Fibonacci

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niemeyjt

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A well-known woodworking tool maker from the US has just sent me an e-mail on their latest tool - a Fibonacci Gauge.

So, folks, a question.

Do any of you use the "golden ratio" of approximately 1:1.618 for aesthetically pleasing results - or do you stick to decimals and fractions like a quarter and a half?

J
 
I use the Fibonacci rule, for example, just done a planning application for a different style (to the existing) for some replacement windows in a grade 2 listed shop and that was used to set up the transom height, and get passed by the Conservation Officer.
 
I wonder why it has come to be known as a Fibonacci rule. The golden ratio was known many years (maybe 1500 plus) before Fibonacci.

As the rule is to be used with regard to aesthetics, naming it after the golden ratio seems closer to its purpose.

Fibonacci only comes in to his own if you want two whole numbers (ratios of integers) that are close to the golden ratio and you do not need a fancy device to measure 21 units in one direction and 13 in the other.
 
"Golden ratio" is just a popular but meaningless semi-mystical myth. There's a lot of it about!
 
I always understood the "golden ratio" to be the relationship of a side of a pentagon to its diagonal. And the Fibonacci sequence to be the way an idealised population of rabbits could be expected to increase in number. :LOL:
 
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I wonder why it has come to be known as a Fibonacci rule. The golden ratio was known many years (maybe 1500 plus) before Fibonacci.

As the rule is to be used with regard to aesthetics, naming it after the golden ratio seems closer to its purpose.

Fibonacci only comes in to his own if you want two whole numbers (ratios of integers) that are close to the golden ratio and you do not need a fancy device to measure 21 units in one direction and 13 in the other.
It might be because Fibonacci was the first one to document it in writing, which is similar to Hooke and his hanging chain theory, the principal of which was probably known by the Romans.

The geometric form originates in the vesica piscis or mandala, a significant sacred geometric form used in that 15th century fan vault pattern I was researching a while back. The mandala was used in India well before Christ appeared on the scene.

That no.4 shaped bit is the source of the golden ratio and the lozenge shape in two circles which overlap is the mandala and the fish symbol of Christ.

IMG_0944.JPG


That daisy shape is another big deal and is seen inscribed on buildings all over the place.
 
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I made a Fibonacci Gauge years ago -- never found a use for it.
If I can find it tomorrow I will take a photo.
 
As I thought I understood it, the Fibonacci series is simply adding the nth and n-1th term to derive the n+1th term. If continued for a while the ratio of two consecutive terms approaches the so-called golden mean or ratio. The big mystery to me is why such a ratio or proportion should be aesthetically or visually pleasing, and the usual proposal, as far as I know, is that the proportion occurs in nature, owing to the way some organisms grow. Whether there have been any new revelations or insights I to this, I know not, but it's an interesting subject. I might Google it.
 
I made a pair of dividers at a 1 : 1.6 ratio. I like to think it helps a little, but it only really gets used when I am making things on the fly, not when I am designing something.
 

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If only the world was as simple and formulaic! But I do find if I place something a pleasing distance from 2 things it often is around this number anyway.... try it.
 
The "Golden Mean" is a very curious thing. Some artists and designers, especially when starting out in their careers can get quite fixated about it, and use it as some sort of ""crutch", or talisman. Probably, the best that can be said of it, is that if you use it in your work, then the results might not end up looking too bad. :giggle:

If beauty truly is "in the eye of the beholder". then there is no way that it can rely on a specific formula. Lots of other things do come into play in design, and one has to trust ones own instincts.

Whether something looks good or is "just right", depends on ones first impression. That renewed glimpse of ones work after having not having seen it for a while can give one a valuable insight. And, if you are not pleased with it - then change it, or start again.
 
As I thought I understood it, the Fibonacci series is simply adding the nth and n-1th term to derive the n+1th term. If continued for a while the ratio of two consecutive terms approaches the so-called golden mean or ratio. The big mystery to me is why such a ratio or proportion should be aesthetically or visually pleasing, and the usual proposal, as far as I know, is that the proportion occurs in nature, owing to the way some organisms grow. Whether there have been any new revelations or insights I to this, I know not, but it's an interesting subject. I might Google it.
Yep, that's it. 5+8=13, 8+13=21 etc.

1716981391341.png
 
There is a free phone app, golden ratio calculator, no need to buy anything. Or just work it out yourself, or do an excel, Google sheets, ios numbers calculator. Simple sums.
 
A well-known woodworking tool maker from the US has just sent me an e-mail on their latest tool - a Fibonacci Gauge.

So, folks, a question.

Do any of you use the "golden ratio" of approximately 1:1.618 for aesthetically pleasing results - or do you stick to decimals and fractions like a quarter and a half?

J
The Fibonacci proportions apply in almost all areas of stringed instrument making, beginning with the scroll-shape of a (classical) violin head, to the outlines of guitars and lutes. Kevin Coates's 1985 book 'Geometry, Proportion, and the Art of Lutherie' (Oxford University Press) is well worth seeking out.
 
As I thought I understood it, the Fibonacci series is simply adding the nth and n-1th term to derive the n+1th term. If continued for a while the ratio of two consecutive terms approaches the so-called golden mean or ratio. The big mystery to me is why such a ratio or proportion should be aesthetically or visually pleasing, and the usual proposal, as far as I know, is that the proportion occurs in nature, owing to the way some organisms grow. Whether there have been any new revelations or insights I to this, I know not, but it's an interesting subject. I might Google it.
It certainly is found in nature, the female leg (the two components: thigh to knee, and knee to ankle) being good examples of the Golden Section.
 
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