Tag Archives: hyperbolic geometry

A Transversion Machine Redux

Thoughts on the Original Design The motivation for constructing a transversion-based spatial automaton was to construct a surface in 3D Euclidean space from as little local geometric information as possible.  It was the automaton’s role to expand the information into … Continue reading

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Hyperbolic Translations

One of the crucial issues in the construction of the implementation of the transversion automaton is how it interpolate its geometric relationships (transversions and rigid body motions) through space to generate a surface in 3D.  The input data is pentagonal … Continue reading

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Navigating Hyperbolic Space with Fibonacci Trees

When moving from the usual Euclidean flat space to a curved space like hyperbolic space, one not only has to work with new models of basic geometric concepts like points, lines, and triangles, but one also has to deal with … Continue reading

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Hyperbolic Geometry: Poincaré Disc Tessellation How-to

Background Figuring out how to draw lines in hyperbolic space is pretty straightforward.  It’s just some basic geometry and the details are easy to find with a little searching.   What is not so easy to find is the details … Continue reading

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Hyperbolic Geometry: Poincaré Disc

One of the most common models used to visualize hyperbolic geometry is the Poincaré disc.  The Poincaré disc maps the point at infinity of a hyperbolic space to a circle where hyperbolic lines are represented as arcs of circles intersecting … Continue reading

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