Geometry: Voronoi Diagrams

Objectives

• Students will create Voronoi Diagrams and apply them to real world situations.
• Students will draw triangles and find their circumcenters using perpendicular bisectors.
• Connect the use of Voronoi Diagrams with finding the equations of lines in the form ax + by + c = 0 form, where a, b, and c are all integers.

Vocabulary

• Voronoi Diagrams
• circumcenter
• seeds
•  Delaunay Triangulation
• perpendicular bisector

About the Lesson

This lesson involves the creation and application of Voronoi Diagrams. As a result, students will:

• Perform Delaunay Triangulation given a set of coordinates or seeds.
• Find the circumcenter of each triangle created, using perpendicular bisectors.
• Use the circumcenters to separate regions or cells in the Voronoi Diagram.
• Apply Voronoi Diagrams to real world situations.