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Flatland: A Romance of Many Dimensions Paperback – Sep 21 1992

4.4 out of 5 stars 114 customer reviews

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Product Details

  • Paperback: 96 pages
  • Publisher: Dover Publications; 1 edition (Sept. 21 1992)
  • Language: English
  • ISBN-10: 048627263X
  • ISBN-13: 978-0486272634
  • Product Dimensions: 13.2 x 0.6 x 21 cm
  • Shipping Weight: 68 g
  • Average Customer Review: 4.4 out of 5 stars 114 customer reviews
  • Amazon Bestsellers Rank: #26,172 in Books (See Top 100 in Books)
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Product Description


"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

--This text refers to an alternate Paperback edition.

From the Publisher

Line drawings --This text refers to an alternate Paperback edition.

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Customer Reviews

Top Customer Reviews

Format: Paperback
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.
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Format: Paperback
Flatland is one of those pseudo-scientific novels that has since become a piece of the scientific canon in the same way that Alice's Adventures in Wonderland has; when attempting to explain theoretical physics to a class, and at a dead-end, a professor is most liekly to turn to an analogy from Flatland. Which makes sense. Flatland is the story of A. Square, a resident of the two-dimensional Flatland, and how he comes to understand that there are universes in every dimension. Previous to this, the idea of any universe but his own two-dimensional universe was unthinkable; by the end of the novel, he is positing the existence of a great, infinitely-dimensional being-- god. This is not surprising; Edwin Abbott was a theologist first and foremost. What is surprising is how modern eyes have seen this tale, and it gives us a perspective on the endless debate as to whether the author's belief about his story is the final and "right" one.
Abbott meant his book as a treatise on theoretical physics-- if at all-- in only a minor way. According to Abbott himself, his main goal in the writing of Flatland was to produce a kind of "satire of manners" on Victorian England. And, given what little I know of the ways of life in Victorian England, he seems to be right on the money. But what do I know? Abbott's assertion is backed up by the structure of the novel, certainly; the first hundred pages of this small (hundred fifty page) tome are devoted to the customs and mores of Flatland. How stinging a criticism they are of the values and mores of Victorian England is not for me to say.
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Format: Paperback
Do not miscast this wonderful little book as being merely "sci-fi". Two-dimensional "worlds" exist within ours, if only in a somewhat pragmatic sense. If we imagine some "thing" intellective within such a world, then we have little difficulty seeing that our humble narrator, Mr. A. Square, might be such a world's most insightful oddball. The book is a classic exposition in basic geometry, but it is more than this. Abbott uses mathematics to make some very telling observations about human minds and psychologies.
Edwin Abbott (1838-1926) was a clergyman and a math geek. He was an educator, an expositor of English literature and New Testament studies, a notable headmaster, and the author of something like 40 books on widely varied themes. Today you will probably have a difficult time finding any of his other volumes, but Flatland is said to have never been out of print since it was first published in 1884.
No need to retell A. Square's big adventures here, other than this bit of dialog between our two-dimensional thinker and his three-dimensional visitor/teacher (Square is given to thoughts of still higher-dimensional worlds):
"SPHERE. But where is this land of Four Dimensions?
[A. Square]. I know not: but doubtless my Teacher knows.
SPHERE. Not I. There is no such land. The very idea of it is utterly inconceivable."
Abbott offers his allegory of physical and conceptual limits with an economy of word and thought that is nothing less than extraordinary. A great many volumes, five to ten times as large, conclude having said far less than this little parable. Read it. You will take from it what you are willing to take. If you find little or nothing here, you are indeed a citizen of Flatland.
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