Golden Ratio

Ancient Greeks used a certain ratio of height to width in rectangles that they believed was pleasing to the eye.

The ratio between the height and width is 1:1.618.

Consider classical architecture (e.g. the Parthenon), sculpture and painting and the works of Renaissance artists such as Leonardo Da Vinci.


Watch the video and take some notes about what the Golden Ratio means.


Leonardo and the Golden Ratio

Leonardo Da Vince called it the "divine proportion" and featured it in many of his paintings.

Below is the famous "Mona Lisa".


mona.jpg
Mona Lisa or La Gioconda (c. 1503–1505/1507)—Oil on poplar, Louvre, Paris, France




This image was found at: http://cellini.leonardo.net/museum/2.jpg
ACTIVITY 1:

Download the PDF below and complete the following:

Try drawing a rectangle around her face. Are the measurements in a golden proportion? You can further explore this by subdividing the rectangle formed by using her eyes as a horizontal divider. He did an entire exploration of the human body and the ratios of the lengths of various body parts.



Fibonacci Sequence

Another way of understanding the logic behind the Golden ratio is connecting it to the Fibonacci Sequence.
Look at the diagram below.

external image activi9.gif

ACTIVITY 2:
Create your own

You start off with a box that has a length and width of 1. You then draw a box that has the same length and width as that box. For the rest of the boxes you make their length and width the same as the previous two boxes' combined. What are the next three numbers?


More information about the Fibonacci Sequence can be at the following websites:
Fibonacci "A Man of Many Numbers"
Fibonacci Numbers and Golden Section