Mathematical Modeling

1
Mathematical Modeling

• A mathematical model can be used to examine the
  behavior and characteristics of real-world or
  geometric systems.
• Drawing a picture to represent the model can help
  illustrate its behavior.
• Making a table of values for successive terms in
  the model can help clarify or check its behavior.

2
Mathematical Modeling

• If everyone in the class shakes hands with
  everyone else, how many handshakes are there?
• Break into groups of 4 or 5, and determine how
  many handshakes there are for sets of 1, 2, 3, 4,
  and 5 people.
• Do you see any pattern?

3
Mathematical Modeling

• Model the problem using points for people and
  line segments for handshakes.
• Notice that the pattern is not linear. Can you
  find another pattern?

4
Mathematical Modeling

• Look for a pattern
• Each person shakes hands with everyone else
• So each of n people shake hands with n-1 others
• But each handshake only needs to be counted once,
  since Jeff shaking hands with Sean is the same as
  Sean shaking hands with Jeff
• Combining these observations gives the formula

n(n-1) 2