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# Math 1332 - PowerPoint PPT Presentation

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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Presentation Transcript

### Math 1332

Draw without lifting your pencil or crossing (or re-tracing) any lines.

Chapter 10.7

Non-Euclidean Geometry

(edges)

Graph – a combination of vertices and edges

Even Vertex – has an even number of edges

Odd Vertex – has an odd number of edges.

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)

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

• Moebus Strip

http://www.metacafe.com/watch/868152/mobius_strip/

http://www.math.psu.edu/dlittle/java/geometry/spherical/toolbox.html

The sum of the angles of a triangle can be more than 180º

http://www.flatlandthemovie.com/