Golden Rectangle
A golden rectangle is a rectangle whose side
lengths are in the golden ratio, 1:φ.
The golden ratio, φ, is pronounced “Fee” and
is approximately 1.618.
1
φ
Constructing a Golden
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 Midpoint
long dimension of the rectangle. Square
Constructing a Golden
Rectangle
The Golden Rectangle φ
1
Proving a Golden Rectangle
We will have to use the Pythagorean Theorem
2
a
c2 a2
2
a c
a2 5a 2 a 5
c
4 a2
4 2
a a aa c5
2 2
2 a a 5 aa 5 1 5
a 5
a 1 5 a
a 2
2 22
2 2 2
1 5
a
Longer Side 2 1 5
Ratio = = =
1.618
Shorter Side a 2
Which is the “Golden Ratio” or “Phi”
“Golden Rectangle”, GSP, and
Pictures
1.) Construction of the Golden Rectangle using GSP.
2.) Parthenon (using pictures).
3.) Mona Lisa (using pictures).
Quadrature of the Rectangle