Painting Problem: School 1
Watch the video or read the text below to be introduced to this problem.[br]If you watch the video, scroll to the first applet.
READ THIS IF YOU SKIPPED THE VIDEO. Else, continue to the applet below.
You have been hired to paint the hallways at your local school. A floorplan of the area you'll be working in is shown below. Not all walls, however, need to be repainted at this time--only the ones shown in red. All the exterior walls will be painted, as well as both sides of the interior hallways.[br][br]You want to figure out the shortest path to take to make sure you paint all the walls, but don't do any extra walking. [br][br]We can make a simplified drawing, called a vertex edge graph, to represent this situation. Vertex (or vertices for more than one) are points. Edges are lines. In the painting situation we can use vertices, or points, to represent where the hallways intersect, as indicated by letters in the floor plan below.[br][br]For my vertex edge graph, I drew points for the letters. I connected these points with lines to show where painting is needed. Since the interior hallways needed to be painted on 2 sides, I needed to make a curved line to represent the second side. [br][br]Notice that my sketch is not to scale. The lines do not need to be straight. Vertex-edge graphs should be a very basic and simple drawing.[br]
The Painting Applet: Use the pen tool to trace the path you would take. Trace each line exactly once.
[b]Share your path by listing the points in order.[/b] For example, ABGH would mean you traveled from A to B to G to H.
[b]In an Euler Circuit:[/b][br]-You need to start and end at the same point[br]-And you cover all of the edges exactly once. [br][br]Is the route you listed above an Euler Circuit?