anonymous

    Have read before, is AWESOME!!!!!

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  • Posted December 25, 2011

    Excellent

    Great book, it does not age

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  • Anonymous

    Posted December 6, 2011

    A Sci Fi Classic

    It was mentioned in Infinite Jest, so I bought it. It's a little dry, but it contains some great concepts.

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted October 31, 2011

    ONE GIANT TYPO

    It is clear that no one proof read this ebook
    I have enjoyed flatland since childhood but this is a disgrace even for a free book

    0 out of 2 people found this review helpful.

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  • Posted October 18, 2011

    more from this reviewer

    Math, Social Commentary, and Theology

    This book, narrated by 'a square', explores what life in a two-dimensional world would be like. The first half of the book which describes Flatland's society is not only interesting sci-fi worldbuilding, but is a biting satire on Victorian society.

    In the second half, the narrator meets a three-dimensional being from Spaceworld (our world) and has visions of one-dimensional Lineworld and no-dimensional Pointworld. The recurring effort of explaining additional dimensions to a being who cannot see, feel, or even imagine them brings up interesting questions about faith/spirituality/religion. Even though this book was written over 125 years ago it remains fascinating and thought-provoking.

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  • Posted January 29, 2011

    interesting book

    with all the recent talk of a 'multiverse', Flatland is a good way to start thinking about the topic.

    Was this review helpful? Yes  No   Report this review
See All Sort by: Showing 1 – 20 of 131 Customer Reviews

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