GEOMETRY MAJOR PROJECT: Networks
DUE DATE: ________________
In math, it’s called the “traveling salesman problem”. In computers, it’s called a minimum spanning tree
(which is how we send a message to several people). To the rest of us, it’s a child’s game. Can you trace
this picture without lifting your pencil and without going over the same segment more than once?
This picture is called a network. The points on this picture are called vertices (one point is a vertex). The lines are
called edges. A vertex is even if an even number of edges meet at the vertex. (The middle one is even because 4
edges meet there.) A vertex is odd if an odd number of edges meet at the vertex. (The left corner vertices are odd
because 3 edges meet at each.)
For this project, you’re going to make a conjecture to predict which networks are traceable.
 To begin, try to trace each of these pictures without lifting your pencil and without going over the
same edge more than once:
 Next, count how many edges meet at each vertex.
 Make a table to show three things for each network: the number of vertices that were even, the
number that were odd, and if it was a traceable network.
 Describe any patterns that you notice and make a conjecture about how you can tell if a network
is traceable.
 Is a network with 4 odd and zero even vertices traceable? Sketch one and try your conjecture.
 What’s the most complicated traceable network you can sketch?
WHAT YOU WILL HAND IN: Either a report or a poster with this information:
PART
Pictures of these networks (you can cut out the ones on this sheet)
Description/diagram of how you would trace each (or why you can’t)
A complete and accurate table
Patterns that you notice are well described. Conjecture is well written.
The 4 odd, 0 even network is drawn and includes written results of
your test.
The “most complicated” network is drawn and includes written results
of your test.
Professional or creative submission
Has the MOST complicated network in the class!
NOTE: LATE projects lose 5 points EACH DAY!
POINTS
5 points
20 points
20 points
25 points
10 points
10 points
10 points
BONUS 5 points.