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Copyright © 2005 Pearson Education, Inc. Slide 11-1
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Copyright © 2005 Pearson Education, Inc. Slide 11-1
Copyright © 2005 Pearson Education, Inc.
Chapter 11
Copyright © 2005 Pearson Education, Inc. Slide 11-3
Music Scales and Mathematics
11-A
Copyright © 2005 Pearson Education, Inc. Slide 11-4
Perspective and Vanishing Point
11-B
Copyright © 2005 Pearson Education, Inc. Slide 11-5
Regular Polygon Tessellations
11-B
Copyright © 2005 Pearson Education, Inc. Slide 11-6
A Curious Golden Ratio Limit
Nested Square Roots of 1 Value
1 + 1 1.41421356237 . . .
11-C
Copyright © 2005 Pearson Education, Inc. Slide 11-7
A Curious Golden Ratio Limit
Nested Square Roots of 1 Value
1 + 1 1.41421356237 . . .
1 + 1 + 1 1.55377397403 . . .
11-C
Copyright © 2005 Pearson Education, Inc. Slide 11-8
A Curious Golden Ratio Limit
Nested Square Roots of 1 Value
1 + 1 1.41421356237 . . .
1 + 1 + 1 1.55377397403 . . .
1 + 1 + 1 + 1 1.59805318248 . . .
11-C
Copyright © 2005 Pearson Education, Inc. Slide 11-9
A Curious Golden Ratio Limit
Nested Square Roots of 1 Value
1 + 1 1.41421356237 . . .
1 + 1 + 1 1.55377397403 . . .
1 + 1 + 1 + 1 1.59805318248 . . .
1 + 1 + 1 + 1 + 1 1.61184775413 . . .
11-C
Copyright © 2005 Pearson Education, Inc. Slide 11-10
A Curious Golden Ratio Limit
Nested Square Roots of 1 Value
1 + 1 1.41421356237 . . .
1 + 1 + 1 1.55377397403 . . .
1 + 1 + 1 + 1 1.59805318248 . . .
1 + 1 + 1 + 1 + 1 1.61184775413 . . .
1 + 1 + 1 + 1 + 1 + 1 1.61612120651 . . .
11-C
Copyright © 2005 Pearson Education, Inc. Slide 11-11
A Curious Golden Ratio Limit
Nested Square Roots of 1 Value
1 + 1 1.41421356237 . . .
1 + 1 + 1 1.55377397403 . . .
1 + 1 + 1 + 1 1.59805318248 . . .
1 + 1 + 1 + 1 + 1 1.61184775413 . . .
1 + 1 + 1 + 1 + 1 + 1 1.61612120651 . . .
1 + 1 + 1 + 1 + 1 + 1 + . . . 1 + 52 =
As you continue to nest more roots, you will get infinitely closer to the golden ratio.
11-C
Copyright © 2005 Pearson Education, Inc. Slide 11-12
Parthenon Proportions & Golden Ratio
11-C
