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### 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!