Authors: Lacy Christensen and Lane Messick
Topics: Graph Theory, Modeling
Connection to Core Curriculum: 8th Grade Math Honors Graph Theory - using graphing techniques to model situations that extend beyond the coordinate plane.
Objectives: Participants will:
Materials Needed: Computers for all the students, projector, and smartboard.
Technology: Online application and use of smartboard
Role of Technology: Facilitates the creation and analyzing of a graph to see if it has an Euler circuit. This applet provides feedback if the students’ attempt to make a circuit was wrong. Also allows the students to see the instructor making and analyzing a graph using the conditions of Fleury’s algorithm.
Web Reference:
Activity Plan:
1. Define the terms Euler Trail and Euler Circuit as follows a. An Euler trail is a trail that uses every edge of a graph exactly once i. An Euler trail starts and ends at different vertices b. An Euler circuit is a circuit that uses every edge of a graph exactly once i. An Euler circuit starts and ends at the same vertex 2. Explain the conditions of Euler Trail 3. Explain the conditions of Euler Circuit 4. Show on the smartboard how to create the vertices and bridges. 5. On the student’s computers find the following applet (http://illuminations.nctm.org/Activity.aspx?id=3550)Euler Circuit Applet Link
Play with the applet to see if they are able to create a Euler Trail or Euler Circuit. Walk around and answer questions 6. Ask the question Is there an easier way to find if we have an Euler Trial or Euler Circuit? 7. Explain that every Euler Circuit will exactly 0 odd vertices 8. Explain that every Euler Trail will have exactly 2 odd vertices 9. Pass out worksheet and have the students work through the first section of problems They are determining how many odd vertices 10. Go over the answers of the worksheet as a class. 11. Explain ’’Burning the Bridges:‘‘ 12. Have the students play with the Applet to see if they are able to create a Euler Trial and Euler Circuit.
Background: The students should understand the history behind Euler creating graph theory and how they came to be to know how this apply to life today.
Extensions: Solve for Hamiltonian circuits using weighted graphs to simulate distance between points. Use the applet to weight the edges and add it for you.
Included documents: Worksheet for students.
