Over a hundred years ago, 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.

• This World
  • Of the Nature of Flatland
  • Of the Climate and Houses in Flatland
  • Concerning the Inhabitants of Flatland
  • Concerning the Women
  • Of Our Methods of Recognizing One Another
  • Of Recognition by Sight
  • Concerning Irregular Figures
  • Of the Ancient Practice of Painting
  • Of the Universal Colour Bill
  • Of the Suppression of the Chromatic Sedition
  • Concerning Our Priests
  • Of the Doctrine of Our Priests
• Other Worlds
  • How I Had a Vision of Lineland
  • How I Vainly Tried to Explain the Nature of Flatland
  • Concerning a Strange from Spaceland
  • How the Stranger Vainly Endeavoured to Reveal to Me in Words the Mysteries of Spaceland
  • How the Sphere, Having in Vain Tried Words, Resorted to Deeds
  • How I Came to Spaceland, and What I Saw There
  • How, Though the Sphere Shewed Me Other Mysteries of Spaceland, I Still Desired More; and What Came of It
  • How the Sphere Encouraged Me in a Vision
  • How I Tried to Teach the Theory of Three Dimensions to My Grandson, and with What Success
  • How I Then Tried to Diffuse the Theory of Three Dimensions by Other Means, and of the Result