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How to Find Euler Angles

As students enter intermediate and middle school, they will most likely have to determine if vertex edge graphs are Euler circuits or Euler paths (pronounced like "oiler"). An Euler circuit is a graph that follows a route where every edge is traced exactly once and ends at the same vertex as it began. An Euler path is the same as an Euler circuit, except it does not have to end where it started. Every angle, or vertex, in these graphs has an angle degree, and determining this degree is an essential step in determining the difference between Euler circuits and Euler paths.

Instructions

- 1
  Circle one vertex on the graph. A vertex on a graph is a point that has lines running into it, and every vertex edge graph has at least three vertices. It does not matter which vertex you choose to start with.
- 2
  Count the number of lines, or edges, that run directly into the vertex and label it with that number. This number is the angle degree of that vertex. For example, if a vertex has four lines that run into it, it has an angle degree of 4.
- 3
  Continue circling, counting, and labeling the angle degrees of each vertex on the graph. Every vertex should be labeled with a degree. For example, a rectangular vertex edge graph has four vertices, and each has an angle degree of 2 because two edges run into each of the four vertices.

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