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The Fibonacci Sequence The Fibonacci sequence is possibly the most simple recurrence relation occurring in nature. It is 0,1,1,2,3,5,8,13,21,34,55,89, 144... each number equals the sum of the two numbers before it, and the difference of the two numbers...
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In Michelangelo’s painting of “The Creation of Adam” on the ceiling of the Sistene Chapel, look at the section of the painting bounded by God and Adam. The finger of God touches the finger of Adam precisely at the golden ratio point of the width and height of the area that contains them both. Alternatively, you can use the horizontal borders of the width of the painting and get the same result

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The Golden Section was used extensively by Leonardo Da Vinci. Note how all the key dimensions of the room, the table and ornamental shields in Da Vinci’s “The Last Supper” were based on the Golden Ratio, which was known in the Renaissance period as The Divine Proportion.

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The golden section:

Leonardo da Vinci‘s illustrations of polyhedra in De Divina Proportione (On the Divine Proportion) and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his paintings. But the suggestion that hisMona Lisa, for example, employs golden ratio proportions, is not supported by anything in Leonardo’s own writings.

Salvador Dalí explicitly used the golden ratio in his maste...rpiece, The Sacrament of the Last Supper. The dimensions of the canvas are a golden rectangle. A huge dodecahedron, with edges in golden ratio to one another, is suspended above and behind Jesus and dominates the composition.

Mondrian has been said to have used the golden section extensively in his geometrical paintings, though other experts (including critic Yve-Alain Bois) have disputed this claim.

A statistical study on 565 works of art of different great painters, performed in 1999, found that these artists had not used the golden ratio in the size of their canvases. The study concluded that the average ratio of the two sides of the paintings studied is 1.34, with averages for individual artists ranging from 1.04 (Goya) to 1.46 (Bellini).[33] On the other hand, Pablo Tosto listed over 350 works by well-known artists, including more than 100 which have canvasses with golden rectangle and root-5 proportions, and others with proportions like root-2, 3, 4, and 6

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