The Golden Section of Art

Mathematics can be enjoyed by graphical art. To make images more pleasing to the eye, artists have transformaed images by a particular ratio known as The Golden Section Ratio (A:B=B:A+B). Some artists that have used this include Phidias, Leonardo da Vinci, Marcel Duchamp and Juan Gris. Even the ancient Egyptians used The Golden Section Ratio!

Objective: to understand the meaning of The Golden Section Ratio.

Materials: ruler

Procedure:

1. Measure the length of your mouth.
2. Examine the following picture of the famous "Mona Lisa" by Leonardo da Vinci:
   

   With your ruler, measure the length of Mona Lisa's mouth.

   In real life, the length of Mona Lisa's mouth was about 5cm.

3. Notice how the dimensions of Mona Lisa's mouth in real life are not the same as in the drawing. That is because it is more "pleasing to the eye" to view a drawing not in its true dimension, but instead the images' dimesions are affected by The Gol den Section Ratio.
   And so, letting p represent the pictorial length and r represent the real-life length we get: p:r=r:p+r
   x:5=5:x+5
   Manipulating the means to solving a proportional, we find that x=3.
   This means that Leonardi made the length of the mouth to be a multiple of 3.
   
4. Answer the following questions then email your answers by clicking the email icon below. Email all your answers together with your name on the document.

Assessment

1. What is the length of your mouth?
2. What would be the length of your mouth when drawing it?
3. Find a picture on the internet that demonstrates The Golden Section Ratio. Save this picture and attach it to the email.
4. Explain how your picture illustrates The Golden Section Ratio.

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