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#### Dimitri M

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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

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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.

#### Dimitri M

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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

#### harrysin

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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.

#### Dimitri M

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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

#### harrysin

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

#### cagenuts

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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.

#### jw2170

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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

#### Cherryville Chuck

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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.

#### Gene Howe

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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.

#### jw2170

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Gene, it sounds like you had a great teacher.

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

#### Dimitri M

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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

#### cagenuts

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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..........

#### curiousgeorge

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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.

#### IRONMULE31014

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

#### Dimitri M

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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 ??? !!!

#### cagenuts

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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.

#### Dimitri M

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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.

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#### cagenuts

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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>

#### papasombre

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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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