title: Gravity's Arc: The Story of Gravity from Aristotle to Einstein and Beyond
author:  David Darling 
description: Darling, the author of The Universal Book of Astronomy and a host of other books and articles on space flight, mathematics and physics, provides a strikingly readable explanation for the complex phenomena at the cutting edge of contemporary physics. Beginning with the ancient Greeks' ruminations on the nature of the physical world and concluding with a forecast for where physics is headed, Darling uses a conversational tone and narrative storytelling to coax readers through the finer points of dark energy and dark matter, string theory, inflationary universes, black holes and wormholes. Unfortunately, the book's lack of illustrations hobbles the discussion of some topics, though readers with a cursory knowledge of high school physics should be able to navigate the sections on, say, Keplerian planetary orbits or ballistic trajectories. Darling's done an admirable job of making physics palatable to a general audience, though it seems incomplete without at least a few line drawings.<br />Copyright  Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.
zlib_text: © Springer International Publishing Switzerland 2014
  
  Stephen Leon LipscombArt Meets Mathematics in the Fourth
  Dimension10.1007/978-3-319-06254-9_1
  
  # 1\. 3-Sphere
  
  Stephen Leon Lipscomb1
  
  (1)
  
  University of Mary Washington, Fredericksburg, VA, USA
  
  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 