# Some stools and Fibonacci numbers



## Dimitri M (Oct 4, 2011)

Elementary stools and benches have always attracted me for their simple lines, multiple uses and time-honored style ("styles fade, style never does" somebody wrote a long time ago). As they need very little skill and accuracy is not mandatory, they immediately became my favorite construction item.

Some of their dimensions are defined by practicality - for example, a height of 45 cm is useful because the stool can be used as an extra seat at a dining table or as a side table next to a comfortable sofa; it is also comfortable for a seated person to stretch his legs on, so no doubt I will use 45 cm as a height. What about the rest of the dimensions? Is 5 or 7 cm a good width between the leg and the edge of the surface?

To provide ready answers to these problems, I decided to use Fibonacci numbers wherever possible. These numbers are a series in which every number is the sum of the previous two. Here is the first part of the series, useful for my woodwork:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233
It is beyond the scope of this forum to analyse the particularities of this number series, I just want to mention that the series includes the numbers 5 and 8, believed to be the elements of "golden analogy" (proportion) by the ancient Greeks, and said to give "aesthetic" results, i.e things that look beautiful.

So, the surface width of the top will be 34, the length 55, the distance of leg from the edge 5, etc.

Is the result beautiful? "Beauty lies in the eye of the beholder" says an old proverb. Here are some of my results (you can see some other stools and benches as well as my dowelling techniques in my other threads posted earlier).

The material I use is cypress. I always like to keep the natural edges - even woodworm holes play their part in the final picture. Any questions and comments are welcome.

I have been silent for a long time due to health problems - hopefully I am back for good - I hope I have solved them efficiently.

Thank you all for your time and kindness.


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## jw2170 (Jan 24, 2008)

Hi Dimitri, I trust your health is on the improve.

You did a great job with those stools.

I have been fascinated by the "golden ratio" for a while now and find it amazing of how often the ratio [1.6180339887....] occurs in nature.


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## Dimitri M (Oct 4, 2011)

Hi James, thank you for your kind remarks. It is fascinating to note that any Fibonacci number divided by its preceding number does not give the same ratio, but it is always near 1.6. 

In the end, I hope this quick "idea offer" everytime I need to choose a dimension, it will result in a nice object.

Best wishes


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## harrysin (Jan 15, 2007)

Welcome back my friend, it's been a while. I'm pleased that you have regained your health. The stool, what can I say, it's just beautiful. The "golden rule has withstood the test of time.


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## Dimitri M (Oct 4, 2011)

Thank you Harry, I am very happy to see your remarks. Hopefully I have got a fruitful year in front of me; I just got an "order" (this time from my son who lives in the UK) for a coffee table and two narrow stools under it, that will serve as side tables or extra seats when needed. I am just waiting for one more month and then I will be able to lift heavy planks and saw them.

All the best

D


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## harrysin (Jan 15, 2007)

Take it easy Dimitri, I hardly need to remind a surgeon that hernias can burst.


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## cagenuts (May 8, 2010)

jw2170 said:


> I have been fascinated by the "golden ratio" for a while now and find it amazing of how often the ratio [1.6180339887....] occurs in nature.


Bit like if you don't comment on your wife's hair in the morning you have 1.6180339887% chance of getting lucky in the evening.

Nature, bless it's soul.


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## jw2170 (Jan 24, 2008)

cagenuts said:


> Bit like if you don't comment on your wife's hair in the morning you have 1.6180339887% chance of getting lucky in the evening.
> 
> Nature, bless it's soul.


Spot on, Hilton


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## Cherryville Chuck (Sep 28, 2010)

Excellent job Dimitri and good to see you back. A very well balanced design that is very pleasing to the eye. The ancient Egyptians were absolutely obsessed with the golden proportion and they built the pyramids and knew the true length of a day to 4 decimal points thousands of years ago.


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## Gene Howe (Jul 10, 2007)

Very nice stools/benches Dimitri. 
It's good to see your posts again. I too, hope you are back for good. 
A loooong time ago, in college, I applied the principle to a life sized picture of the face of Michelangelo's David. It was applicable in every respect. Being totally uninformed of such arcane things (I was a VERY naive farm boy) I was amazed and thought I had made a great discovery. When I discussed my wonderful findings with the art professor, she (bless her soul) listened with great interest as if she had never heard of such a thing. Then she casually suggested that maybe I should apply my wonderful discovery to other things, like maybe a picture of the Parthenon. I did, and ...well you can guess the rest.


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## jw2170 (Jan 24, 2008)

Gene, it sounds like you had a great teacher.

Not to give you the answer, but to show you how to find the answer.


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## Dimitri M (Oct 4, 2011)

Gene, thank you for your remarks, I really like such remarks, only I must say that in my life I found no relation between the study of ancient art and modern appliances.
When I came to design my own "furniture", as I do not use ready cut timber (in Greece there is no std 2 x 4" wood for example, and all equivalents are "approximately", so in order to make something I need to start by converting the proposed measures to realistic ones, and finally I buy planks and cut my own, which then means I make my own plans in advance. Exactly there, I needed to choose several arbitrary distances, and the Fibonacci series gave me a readily available range of measures. This is why I mentioned these here, because finally I find the results really pleasing to the eye.
Thank you for mentioning your encounters with classical art - we very often stay away from it because we consider it too huge for our grasp, but in many ways it can help with little things as well.


Charles, thank you for your comments. It is true that the Egyptians knew a lot about the golden ratio, I must only say that WE don't know about it enough to use it in our everyday life.

Thanks to all for your wishes

D


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## cagenuts (May 8, 2010)

Dimitri M said:


> It is true that the Egyptians knew a lot about the golden ratio, I must only say that WE don't know about it enough to use it in our everyday life.


They also divided the day up into 24 hours using the 12 finger knuckles of each hand instead of the standard 10 digits (literally).

Oh and of course we mustn't forget that really cool dance..........


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## curiousgeorge (Nov 6, 2006)

Welcome back, Dimitri. Very nice job on the bench/stool. As we say here in Texas; "Beauty is in the eye of the beer holder". Here is a link to a post I made back in 2007 relating to a Fibonacci gauge I made that might interest you. Hope your health steadily improves and your future is full of woodworking to your hearts content.


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## IRONMULE31014 (Feb 16, 2013)

Welcome ,Dimitri the stool looks great,but doing things with numbers like that makes my head hurt.


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## Dimitri M (Oct 4, 2011)

George, the remark with the "sprained" proverb is VERY clever, thank you. I find the 
Fibonacci gauge very interesting, will study it a bit better tonight, and remark on it.

David, you don't need boggling number games here - just a list to choose - I don't apply the ratios hewre, JUST CHOOSE numbers as needed from this list. That is why I mention it here.

Hilton, pardon me for asking, but as an Orthopaedic surgeon, I find very mysterious your comments about the Egyptians counting 12 knuckles? How do they find 12 knuckles in 10 fingers? Do they add the bunions as well ??? !!!


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## cagenuts (May 8, 2010)

Dimitri M said:


> Hilton, pardon me for asking, but as an Orthopaedic surgeon, I find very mysterious your comments about the Egyptians counting 12 knuckles? How do they find 12 knuckles in 10 fingers? Do they add the bunions as well ??? !!!


I was referring to the two (2) Interphalangeal Joints and one (1) Metacarpophalangeal Joint per finger.

So excluding the thumbs, there would be 12 joints (knuckles) per hand.

2 hands = 24 hours.

I'm at the extent of my anatomical knowledge here so please correct me accordingly.


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## Dimitri M (Oct 4, 2011)

Thank you, Hilton ! I did not have a clue about that - and of course, all time calculations are very complicated, even today. We see this everytime we need to teach a young child how to read the clock, and then again later in adolescence: it is hard to read that immediaterly after 29 past, comes half past, then 29 to, etc. and later this becomes 18:34, 14:03 or 8:00 pm etc.

The story here is that I never think of ratios - I only choose measures from the list when I don't need to apply something for necessity reasons, eg the height of a seat.

Well, to cut the philosophy short, here is another example of a stool: length 55, height 34 (shorter than the previous at 45 cm) and width 21. Although it looks awkward, it fits very well as a side table next to an arm chair, and it is a cosy little stool to sit on next to the fireplace.

Comments and criticism welcome


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## cagenuts (May 8, 2010)

Dimitri, that's a fine looking stool. I suspect though that the joinery would have been infinitely easier and quicker with pocket holes as opposed to dowels. If you don't have a pocket hole jig or don't want to use that form of joinery then I guess my statement should be ignored.

I've always thought of dowel joinery as being quite awkward but I have to confess I've never given it a proper go.

You make it look easy though.

<grumpy rant>
On the time issue, my biggest bug bear is when people refer to time as 12:00 am or 12:00 pm. If you think about it carefully, it refers to the same part of the day (midnight), just 24 hours difference (last night and tonight or tonight and tomorrow night but never noon).

We should rather just say 12 noon or 12 midnight.

</grumpy rant>


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## papasombre (Sep 22, 2011)

Hi, Dimitri.

Very nice stool. I like the wood´s natural appeal and its dimensions.

It´s very good to have you back. Good look with your "new order"


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## greenacres2 (Dec 23, 2011)

Thanks Dimitri. I've done several calculations, and the Fibonacci ratio has not varied by more than 1/1000--close enough for me!! Beautiful work.

Also--i appreciate what you do with the live edge. Always seems a shame to me to see how much lumber i waste to get to square. Helping me dream in curves!!

earl


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## Dimitri M (Oct 4, 2011)

Hilton, friend, thank you for your comments; pocket screws are not something I know, for a number of reasons, among them being (a) the lack of specific screws from our market here (b) no jig in the market here either. Deeper down, I tend to leave screws out of woodwork as much a possible - it is a very long story, starting with the first furniture I made which was my marriage bed (1978), mahogany, knock-down, all sides area used for four gigantic drawers, held with 622 screws, 2/3 of which were brass- it seems I screwed too many then, and disliked them since !

I managed to make dowel joinery simple and accurate - at least for me. Have a look at my threads:

http://www.routerforums.com/jigs-fixtures/38153-dowel-joints-using-router.html

http://www.routerforums.com/project-plans-how/32176-wardrobe-closet-shoes-3.html#post313168

As I said many times before, an amateur has the benefit of "licking" a piece of wood for ever, while a professional has to finish it as fast and as cheap as possible, to deliver it and take the money for it; my methods need to be neither easy nor fast not appealing to the customers, so I chose dowels and work mainly with them - if anything, I find them strong and efficient.

Hypothetical expressions about time remind me of a colleague gone a longtime ago; if he was in a humorous mood, and someone asked him the time, he would answer with such a long sentence that would drive anyone crazy " Well, it is 7:02 pm, that is evening, not just past midday, but with the time saving policy now we call it 7:02, but it actually is 6:02, that is not so much evening, very late afternoon I would say, etc, etc..."
He used to drive everyone crazy with these eternal calculating sentences. since then, I keep the timesentece short - whatever the format !

Alexis,from Venezuela, thank you for your welcome. I envy the wonderful tropical woods you must have there and we don't even know their names here. I don't understand, what "new order?"

Earl, thank you for your comments, I haven't heard from you for a long time.

The free edge has proved to be very appealing, as the smooth curves remind us of much-used items, where the smooth curves were obtained via long use by hand - I can't explain it in any other way. If you remind me with a message I wil ltake several photos of a kitchen side-table I made 3 years ago, where not only the free edges,but also the woodworm marks on it play an important aesthetic role. Plus, to mention, a lot of the wood I use came out of the woodmill as scrap because it was too near the edges.

Best wishes to all and many thanks

D


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## greenacres2 (Dec 23, 2011)

Dimitri M said:


> The free edge has proved to be very appealing, as the smooth curves remind us of much-used items, where the smooth curves were obtained via long use by hand - I can't explain it in any other way. If you remind me with a message I wil ltake several photos of a kitchen side-table I made 3 years ago, where not only the free edges,but also the woodworm marks on it play an important aesthetic role. Plus, to mention, a lot of the wood I use came out of the woodmill as scrap because it was too near the edges.
> 
> D


Ah, Dimitri...i'm learning to appreciate that!! On April 15 we will complete 20 years of living in our old farm house. The first summer we were here, there was much work done, including a fresh railing and newel post on the upstairs landing, and a complete remodel of the kitchen. I've been noting signs of wear, and a need to freshen things up a bit.

A few months ago my younger son, now 24, was home from the US Air Force and commented on how smooth the large knob had become on the newel at the top of the stairs--how it felt good in his hand as he headed to his bedroom. His older brother commented on how he puts his hand in the same worn spot on the back door molding that i put mine to balance as i remove my shoes and boots. Suddenly the stained and worn wood was a great source of peace, and home.

Recently, i built a long, narrow table for my wife to put under a bedroom window. When i ripped the ash (locally harvested--another long story) for the apron, there was a worm spot right in the center that my bride refers to as her "Angel". It's subtle, and was hard to photograph, but perhaps you can see her as well.


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## Dimitri M (Oct 4, 2011)

Earl, in all sincerity, such a worm mark will only deter a customer from your product-for-sale. As long as there is no customer, and you deduce that the surface underneath is not destroyed, and all worms are dead for sure, you leave it as it is. Sometimes I fill them with a mix of sawdust, glue and dark brown acrylic color, you can see them on the surface of the stool at the beginning of this thread.

Touch is an essential sense, developing earlier than vision, from the early stages inside the womb. Smell is also dominant especially for childhood memories, and because of that you see many children attached to an old wornout piece of blanket, which theye stick to their nose all day. So, touching the old wornout bit, actually caressing it, is a reassurance that everything is smooth and familiar.

Over the weekend I hope I will find some time to photograph a few things for you, among them an old bullet embedded on the surface of one of the bookshelves I have made.

Back to work now, best wishes.

D


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## ggom20 (Feb 1, 2012)

Hello dimitri !
Glad to see you are back!
Nice works!
If you just getting better, i' ll suggest not go to fast on heavy jobs , 
you might get one helper/ apprentice for heavy planks.

It' s a good thing to share knowledge, beeing an apprentice is learning
directly from ages ago.

Golden number is real usefull to me in designing overall, global aspect of things.
I'll never make a plan without checking this.
There are some interesting variants, i'll post them soon.
Got to scan some pictures.

Regards.
Gérard
Regards


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## Dimitri M (Oct 4, 2011)

Bonjour, Gerard!

Thank you very much for remembering me, and for your kind remarks about my health and heavy planks. I just change the order of carrying out various tasks until enough time passes for me to heal. As for an apprentice, I am totally disappointed with what I found. Local Greek youth do not want this kind of apprenticeship as I do not teach how to make kitchen cupboards overnight, then charge an arm and a leg for the cupboards, so they can go and buy a BMW the next day, so I am not a good teacher for them. On the other hand I have an Albanian who comes for the garden now and then, but he is totally ignorant in the workshop, and I am very worried about him running the radial saw over his fingers - he thinks that now I can show him something, the next minute he thinks he can do it by himself, so I can't do something else because I need to babysit for him, plus he wants his regular hourly pay - so it is not a good idea for me, lots of anxiety, 1 - 2 broken jigsaw blades, so I gave it up! For such cases we say "if you can put a tape measure in your pocket, automatically you are a master of the art" !

I am getting better all the time, I am finishing the polish for the shoe closet (in another thread here) and then started cut - and - glue a coffee table for my son, and eventually the big trestle dining table I mentioned in a thread (trestle table and benches), started 2 years ago, (233 x 89) will have to wait 1 - 2 months more as the table top is only made of two planks 5 cm thick and they are very heavy to work with for now.

See you around !!

D


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## jw2170 (Jan 24, 2008)

Hi Dimitri,

I suspect that you are a very caring person, but I am very concerned with you letting your gardener in the shop to play with your machinery. Especially as he is an employed person.

If he were to injure himself, you could be in great trouble.


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## Dimitri M (Oct 4, 2011)

Hi James, thank you for your advice, you are very right and I must clear a point here:

The story with the garden fellow is very short, I asked him to give me a hand with a few things I could not do after my operation, he thought this would automatically turn him to a carpenter, and I did not repeat the experiment, fearing not only the legislation problems, but also that if he injured himself I would have to stop the carpentry and take him to hospital, operate on him and keep him under my care, which would be an extra psychological burden on top of all others. I must also point that although the law is clear inGreece as well, it is not as scalding as in the USA. And finally, being an amateur I do not make any money out of my woodwork, I only pour money into it, so I keep the "business" to myself.

To laugh a bit, I was asked by a colleague of mine to make two benches for him, like the one pictured in another thread here, 
http://www.routerforums.com/project-plans-how/37491-trestle-table-benches.html
and he would like to pay for them, so I said I would have to charge as a surgeon and not as a carpenter, so he answered he couldn't say which was more expensive nowadays!!

best wishes

D


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## ggom20 (Feb 1, 2012)

*Fibonacci numbers and geometrical suite based on PHI*

Hello!

Never used this Fabonacci suite for practical things , looked at it as part of the golden number various aspects and mysteries.
Whent trout fishing, and did my gardening , so did'nt had much time for maths.

But a little:

At a reasonably hight level in fabonacci suite of numbers
the ratio between two numbers is very close to the golden number.

At beggining of fabonacci suite of numbers its not so close to it and 
variates, one time, ratio is too big , then too small.

Practical calculations:



fab. number ratio comment objective is 6.18.....

1 ?
1 1 lower 39%
2 2 Higher 24%
3 1.5 Lower 7.8 %
5 1.66 Higher 2.53 %
8 1.60 lower ..
13 1.62 Higher ...
21 1.615 lower ..
34 1.619 Higher but close enought 6/10 000 error.
55 1.6176 Lower But close enought 2/ 10 000 error.


The biggest the numbers, seems the ratio coming closest to the golden number.

So using fibonacci numbers is a bit like using numbers in a geometric
suite based on the golden number. (PHI)

Like if your first measure is 1 =1
the secund wiil be 1 * (phi) = 1 * 1.618 =1.618
The third will be 1* (phi)*(phi)= 1* 1.618* 1.618 = 2.618
the fourth 1* (phi)*phi)*phi)=1*1.618*1.618*1.618 =4.236


the general expression is

x = your starting measure one inch , one foot, one specific unit like 32mm
phi= 1.618 ( say not so different , for peace with true mathematicians)
n = order of size 
size = x * (phi) at power of n

Hope this was not too annoying ...
In fact I did never use fibonacci numbers to give sizes but only this geometrical suite.
And some variations :
There are other interesting ratios around PHI
Did make a few interesting scans of a really good book that I stiil use in printed form.

But used for years so and not easy to read now , I keep investigating in my backups to send you thoses. At whorse the used ones will be scanned again.

You also can google around for golden triangle and a lot of other figures.
golden spiral; golden triangle spiral, and so on.


I use those things, but final touch will always be yours and no math will help.
A precise fullscale drawing is very helpfull when possible.

At least a reduced one and then adjusting by drawing on real material gave me 
my best results when had time enought to spend on thoses things.

Best Regards.
Gérard


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## jw2170 (Jan 24, 2008)

> but final touch will always be yours and no math will help


Agree 100%, Gerard.

Beauty is in the eye of the beholder.


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## ggom20 (Feb 1, 2012)

Hello!

Will certainly find this CD rom backup one day.

But here is the most useful page :

A list of various variants around the golden section.
That should be printable.

Best Regards.
Gérard.


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## rout66 (Oct 19, 2011)

*Archimedean Spiral Lazy Susan Router Bit Holder*

Archimedean spiral math can be as entertaining as using Fibronacci numbers to create useful and pleasing results. Using a string and a pencil, I fabricated a lazy susan holder for some of my router bits.


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## jw2170 (Jan 24, 2008)

markm said:


> Archimedean spiral math can be as entertaining as using Fibronacci numbers to create useful and pleasing results. Using a string and a pencil, I fabricated a lazy susan holder for some of my router bits.



Welcome to the forum, Mark.


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## ggom20 (Feb 1, 2012)

*beauty is in the eye of the beholder*



jw2170 said:


> Agree 100%, Gerard.
> 
> Beauty is in the eye of the beholder.


Thanks for that James.( jw2170)
I'm using those maths , but I' m sure a lot is left to personnal creativity.

Regards.
Gérard.


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