In 1884, Edwin Abbott, a British clergyman, wrote Flatland, a fantasy novel about a world in two dimensions. (More detail on taht added by rebecca/isabelle since they read the book, if they want.) Since then, several variants on Flatland have been written, expanding upon its ideas and improving flaws in its conception, including Hinton's An Episode of Flatland, and Burger's Sphereland.
A.K. Dewdney is a Canadian computer scientist based at the University
of Waterloo. In his acknowledgments to Planiverse, he explains the
genesis of the work:
The next year, a flurry of interest was sparked by an article Martin Garnder wrote in Scientific American about the planiverse project (ironically, Dewdney would later follow Douglas Hofstadter as Gardner's replacement at Scientific American). In response, Dewdney received over a thousand letters of interested, and edited A Symposium of Two-Dimensional Science and Technology.
According the Dewdney's acknowledgment, it was the publishing of a press release in the campus newspaper that led to publicity outside the world of mathematical games and the like. Articles were published in Newsweek and Maclean's. (The articles, of course, teased the reader along; the Maclean's articled, titled "Scientific dreamers' worldwide cult," ended: "As to whether a 2-D universe might actually exist, Dewdney admits that it is unlikely. However, he muses, 'to people living in the fourth dimension, our universe would appear just as improbable.'")
Finally, in 1984, Dewdney compiled the insights from many contributors, added a story element, and published the result as the book The Planiverse. Written in, as he described it in his preface to the new edition, "the style of an academic whose literary opportunities are continually overwhelmed by events," it--to the author's surprise--confused some people who thought the world was real. The book received a positive review in the New York Times, and a Lexis-Nexis search turns up the occasional allusion to it.
In 2001, an updated version of the book was published. Still, its popularity seems low; a google search for "planiverse" yields less than a thousand hits.