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Math 1332

Math 1332. Draw without lifting your pencil or crossing (or re-tracing) any lines. Chapter 10.7 Non-Euclidean Geometry. Vertex: the intersection of two or more segments (edges) Graph – a combination of vertices and edges Even Vertex – has an even number of edges

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Math 1332

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  1. Math 1332 Draw without lifting your pencil or crossing (or re-tracing) any lines. Chapter 10.7 Non-Euclidean Geometry

  2. Vertex: the intersection of two or more segments (edges) Graph – a combination of vertices and edges Even Vertex – has an even number of edges Odd Vertex – has an odd number of edges.

  3. Traversable Graph – can be traced without lifting your pencil and without re-tracing edges • Rules for Traversability : • If all vertices are even a graph is traversable • If you have 2 odd vertices (the rest even) a graph is traversable. Start at one of the odd vertices and end at the other. • More than two odd vertices is not traversable. Not Traversable (4 odd) Traversable (all even)

  4. Topology – looks at shapes as being able to be twisted. Rules for Topology : Classify by the number of holes – genus Genus = 1 Genus = 1 Genus = 4

  5. More Possibilities • Moebus Strip http://www.metacafe.com/watch/868152/mobius_strip/

  6. Spherical Geometry http://www.math.psu.edu/dlittle/java/geometry/spherical/toolbox.html The sum of the angles of a triangle can be more than 180º

  7. Flatland – Book & Movie http://www.flatlandthemovie.com/

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