Flatland: A Romance of Many Dimensions

Front Cover
Princeton University Press, Mar 22, 2015 - Mathematics - 104 pages

In 1884, Edwin Abbott Abbott wrote a mathematical adventure set in a two-dimensional plane world, populated by a hierarchical society of regular geometrical figures-who think and speak and have all too human emotions. Since then Flatland has fascinated generations of readers, becoming a perennial science-fiction favorite. By imagining the contact of beings from different dimensions, the author fully exploited the power of the analogy between the limitations of humans and those of his two-dimensional characters.


A first-rate fictional guide to the concept of multiple dimensions of space, the book will also appeal to those who are interested in computer graphics. This field, which literally makes higher dimensions seeable, has aroused a new interest in visualization. We can now manipulate objects in four dimensions and observe their three-dimensional slices tumbling on the computer screen. But how do we interpret these images? In his introduction, Thomas Banchoff points out that there is no better way to begin exploring the problem of understanding higher-dimensional slicing phenomena than reading this classic novel of the Victorian era.

 

Contents

Of the Nature of Flatland
3
Of the Climate and Houses in Flatland
4
Concerning the Inhabitants of Flatland
6
Concerning the Women
8
Of our Methods of Recognizing one another
12
Of Recognition by Sight
16
Concerning Irregular Figures
20
Of the Ancient Practice of Painting
22
How I had a Vision of Lineland
39
How in my Vision I endeavoured to explain the nature of Flatland but could not
42
Concerning a Stranger from Spaceland
46
Having been previously conversant
47
How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland
49
How the Sphere having in vain tried words resorted to deeds
55
How I came to Spaceland and what I saw there
57
How though the Sphere showed me other mysteries of Spaceland I still desired more and what came of it
61

Of the Universal Colour Bill
24
ΙΟ Of the Suppression of the Chromatic Sedition
27
Concerning our Priests
30
Of the Doctrine of our Priests
32
Other Worlds
37
So the Citizens of that Celestial Region
62
How the Sphere encouraged me in a Vision
66
How I tried to teach the Theory of Three Dimensions to my Grandson and with what success
68
How I then tried to diffuse the Theory of Three Dimensions by other means and of the result
70
Copyright

Other editions - View all

Common terms and phrases

About the author (2015)

Edwin Abbott Abbott (1838-1926), the author of more than fifty books on classics, theology, history, and Shakespeare, was headmaster of the City of London School and one of the leading educators of his time. Thomas Banchoff is professor emeritus of mathematics at Brown University and author of Beyond the Third Dimension.

Bibliographic information