Golden Rectangle

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Golden Rectangle

• A golden rectangle is a rectangle whose side
  lengths are in the golden ratio, 1f.

• The golden ratio, f, is pronounced Fee and is
  approximately 1.618.

1
f
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Golden
Constructing a Golden Rectangle
Rectangle
1.) Construct a unit square
2.) Draw a line from the midpoint of one side to
an opposite corner.
3.) Use that line as the radius to draw an arc
that defines the long dimension of the rectangle.
Midpoint
Square
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Golden
Constructing a Golden Rectangle
Rectangle
The Golden Rectangle
f
1
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Golden
Rectangle
Proving a Golden Rectangle

• We will have to use the Pythagorean Theorem

Longer Side


Ratio
1.618
Shorter Side
Which is the Golden Ratio or Phi
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Golden Spiral
Constructing a Golden Spiral
1.) Start with a golden rectangle on its side
2.) Take another golden rectangle, turn it
clockwise
3.) Shrink it to fit into the smaller portion of
your original golden rectangle.
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Golden Spiral
Constructing a Golden Spiral
1.) Start with a golden rectangle on its side
2.) Take another golden rectangle, turn it
clockwise
3.) Shrink it to fit into the smaller portion of
your original golden rectangle.
4.) Now keep repeating that process with each
new rectangle you create!
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Golden Spiral
Constructing a Golden Spiral
1.) Start with a golden rectangle on its side
2.) Take another golden rectangle, turn it
clockwise
3.) Shrink it to fit into the smaller portion of
your original golden rectangle.
4.) Now keep repeating that process with each
new rectangle you create!
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Golden Spiral
Constructing a Golden Spiral
1.) Start with a golden rectangle on its side
2.) Take another golden rectangle, turn it
clockwise
3.) Shrink it to fit into the smaller portion of
your original golden rectangle.
4.) Now keep repeating that process with each
new rectangle you create!
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Golden Spiral
Constructing a Golden Spiral
1.) Start with a golden rectangle on its side
2.) Take another golden rectangle, turn it
clockwise
3.) Shrink it to fit into the smaller portion of
your original golden rectangle.
4.) Now keep repeating that process with each
new rectangle you create!
5.) Now you are ready to draw your spiral!
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Golden Spiral
Constructing a Golden Spiral
1.) Start with a golden rectangle on its side
2.) Take another golden rectangle, turn it
clockwise
3.) Shrink it to fit into the smaller portion of
your original golden rectangle.
4.) Now keep repeating that process with each
new rectangle you create!
5.) Now you are ready to draw your spiral!
Now thats a golden tattoo!
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Golden Rectangle, GSP, and Pictures
1.) Construction of the Golden Rectangle using
GSP. 2.) Parthenon (using pictures). 3.) Mona
Lisa (using pictures).
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Quadrature of the Rectangle