Mortgages and Seashells. 1. Iterating Linear Functions

Click here to load reader

  • date post

    24-Dec-2015
  • Category

    Documents

  • view

    216
  • download

    0

Embed Size (px)

Transcript of Mortgages and Seashells. 1. Iterating Linear Functions

  • Slide 1
  • Mortgages and Seashells
  • Slide 2
  • 1. Iterating Linear Functions
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • A Useful Linear Function
  • Slide 7
  • A General Financial Formula
  • Slide 8
  • Suppose you borrowed $10,000 from a bank that charged.05% interest per month and would like to make payments of $500 per month. How long would it take to pay off the loan? An Application
  • Slide 9
  • -10000, B(n) = 0
  • Slide 10
  • 2. Iterating Geometric Transformations
  • Slide 11
  • Rotate thru -90
  • Slide 12
  • Dilate about the origin by a factor of.618
  • Slide 13
  • Translate over 1, up 1
  • Slide 14
  • Rotate thru -90
  • Slide 15
  • Dilate about the origin by a factor of.618
  • Slide 16
  • Translate over 1, up 1
  • Slide 17
  • The Golden Spiral
  • Slide 18
  • Golden Spiral?
  • Slide 19
  • 3. Iterating Complex Linear Functions
  • Slide 20
  • Slide 21
  • 3. Complex Linear Functions
  • Slide 22
  • The Golden Rectangle Function
  • Slide 23
  • Slide 24
  • Putting DeMoivres Theorem to Work
  • Slide 25
  • Problem: This gives complex numbers as a function of a real variable. How do you plot g(x)? Need to plot ( real[g(x)], imaginary[g(x) ) for x = 0 to 20 Mathematica to the rescue!