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3-Sphere

In: Art Meets Mathematics in the Fourth Dimension

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  • Stephen Leon Lipscomb

    (University of Mary Washington)

Abstract

Since the beginning of human civilization, man has struggled to understand his universe. Ironically, the Aristotle (384-322 BC) spherical model, with earth at the center, was fundamental to Dante’s (1265-1321 AD) model which, in turn, underlies the so-called Einstein (1879-1955 AD) Universe. In common language, the Aristotle model involves a solid ball with a spherical surface, and Dante’s model adds a mirror-image solid ball to Aristotle’s and then joins them by “gluing their surfaces.” In 20th Century language, Dante constructed a three-sphere S 3; and the three sphere S 3 turned out to be fundamental to what is commonly called “Einstein’s Universe”. All of these models involve spheres constructed inside universes of dimensions three and four.

Suggested Citation

  • Stephen Leon Lipscomb, 2014. "3-Sphere," Springer Books, in: Art Meets Mathematics in the Fourth Dimension, edition 2, chapter 0, pages 1-9, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-06254-9_1
    DOI: 10.1007/978-3-319-06254-9_1
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