What is a Fibbonacci and Who Cares?

   What in the world is a “Fibonacci” and what does it have to do with woodturning? Well, it is not a pasta or some old exotic dance, but it is all around us. It is in almost everything in nature, architecture, art, even your face. Touching on the “who cares” part first, it has a lot to do with the proportions of the elements of an object in its design.
When we look at something there is a built in sense to our perception that gives us a feeling of agreeableness or uneasiness about that object. It has to do with the proportions in the design of that object. If the proportions are out of relationship with one another we feel a somewhat questionable attitude toward it. But if the proportions are within a certain range, we feel a comfortable and acceptable attitude about it and maybe even a little excited. The ancients clear back to the early Egyptian and early Grecian times or maybe even before, figured this out and it is seen in their architecture, sculpture, art and utility items. And, since human nature has not changed, neither has this aspect of human perception. Therefore, it is still with us and is just as important in our design. We will get into more detail later, but for now we will address the basis of how we get those proportions using the rule of Fibonacci.
Fibonacci was the nickname of an Italian mathematician, Leonardo BonacciLeonardo of PisaLeonardo Pisano Bigollo, or Leonardo Fibonacci from the 12th century. He is the one that came up with the number sequence referred to as the Fibonacci Sequence. That sequence of numbers is; 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ….. and so forth. The sequence of numbers is generated by starting with either 0 or 1 and the next number is created by adding the last two numbers. When you divide the current number with the number before it, the result is 1.618…. which is the ratio referred to as the Golden Mean, Golden Ratio, Golden number and is denoted by the Greek letter “Phi” (ø).The math between the Golden Mean and the Fibonacci sequence are intimately related. The math behind this can get very involved and way beyond what we need to know in using it. Suffice it to say that that is what it is. So, the number 1.618 is really about all we need to know.
Now, how do we use it? Here again, the answer to that question goes way beyond the scope of this article, but we’ll attempt to give some practical application usage.
In the design of an object it is the Golden Ratio or Fibonacci rule that gives us the relationship of proportions in the elements of that object. First of all let’s look at the familiar Fibonacci square.

If you build a square starting with 1 and continue to add squares/rectangles using the Fibonacci sequence, every next rectangle is the sum of the previous two sides.

Then if you draw an arc in each box that has the radius of its side, you get the familiar Fibonacci spiral.
This spiral is seen in many places in nature such as the nautilus shell, sunflower seed pattern, and many other flowers in the petals, seeds or leaves, the pattern of clouds and wind in a hurricane or the stars in the Milky Way Galaxy and on and on.

So, to use this concept in designing a turning, plan the elements of the object to conform to these ratios. For instance, the bottom part of a box would be .618 the length of the whole box or the wide spot in a hollow form would be .618 of the total height from the bottom. For example; for a 6 inch box, the bottom part would be: 6 x .618 which equals 3 11/16 making the top of the box 2 5/16. (Or you could round to 3 ¾ and 2 ¼.)  And for a 10 inch hollow form the wide spot or feature ring would be at 6 ½ from the bottom. (10 x .618 = 6 3/16 (and rounding to 6 ½ )) Also, the height and width of an object would be in the proportions of 1.618 or .618 of one another. These proportions are also equal to 5/8 or 5 to 8, for instance if the height of a box is 8 inches, the bottom would be 5 inches and the top 3 inches. These ratios can be further defined within the individual elements themselves, for instance a bead or cove or line on the lid or box bottom could be placed within those ratios. Or, a feature ring would be placed within those guidelines. The length of a finial could be in these proportions to the object it is on and the features within the finial could be proportional to itself. The possibilities are endless.
Another close ratio is the rule of thirds. In other words, one part would be 1/3 and the other part 2/3 in proportion. Each are close, but the Golden ratio seems to be more pleasing.
To avoid all the math and head scratching, you can make your own Fibonacci or Golden mean calipers. Here are a couple of links to help; Wood magazine video or Plans . I have made some for myself and they are very handy.
So, did you know you have Fibonacci on you face? Your nose is at a Golden section of the distance between the tip of your chin to your eyes from the tip of your chin. And your mouth is at a Golden section of that same distance between your eyes and the tip of your chin from your eyes. Even from the side, you ear is in golden mean proportions. Needless to say, the examples of Golden mean or Golden section abound in nearly everything Therefore, when planning a piece, take all the elements into account and place them within the golden ratio guidelines and it is bound to be more pleasing. So even in design, it’s a good idea to try and follow “the golden rule”.

Written by Mel Bryan

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