Writing pseudonymously as "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions. The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides. The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions. The Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points", and attempts to convince the realm's monarch of a second dimension; but is unable to do so. . .
"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 Intro¬duction 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
In 1884, Edwin Abbott wrote a strange and enchanting novella called Flatland, in which a square who lives in a two-dimensional world comes to comprehend the existence of a third dimension but is unable to persuade his compatriots of his discovery. Through the book, Abbott skewered hierarchical Victorian values while simul¬taneously giving a glimpse of the mathematics of higher dimensions.-Science News
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