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Trisecting angles in an alternate topology

  1. Jun 2, 2009 #1
    Is there any topology where it is possible to trisect an angle using only straight lines and circles?
     
  2. jcsd
  3. Jun 3, 2009 #2

    HallsofIvy

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    In other topologies, what do you mean by "straight lines" and "circles"? And how do measure angles?
     
  4. Jun 3, 2009 #3
    Lines are curves such that between every pair of points on the line, the segment there is a minimal geodesic; circles are a set of points all equidistant on lines from a center point; angles are measured regarding the curvature from local triangles.

    Changing the problem slightly, all of these constructs are assumed to be on an arbitrary two-dimensional manifold. Is there any such topology where it is possible to trisect an angle using only lines and circles?
     
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