# perfect size box?



## Brucio (22 Jun 2007)

There are some things in life which seem to be "just right".
There is a "perfect size box" which fits this description.
It's not the actual size, but rather the ratio of the three sides, something like 9:6:3.
My problem is, I can't remember what that ratio is.
If anyone knows, I would like to, too please.
What's this to do with scrollsawing?
I want to make a trinket box, with my usual "hidden locking" system, but without all the bits sticking out when it's open.
I've got the idea in my head, but to make it attactive to other people who might want to make it, the box has to be one of those "just right" things...
If someone gives me a list of possible ratios, I could probably pick the right one.
Like the name of someone you recognise, but just can't think of their name...
It's on the tip of my tongue...
brucio


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## andrewm (22 Jun 2007)

I have never come across anything stated but from first principles the "Golden Ratio" is about 1:1.62. If you were talking about a box where the length is 1.62 * the width and the width is 1.62 * the height then this would give approximate proportions of:

5 : 8 : 13

Is this what you were looking for?

Andrew


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## Brucio (22 Jun 2007)

Thanks, Andrew for your fast reply.
It doesn't ring any bells, but that ratio must be pretty near to what I'm looking for.
bruce


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## Anonymous (24 Jun 2007)

A ratio for the 'perfect size box' ?
I doubt such a thing exists as how can there be, (and who decides), a perfect sized box ?


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## Gill (24 Jun 2007)

There seems to be a consensus among such luminaries as Hemon, Pythagoras, Euclid, Leonardo Bonacci (aka _Fibonacci_), Johannes Kepler, Martin Ohm, Luca Pacioli, Leonardo da Vinci, Uqba ibn Nafi, Charles-Edouard Jeanneret (aka _Le Corbusier_), Mario Botta, and Piet Mondrian that the Golden Ratio produces the most pleasing ratios.

I agree!



Gill


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## Anonymous (24 Jun 2007)

Gill":a0ctwdth said:


> There seems to be a consensus among such luminaries as Hemon, Pythagoras, Euclid, Leonardo Bonacci (aka _Fibonacci_), Johannes Kepler, Martin Ohm, Luca Pacioli, Leonardo da Vinci, Uqba ibn Nafi, Charles-Edouard Jeanneret (aka _Le Corbusier_), Mario Botta, and Piet Mondrian that the Golden Ratio produces the most pleasing ratios.
> 
> I agree!
> 
> ...




Seems to be ?..........Prove it ! :lol:


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## Brucio (25 Jun 2007)

Thanks to everyone who replied.
As Gill says, there's a whole sackful of gifted artists who have used the "Golden Ratio" to produce works of art that now sell for millions of pounds (sterling, not weight).
Until you can produce a similar piece of artistry that someone else will pay millions for, I think that proves the point.
In any case, pleasure is a relative thing.
It all depends on how you are feeling at the time.
Especially if you were out on the pop last night....
Bruce


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## Anonymous (25 Jun 2007)

Brucio":1il67xrb said:


> Until you can produce a similar piece of artistry that someone else will pay millions for, I think that proves the point.
> Bruce



My 'prove it' challenge to Gill was tongue-in-cheek Bruce as I know it would be an almost impossible thing to prove !
However, the point could be proved if all works of art sold for millions were based on a so-called 'Golden Ratio'. As this is far from the case it's a very weak argument and proves nothing.


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## Gill (25 Jun 2007)

I'd love to invite all those brilliant men to contribute to this thread and confirm my opinion, but let's face it - it ain't gonna happen  ! So instead I'll just suggest that you look out for great works of art and see how many of them incorporate the Golden Ratio in their design. I'll start you off with the Hemon's Great Pyramid of Cheops, Da Vinci's Mona Lisa and Vetruvian Man and Uqba ibn Nafi's Great Mosque of Kairouan.

Okay, so it isn't a prerequisite that a work of art should incorporate the Golden Ratio; there again, I doubt we could all agree on a definition of 'art'. A lot of people would actually question if the likes of Damian Hirst and Tracey Emin are artists at all, yet their works are highly valued and displayed in galleries. Nevertheless, I think you'd be surprised at how many pieces that are considered beautiful do have proportions which conform to the Golden Ratio.

The Golden Ratio springs up time and again in nature. Cosmetic surgeons use it extensively when reconstructing the human face to produce the most beautiful results. These links are quite informative:

http://www.intmath.com/Numbers/mathOfBeauty.php

http://www.qmul.ac.uk/research/newsrele ... news_id=99

Oh, I know a lot of the comments on this thread are tongue in cheek and I accept them in the good natured way that they're obviously intended. But joking aside, the Golden Ratio is a very useful concept to be aware of when you're producing something which you want to look good.

Gill


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## hawkinob (25 Jun 2007)

Just finished reading "Making Heirloom Boxes" (x Peter lloyd) think it was a GMC Publication. He mentions 1:1.6 ratio for the side lengths, don't recall that he quoted the depth (height of the sides - depended on use I think)
Bob H.


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## StevieB (25 Jun 2007)

The golden ratio is actually copied from Nature rather than being 'designed' as pleasing to the eye. This is why Da Vinci's Vitruvian man, which was the most anatomically correct diagram of the human form of its day, conforms to the ratio - because it is that ratio in real life. 

Of more interest to me is 'why' such a ratio is pleasing to the eye? 

In terms of Nature it must have a selective advantage to be so ubiquitious - anything that does not increase the survival chances of the species it is found in does not last long in evolutionary terms. Are we therefore so used to seeing such a ratio that using it in art appears pleasing, or to put it another way 'looks right'? If we were referring to anatomy then I would say yes, in terms of a box or construction, or even the painting of a structure I am not so sure.

Going a bit off topic here, sorry  

Steve.


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## andrewm (25 Jun 2007)

I first came across the 'Golden Ratio' some time ago and the Fibonacci sequence even longer ago. However it is only recently that I found out that they are connected and that the ratio between successive numbers in the Fibonacci sequence tends towards the 'Golden Ratio'

Andrew


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## DomValente (25 Jun 2007)

Another interesting fact. If you have a rectangle in the proportions of the Golden Ratio and remove a square section what remains is a rectangle with the proportions of the Golden Ratio.
This post should also appear under General Woodworking, many could benefit.

Dom


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## andrewm (25 Jun 2007)

DomValente":1e15ue91 said:


> Another interesting fact. If you have a rectangle in the proportions of the Golden Ratio and remove a square section what remains is a rectangle with the proportions of the Golden Ratio.



Which comes about as a result of one of the derivations of the golden ratio, namely that x = 1/x + 1 which for any starting value of x will tend quite rapidly towards the golden ratio with repeated iteration. But that is probably more than you wanted to know.



DomValente":1e15ue91 said:


> This post should also appear under General Woodworking, many could benefit.


I was wondering how it ever started in Scrolling.

Andrew


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## Gill (25 Jun 2007)

Oy you lot - mitts off! This is interesting _and it's *ours*_!

Stick around. Scrollers do sometimes slip accidentally into interesting conversations.



Gill


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## DomValente (25 Jun 2007)

Gill":r425h1zc said:


> Oy you lot - mitts off! This is interesting _and it's *ours*_!
> 
> Stick around. Scrollers do sometimes slip accidentally into interesting conversations.
> 
> ...



I know, I read every post. Just don't know enough to comment more.

Dom


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## Anonymous (26 Jun 2007)

This has been an interesting thread with many throwing their ideas into the pot.
I've become convinced that there exists a certain mix of elements that make up something that is 'attractive to the eye'.
I'm not sure what those elements are as the combinations of size,style,colour,tone etc are too numerous to pin down.

My line of thought........
If a 'Golden Ratio' box is drawn as black lines on white paper, it won't look very much at all and would be difficult to call 'pleasing' as it is just a box made from lines.
Begin adding other elements like colour,shading and design work and things start to become more interesting. Whether those added elements are pleasing to the eye would be down to the viewer.

There may be a case for certain dimensions being more pleasing to the eye than others but it's my belief that additional elements such as design and colour have more importance.Get those right and you stand a good chance of creating something that many will find 'pleasing' to the eye !

I spent 30 years as a carpenter/joiner and constantly came across situations where a certain moulding/colour/shape looked better than others in any given situation. There is no way to explain my reasoning on this other than to say it looked right. Maybe there is a certain ratio playing it's part but I'm convinced it's a combination of many elements in any given situation that we judge as 'pleasing to the eye'.


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## StevieB (26 Jun 2007)

As has already been said, 'art' is personal. What looks good to one person is awful to another - I wouldnt give you tuppence for anything of Tracy Emins for example but others are happy to pay _alot_ more than that for some of her pieces.

As to why some things look good or 'right' could be considered subjective but again I am going to come at it from an evolutionary perspective (I am a scientist - indulge me!). The human brain is extremely good at pattern recognition. Awesomely good in fact. Its a definite survival trait to be able to be able to recognise a predator or prey as early as possible. We have evolved to know instantly what looks right and what looks wrong. So have alot of other species, its not a human uniqueness. 

Humans are, to my knowledge, the only species to have 'invented' or 'created' art however. (giving an ape a paintbrush does not count - its artificial. If apes piled leaves into pleasing patterns in the jungle then that would be art by my definition). We have enough free time to be able to indulge in the making of patterns, shapes, designs that appear nice. Someone mentioned earlier that symmetry plays a large part in this. Studies have shown that faces percieved as beautiful are more symmetrical than those that are not. Indeed body symmetry can be associated with fitness since having 4 legs the same length makes running faster for example. Thus symmetry, or looking right, is something we have evolved to recognise and seek out.

This same principle can be applied to the golden ratio. It is a recurring fractional ratio so maximises space and efficiency for things like leaves spiralling round a stem for example. The spacing of them conforms to the golden ratio to expose maximal sunlight to every leaf. Any other arrangement is less maximal and thus is at an evolutionary disadvantage. I dont know but would postulate that the same applies to levers and fulcrums and the body. Any other ratio would require more effort for the same amout of work and therefore put the individual at a selective disadvantage. This equates to fitness for purpose and is something that humans have evolved to recognise as a good trait - something to go for in a breeding partner (symmetry = beauty).

Humans therefore have an evolved ability to recognise what looks 'right' be it symmetry in art, ratios in design or an abstract concept such as beauty in a mate. This alone would tend to increase such features in the art around us.

The flip side is discordance of harmony. Things which do not conform to such principles and have a beauty of their own because of this lack of conformity. A good example is music. Mozart is generally considered to be a genius, unsurpassable for his musical talents. Much of his music is melodic, underscored by a regular tempo and just sounds 'right'. You could almost predict the next note in a sequence. Typically no note is discordant or jarring. His music almost has, if not symmetry then regularity (or a regular melody) to it. Compare him to a modern classical composer - Philip Glass for example. Both produce classical music but to completely different criteria, which some people like and others do not. It is the discordancy or absence of symmetry (in the case of music, melody) which makes it attractive to some. The vast majority prefer melody to discordancy, symmetry to unsymmetrical.

It is of course very difficult if not impossible to ascribe a single cause to an abstract concept such as design. Why something looks right, and there will always be a spectrum of opinion. I have postulated here that it is a function of pattern recognition borne from evolutionary survival and breeding instincts, others will no doubt think thats a load of tosh :wink: I would be interested to hear alternative theories as to why something looks pleasing if this sounds like tosh to you.

Cheers,

Steve.


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## Gill (26 Jun 2007)

Pattern recognition is a strange creature. I quite agree with you Steve, that it's a very powerful ability and one which appears to give mankind an adaptive advantage. Yet Alan's valid observation that colours also play a part is equally valid. Colours can sometimes override the pattern - just look at a Jackson Pollock painting and see how he uses colours to create three dimensional effects.

I'm currently reading Dr Betty Edwards' _Drawing On The Right Side Of The Brain_ which gives fascinating insights into how we perceive the world around us. Research indicates that the different hemispheres of the brain have different functions and we spend most of our time using the dominant left side of the brain which interprets symbols such as words and basic shapes. It's more logical than the recessive right side of the brain which looks for those things we find hard to describe in words such as spacial relationships. After all, if we try to use words to describe what we're seeing, we're using the left side of the brain - and that doesn't understand whatever the right side of the brain is considering.

Dr Edwards says that learning to use the right side of the brain is vital in perceiving the world accurately. Think about a simple drawing of a man - a stick figure. We would see one of those on paper and instantly recognise it as a representation of a man because the pencil strokes symbolically represent the torso, head and limbs. Yet you'll never see Mr Stick Man walking down the street :lol: ! It's an example of how we use the left hand side of the brain to draw with symbols. Our brain will continue to operate through its dominant left side as we draw and continue to use symbols which represent our learned concept of reality rather than the reality which is presented to us. That's why so many people think they can't draw - they work with the left side of the brain and take its symbolism as far as it can go in their drawings. Then the right side of the brain chips in and says, "That's not what I'm seeing", so people end up believing that they can't draw.

The Golden Ratio is a funny old creature. It isn't precisely measurable, so the left side of the brain has difficulty coping with it. However, the right side of the brain can recognise it. I suspect that working with the Golden Ratio can actually exercise your right brain activity and develop your art skills.

By the same token, colours can't be articulated very easily but they can be recognised as being harmonious or otherwise.

Gill


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## StevieB (26 Jun 2007)

Hmm, having done a quick google image search I am afraid that I wouldn't give you tuppence for a Pollock either - Sorry! :lol: 

I wouldn't say colour over-rides pattern recognition, I would argue it is part of pattern recognition. If it wasn't then predators and prey would not use camoflage to hide. If you were no less likely to spot a purple lion than a beige lion then not all lions would be beige. (I am not saying they would be purple, just that there would be no selective advantage for the lion to being beige).

Regarding your analogy of a stick man - would a child who has not seen one before instantly recognise it as a stick man? ie have we learned to associate the picture with the true form or are we truly making a leap of intuition. This is still pattern recognition - the closest thing to the stick man is the human form. As another example I remember seeing an experiment (on one of Robert Winstons programmes I think) where they showed a picture of a lemur to a baby. The child was interested. They showed it another lemur - to adults it was identical, we couldn't distinguish between them. To the baby it was different and the differences were apparent. The brain 'learns' that differentiating between lemurs is not important, so loses the ability. Differentiating between human faces is a skill that is retained however. The brain is the only organ that can remodel itself dependent on its environment, ie the patterns it is exposed to. A truly fascinating and complex organ.

Steve.


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## Gill (26 Jun 2007)

A very young child would probably not recognise the stick man as representing a man because that child won't have yet learned how easy symbols can make our lives. It's as we grow older that we look for short cuts and learn the value of symbols. In fact, we come to depend on them so heavily that we sometimes perceive the world around us in terms of symbols even when those symbols don't depict reality accurately.

If you look at a very young child's drawing, it is often better composed than drawings by older children. That child may not have the hand-eye co-ordination to produce something truly impressive, but the elements in the drawing will have better proportions and be less stylised than the drawings of older children. Young children try to draw what they see rather than what they have learned to see.

Gill


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## StevieB (26 Jun 2007)

I agree there - I dont think young children will recognise a stick man. Young children tend to draw humans to a very strict hierarchy depending on their development (indeed one of the developmental checks is the drawing of a human). They tend to start with a head that has arms and legs, as they develop a round body gets added, then hands and feet and finally facial features such as eyebrows ears and teeth. Children do not tend to draw stick men as a symbol of a human at all. That is why I wondered if they were using a symbol as a self taught shortcut or rather were exposed to the idea of a stickman from an outside influence and adopted it as a visual shortcut. I favour the second, adaptive response rather than the former innate response.

What this means is that pattern recognition can be taught, and that one can 'learn' to appreciate a form, or lack of it, as something to aspire to. As a consequence we all appreciate different forms of art / design / structure as a consequence of both our evolved preferences (symmetry = beauty outlined above) and our environmental exposure. After all if we all liked the same thing we would all be churning out identical pieces and complementing each other on the conformity of our designs!

What was this thread started on again...  

Steve


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## Nick W (26 Jun 2007)

StevieB":rknfffnw said:


> A good example is music. Mozart is generally considered to be a genius, unsurpassable for his musical talents. Much of his music is melodic, underscored by a regular tempo and just sounds 'right'.



Interseting choice of example there, which I think illustrates what is learned quite well. To his contemporaries quite a lot of what Mozart did was new, and extraordinary, rule breaking even; but because we have all heard it so much we can indeed predict what is going to happen remarkably well, even in a piece of his that we may have not have heard before.

As a singer, when working on music by a composer that I have not come across before, I have to work quite hard to read the music and get it right initially. (Luckily I am, as a Japanese applicant to one of our summer schools once said, very good at sightseeing.) After a while though, I get used to the idiom, and can start to predict what is going to happen, I have learned that composer's language.

The same happens with the graphic arts, the more you look at Pollocks, the more you get to understand the language, and the more you can begin to say, ah yes, I see.

This is not to pooh-pooh the idea that there is an inherent sense of good taste as well. I'm just not sure of which is dominant - if either.


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