Flatland: A Romance of Many Dimensions

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More About This Book

Overview

Classic of science (and mathematical) fiction — charmingly illustrated by author — describes the journeys of A. Square and his adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions). A. Square also entertains thoughts of visiting a land of four dimensions — a revolutionary idea for which he is banished from Spaceland.

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.

Editorial Reviews

Asimov
The best introduction one can find into the manner of perceiving dimensions.
— The Forward
Isaac Asimov
The best introduction one can find into the manner of perceiving dimensions.
— The Forward
More Reviews (4) Fewer Reviews
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."
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.
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.
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.

Product Details

  • ISBN-13: 9780486272634
  • Publisher: Dover Publications
  • Publication date: 9/21/1992
  • Edition description: REV
  • Pages: 96
  • Sales rank: 436
  • Lexile: 1280L (what's this?)
  • Series: Dover Thrift Editions Series
  • Product dimensions: 5.20 (w) x 8.27 (h) x 0.25 (d)

Meet the Author

Edwin A. Abbott (1838-1926) was headmaster at City of London School. He was Hulsean Lecturer at Cambridge in 1876 and Select Preacher at Oxford in the succeeding year. He retired in 1889, devoting himself to literary and theological pursuits. Dr. Abbott's liberal inclinations in theology were prominent both in his educational views and in his books. His 'Shakespearean Grammar' (1870) is a permanent contribution to English philology. In 1885 he published a life of Francis Bacon.

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.

Table of Contents

Customer Reviews

Average Rating 3.5
( 102 )

Rating Distribution

5 Star

(43)

4 Star

(17)

3 Star

(19)

2 Star

(11)

1 Star

(12)

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See All Sort by: Showing 1 – 20 of 103 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.

    3 out of 3 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.

    2 out of 2 people found this review helpful.

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  • Posted March 17, 2012

    I Also Recommend:

    9780142003343 2940014323642

    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.

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted June 11, 2009

    Don't Judge a Book by its Cover

    I chose this book (foolishly) to purchase rather than other editions because of the colorful cover. This edition was exactly the same as the "Gutenberg Project's" Ascii edition. It had the same print styles, same illustrations (in ASCII ART) and font styles. This book was just printed out and bound version of the free "Gutenberg Project" edition (http://www.gutenberg.org/etext/201) which is just ridiculous. I of course could be wrong but the similarities are uncanny.

    1 out of 1 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!

    1 out of 1 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.

    1 out of 1 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 1 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

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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.

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  • 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.

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  • Posted October 21, 2010

    more from this reviewer

    Interesting/Quick Read

    Love math, so I thought I'd give this book a try. It was pretty dry, but the descriptions were pretty interesting and it didn't take me long at all to get through it.

    0 out of 1 people found this review helpful.

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  • Anonymous

    Posted June 27, 2010

    great story, very interesting topic

    The book was much better than I was expecting. I wanted to read it because of my interest in math, thinking if nothing else it would maybe help me visualize geometric space a bit better. I wasn't expecting to enjoy the story so much. The author surprised me with great satire and wit.
    The book is quite short and engaging. Most people will finish it in one sitting. Even if victorian satire and geometric space don't sound interesting to you, for $2.00 why not give it a shot? you'll probably be surprised how much you like it.

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  • Posted March 27, 2010

    How would you know of anything outside your universe?

    Flatland is a fun, little tale of the universe as told by A. Square and his wondrous explorations above and below his two dimensional universe. However, while the reader may well enjoy reading Flatland in order to be presented with an example of imagining other dimensions, Abbott's story also serves as a critique of society, which is as relevant today as it was with the original Victorian society within which times it was initially penned. Themes like the character of different classes, upward mobility, the character, disposition, and strictures against women, the suspect knowledge of the ruling class, and even a social uprising and revolution that ends poorly for the upstarts. The reader is cautioned not to think Abbott was advocating for this lifestyle but instead providing a characterization from which the exploration could be based. A favorite of even casual mathematicians and a wonderful peek into imagining other dimensions.

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  • Anonymous

    Posted January 23, 2010

    Here's a story that makes you think . . .

    If this story doesn't get your brain ticking I don't know what will. This story really makes you think. It forces the reader to look at things differently and may open up some new ways of perceiving the world.

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