A Sphere Visits Flatland

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When a sphere from 3D Spaceland visits 2D Flatland, the citizens of Flatland perceive it only as a series of 2D slices that make the sphere resemble their elite class of citizens, the Circles. (The more sides a shape has in Flatland, the more elevated it is in the social hierarchy). In this Demonstration you compare the Flatlanders' point of view with your own as the sphere passes through Flatland. The challenge for you, as a Spacelander, is to imagine what a 4D sphere would look like as it passes through your 3D world.

Contributed by: John Kiehl (March 2011)
Open content licensed under CC BY-NC-SA




[1] E. A. Abbott, Flatland: A Romance of Many Dimensions, London: Seeley and Co., Ltd., 1884.


[2] I. Stewart, The Annotated Flatland, Philadelphia: Perseus Books, 2002.

[3] D. Burger, Sphereland: A Fantasy about Curved Spaces and an Expanding Universe, New York: Sterling Publishing, 1965.

[4] A. K. Dewdney, The Planiverse: Computer Contact with a Two-Dimensional World, New York: Copernicus, 2001.

[5] R. Rucker, Spaceland, New York: Tor, 2002.

[6] R. Rucker, The Fourth Dimension: Toward a Geometry of Higher Reality, New York: Houghton-Mifflin, 1984.

[7] T. F. Banchoff, Beyond the Third Dimension, New York: Scientific American Library, 1990.

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