Figure 4.
[LMa]
Step two, you will find the midpoint between C and D and form point E.
Figure 5.
[LMa]

Step three, requires you to extend the line from point C (on D, C segment) out so you can
complete the rectangle. Place your point (stabby side) of the compass on point E and your
pencil side on point B. Draw an arc from point B until you intersect the line extension from point
C, this intersection forms point F.
Figure 6.
[LMa]
Step four requires you to draw a horizontal line extending up towards point B starting at point F.
Figure 7.
[LMa]
Step five is the final step in completing the triangle as you will extend out your line from point B
(on the AB segment) to intersect with the horizontal line that started at point F. This intersection
will form point G.
Figure 8.

[LMa]
Points A, G, F and D form a golden rectangle. If you were to measure the length and the width
of the rectangle and divide the length of segment A, G by the width of segment A, D you should
come up with a ratio close to the golden ratio. Keep in mind that the size of the rectangle does
not matter, what does matter is the ratio between the two sides.
The golden rectangle also possesses a rather unique property. The golden rectangle is
comprised of smaller golden rectangles. Just like Russian nesting dolls, you open one and there
is another inside of it, and another, and another. If you keep dividing the golden rectangle using
the same method we used above you will find several more golden rectangles inside of your
first rectangle. This particular rectangle has six golden rectangles inside of it. Once you have
found all of the golden rectangles inside of the first something else appears.
Figure 9.

[LMa]
If you look closely at the golden rectangle that has been reduced to many different
golden rectangles something else appears. By drawing a quarter of a circle inside of each square
you will get a golden spiral. The spiral approximates the logarithmic spiral, occurs in nature in
various forms, such as the nautilus sea shell [EBB]. The golden spiral grows from the center as it
expands outward, however, the growth factor is equal to the golden ratio (1.618…). The golden
spiral is also found in nature and is directly related to the golden rectangle.
Figure 10.
[LMa]
As we already know the Fibonacci numbers and golden rectangle are related. There is
also a Fibonacci spiral. To create the Fibonacci spiral with to small squares that are equal in size.
Then we will draw a square on top of the first two and that will be square two. Square two is
equal in size to the addition of the two size one squares. Square 3 will cover the area of all five

previous units. This continues on with each new square having a side that is the sum of the last
two squares side (See figure eleven below), notice that the two square you are adding together
are all Fibonacci numbers. If you look at Figure twelve you will notice that a quarter circle was
drawn in each of the square to form a spiral just like the spiral very much like the golden spiral
that was demonstrated above.

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- Winter '15
- Andrew Martino
- The Da Vinci Code, Golden ratio, golden rectangle