However, all of this holds true only for the males. Subsequent generations do inherit greater numbers of edges, so one has hope for the social advancement of one’s children. All polygons aspire for themselves and their progeny to increase their number of edges, hoping to approach the circular ideal.
The larger one’s number of edges, the larger one’s angles, and larger angles provide greater intelligence and higher social status. Other residents of Flatland include isosceles triangles, who make up the lower classes and aspire to be equilateral, and regular polygons with greater numbers of edges. The book is littered with playful references such as these, many of which are easily missed on a first reading. The name A Square is essentially a spoken version of A 2, which is a play on the author’s double name. A new edition jointly published this year by Cambridge University Press and the Mathematical Association of America contains enough notes and commentary by William Lindgren and Thomas Banchoff to more than double the length of the book.įlatland is the story of a two-dimensional creature, A Square, who is actually a square and is one of the inhabitants of Flatland, a world consisting of a single plane. At that price, members of my department hand them out to students as prizes, and the students don’t have to impress us all that much to merit a copy. The cheapest version is available from Dover Thrift Editions for just two dollars. Just since 2007, more than 20 different publishers have produced editions of the book-a testament to its popularity, profitability and expired copyright.
The book’s appearance in England was followed a year later by its publication in the United States, where it has yet to go out of print. Of the more than 50 books that Abbott wrote, this is the one for which he is remembered. Generations of students have gained their first true appreciation of higher dimensions by reading this slight story written by a schoolmaster more than a century and a quarter ago. In the pantheon of popular books about mathematics, one would be hard-pressed to name another that has lasted so long in popularity or had such a dramatic impact. Flatland helped to set the stage for many of the scientific advances to come. Abbott’s work provided a simple story that allowed lay audiences to grasp the idea of dimensions beyond the familiar three. At that time, there was substantial interest in the idea of higher dimensions, both within the scientific community and also in the more general population. It was both an introduction to the notion of higher dimensions and a satire of Victorian society and norms. In 1884, the English minister, headmaster, and biblical and Shakespearean scholar Edwin Abbott Abbott produced a thin volume titled Flatland: A Romance of Many Dimensions.
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