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Award ID contains: 1708239

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  1. ; ; ; (, Experimental Mathematics)
    Full Text Available 
  2. ; ; ; (, Experimental Mathematics)
    Full Text Available 
  3. ; ; (, Notices of the American Mathematical Society)
    Full Text Available 
  4. (, Notices of the American Mathematical Society)
    null (Ed.)
    Full Text Available 
  5. ; ; (, Computers & Graphics)
    Full Text Available 
  6. ; (, Algebraic & Geometric Topology)
    Full Text Available 
  7. ; ; ; (, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture)
    null (Ed.)
    This article presents virtual reality software designed to explore the Sol geometry. The simulation is available on 3-dimensional.space/sol.html 
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    Accepted Manuscript Full Text Available
  8. ; ; (, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture)
    null (Ed.)
    We introduce cohomology fractals; these are certain images associated to a cohomology class on a hyperbolic threemanifold. They include images made entirely from circles, and also images with no geometrically simple features. They are closely related to limit sets of kleinian groups, but have some key differences. As a consequence, we can zoom in almost any direction to arbitrary depth in real time. We present an implementation in the setting of ideal triangulations using ray-casting. 
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    Accepted Manuscript Full Text Available
  9. ; ; ; (, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture)
    We describe a method of rendering real-time scenes in Nil geometry, and use this to give an expository account of some interesting geometric phenomena. You can play around with the simulation at 3-dimensional.space/nil.html. 
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    Accepted Manuscript Full Text Available
  10. ; (, Proceedings of Bridges 2019: Mathematics, Art, Music, Architecture, Education, Culture)
    We describe geared versions of Buckminster Fuller’s jitterbug mechanism, and a variant cuboctahedral mechanism. In the cuboctahedral case, differences between the triangular and square faces led us to a numerical method to construct acircular gears, allowing for rotation rates that vary with angle. 
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    Accepted Manuscript Full Text Available