The Divine Proportion
Or "The Golden Ratio"

      The Fibonacci Sequence is a series of numbers, beginning with 1, in which each number is created by the addition of the previous two.  The Fibonacci Sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 etc.

      The division of any number in the sequence by the previous number gives a proportion close to 1.618.  The farther into the sequence from which you draw your two numbers, the more closely the proportion will equal “The Divine Proportion”, or 1.61803398874989484820458683...

Proportions of sequential numbers in the Fibonacci Sequence:
1/1 = 1.000000000000
2/1 = 2.000000000000
3/2 = 1.500000000000
5/3 = 1.666666666667
8/5 = 1.600000000000
13/8 = 1.625000000000
21/13 = 1.615384615384
34/21 = 1.619047619047
55/34 = 1.617647058823
89/55 = 1.618181818181
144/89 = 1.617977528089
233/144 = 1.618055555556
377/233 = 1.618025751072
610/377 = 1.618037135278
987/610 = 1.618032786885
1,597/987 = 1.618034447821
2,584/1,597 = 1.618033813400
4,181/2,587 = 1.618034055727
6,765/4,184 = 1.618033963166
10,946/6,765 = 1.618033998521
17,711/10,946 = 1.618033985017
28,657/17,711 = 1.618033990175
46,368/28,657 = 1.618033988205
75,025/46,368 = 1.618033988957
121,393/75,025 = 1.618033988670
196,418/121,393 = 1.618033988780
317,811/196,478 = 1.618033988738
514,229/317,811 = 1.618033988754

      This Divine Proportion is also referred to by the Greek letter Phi () and is named for the Greek sculptor Phidias.  Phidias is widely regarded as the greatest Greek sculptor, and he was one of the first sculptors to intentionally use the Divine Proportion in his work.

      Rectangles with proportions close to 1.6 are referred to as "Golden Rectangles".  The Fibonacci Spiral is a graphic representation of these proportions using a series of Golden Rectangles.  This spiral shows a series of increasingly larger rectangles.  It begins with a square with sides the length of 1, the first number in the Fibonacci Sequence.  Next, additional squares are added (in a spiral formation), each with sides the length of the next number in the sequence.  Each addition of a square creates a new overall rectangle with dimensions that are higher and higher pairs of sequential Fibonacci numbers.  The Fibonacci Spiral or “Golden Spiral” can replicate natural spirals such as those seen in a Chambered Nautilus shell.  You can see this spiral inside the series of rectangles by connecting the adjoining squares, in order, using quarter-circles.

      The images below show the formation of the Fibonacco Spiral, or "Golden Spiral".  You can view the images one at a time by selecting the individual thumbnail images below...

...or, you can watch an animation of these images strung together:

      I first learned about the "Divine Proportion" from a woodworking instructor who was lecturing about furniture design.  He explained to the class that furniture would be more pleasing to the eye if it had 1/1.6 proportions.  He continued explaing about the Golden Rectangle and it intrigued me.  I always remembered his lecture and have tried to utilize those principles when designing many of my woodworking projects.

      Years later, I purchased the book, "Divine Proportion; Phi In Art, Nature, And Science" by Priya Hemenway, and read even more about this topic.  It is a fascinating book and would be enjoyable to anyone interested in history, astronomy, math, science, art, architecture, or any other type of artistic design.

      I hope you enjoyed this page and this very brief introduction to The Divine Proportion.  If you would like to comment on any aspect of this page or topic, please feel free to e-mail me.

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