Product Description

Classic of science (and mathematical) fiction—charmingly illustrated by author—describes the journeys of A. Square, a resident of Flatland, 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.

Product Details

• Amazon Sales Rank: #13397 in Books
• Published on: 1992-09-21
• Original language: English
• Number of items: 1
• Binding: Paperback
• 96 pages

Amazon.com Review
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.

Review
"The best introduction one can find into the manner of perceiving dimensions." -- --Isaac Asimov in the ForewordA

Review
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 )

Customer Reviews

An excellent edition of a classic - extended
If you are not familiar with Edwin Abbott's "Flatland", this is the edition to buy. If you are familiar with it (but presumably do not yet own it), this is still the edition to buy.

You've heard the classic criticism of a story is that it is "two dimensional". Well, Edwin Abbott's tale of an imaginary two-dimensional land adds a whole new twist to that phrase. Flatland, as he describes it, is about as rich as a two-dimensional story can be. And it is marvelously extended by its narrator's encounters with the unknown - the world of 3 dimensions. The challenges that narrator faces as he encounters the incomprehensible, quite closely mirror mine whenever I attempt to think about a 4th (or 5th or 7th) dimension. If you've faced the same struggle, you will be delighted by this book.

If you've ever wondered what a 4th dimension would look like, Flatland provides a lens through which you can imagine that extension of our 3D world. From here you can go on to read Rudy Rucker or Pickover or Hawkins - but this is the place to start your exploration of dimensions beyond experience. Abbot accomplishes this by describing the eye-opening extension of his narrator's 2D world when visited by a 3D apparition, a "sphere". His framing of the foundational issues through the experiences of what you'd expect to be the least interesting character in fiction are really quite engaging. The storyline, however sparse, is as interesting as the mathematics - albeit quite nineteenth-century'ish in tone.

Don't misconstrue Abbott's seemingly misogynist portrayal of women and of his class-stratified society. This element was intended to provide a third layer of sharp, Swiftian satire and critical commentary on the rigid social mores of his era. Abbot succeeds in this (but I, nevertheless, decided not to read it aloud to my 6th grade classes - worrying that they might not be attuned to this subtlety of tone.) Be forewarned.

The neat twist of this edition, the inclusion of Dionys Burger's 1983 "Sphereland", as an upside-down "second book", is quite a nice touch. Although I did not find Burger's stylings quite as engaging as those of Abbott, his extension of the mathematical ideas into non-Euclidian spaces is a nice introduction to that idea for non-mathematicians. Since it was intended as a standalone book, "Sphereland" commences with a detailed review of the "Flatland" story. This can be skipped without loss but is not a substitute for reading the original "Flatland", here, first.

Flatland is a timeless classic; a great book for the mathematician and non-mathematician alike.

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

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

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

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

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

Mind bender anyone?
Although it isn't very long, Flatland does take a long time to read. This isn't because it is boring, or because it is hard to read, but because of the large amount of digestion one need's to fully comprehend (and to fully enjoy) this book. Even this book contains only 82 pages, it is by no means light reading. The book was originally released in 1884 under Abbott's pseudonym A Square. In the story we follow the journey of a square who lives in a land of two dimensions--a flat land. In it class, and ultimately intelligence, is determined by the amount of sides that a shape has. As the amount of sides a shape has decreases, we find that it also is more emotional and apt to cause destruction through their pointed corners. Women are depicted as straight lines, but one has to take into account the time that this book was published. One can also disregard the story as having any relations to anything in our society and enjoy it for what it is, a mind bending social criticism. In this tale we follow the aforementioned square through his everyday life. we learn what it is like to exist in only two dimensions. We learn of how rain falls form the north and disappears to the south and how gravity is a minute force that pulls to the south ever so slightly. We follow him through the government and through social classes, and the discrimination that comes with them. When his son talks of geometric impossibilities such as 23 (cubed) he has a dream of a lesser land than his, a land called line land. IN it there is not two but only one dimension of being. Through discussion with the kind of lineland, we are offered insight into why our hero the square cannot conceive of the third dimension. Later our hero is visited by a great being, a sphere that appears to him seemingly out of nowhere. This confuses the square very much, and even more when the sphere tries to explain how he passed into his dimension from the third. After heated debate, the sphere takes him and shows him the third dimension, turning our hero into an evolved form of him self, a cube. Form his higher vantage point the square is able to see the innards of those who reside in flatland. He receives tutoring from the sphere about this new dimension and all that it entails. He learns of how limited the field of vision is for those living in flatland, both literally and figuratively. With his previous limits of reality stripped and with his eye opened to the truth, the square quickly follows logic and asks to see the insides of the sphere, and wishes to ascend further into greater dimensions, fourth dimensions and fifth and onward and upward. The sphere is appalled by this heresy and send our hero back to the limited realm of flatland. Here he tries to convince others to be enlightened, but cannot find success. He has a second dream involving the dimension of pointland, no dimensions. The being inhabiting this land is of nothing and knows nothing but itself, which is nothing. There fore this being cannot be disappointed by anything, because it cannot conceive of anything other than itself. We can see the religious parallels to Hinduism and Buddhism here. The completely content creature is of nothingness, much like the state that Buddhists try to achieve, and the outward ranking by dimension not sides can be seen in Hinduism in the spiral path towards God that the Hindu believe they travel along passing from one point on the spiral to another with each passing life. In this land of math all of the lands are contained within each other, much like the rings of the spiral. Finally after this dream the square realizes the futility of trying to convince others through speech, and he feels he must do it through demonstration. Folks hear of his heresy and bring him to the court for the climax of the book. Whether or not the plot of the novel itself is very entertaining, the ability to get your head around concepts that can only be experienced through the mind is challenged thoroughly by this novel. It is a must read for anyone who thinks that they are well educated, as it will quickly tell you just where you stand, theologically, philosophically and mathematically.