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Furniture Design #1: Fibonacci gauge

Blog entry by David posted 350 days ago 4020 reads 13 times favorited 23 comments Add to Favorites
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1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 – The Fibonacci Sequence

I have been fascinated with The Fibonacci Sequence and The Golden Rectangle for some time. I finally got around to building a Fibonacci Gauge that was featured in WOOD Magazine.

The guage maintains a consatnt proportion of 1:1.618 between the points. It is used to help determine visually appealing proportional dimensions. I am looking forward to using the guage in future projects.

Follow the text below for some interesting history, a fun video from WOOD Magazine demonstrating the Fibonacci Gauge, and some online resources.

This was a fun afternoon project which provided some much needed therapy and piece of mind!

MY FIBONACCI GAUGE
Constructed from thin cherry cut-offs from a prior project and finsihed with 2 coats of Tung Oil and 4 coats of lacquer. I found the solid brass binding posts in a little hardware store in Sisters, Oregon.

WHO WAS FIBONACCI?

Leonardo of Pisa, known as Fibonacci [pronounced fib-on-arch-ee], was the “greatest European mathematician of the middle ages”. His full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born about 1175 AD in Pisa (Italy), the city with the famous Leaning Tower of Pisa.. Pisa was an important commercial town in its day with links to many Mediterranean ports. Leonardo grew up with a North African education under the Moors. Later, he traveled extensively around the Mediterranean coast meeting with many merchants. He learned of their systems of doing arithmetic realizing the many advantages of the “Hindu-Arabic” system over all the others. He was one of the first people to introduce the Hindu-Arabic number system into Europe, the positional system we use today, which is based on ten digits, a decimal point and a symbol for zero.

THE FIBONACCI SEQUENCE AND ITS RELATIONSHIP TO THE GOLDEN PROPORTION

The Golden Section, also called The Golden Ratio, The Golden Mean and The Divine Proportion was discovered by the Greek mathematician Pythagoras. Later, an Athenian architect using the Golden Section in building design came up with Phi, the number 1.618. Fibonacci made the next leap when he published a book in 1202 called “Liber Abaci”. He introduced a math problem where a pair of rabbits were placed in a field with the provision that they could not escape or die. At the age of 1 month the female gives birth to 2 new rabbits (1 male, 1 female). The female rabbit does this each month for 1 year. How many rabbits would there be at the end of the year? The answer to this question contains a series of numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55…..). This series of numbers is called the Fibonacci Series. If you look at the ratio that occurs after the number 3, you will see the number 1:618, which is the Golden Ratio.

Fibonacci devised a series of proportional relations [ 1 : 1 , 1 : 2 , 2 : 3 , 3 : 5 , 5 : 8 , 8 : 13 . . . ]. If you look closely, you will see the Fibonacci Sequence. This set of ratios, arrived at by adding the 2 previous numbers together to give the next number the new series, is been used in many aspects of life from architecture, finance, biology and engineering. Nestled in the Fibonacci series are the ratios 5:8 and 8:13 which are the classic “golden section” proportions.

WHAT DOES THIS HAVE TO DO WITH WOODWORKING?

The Golden Section or Fibonacci Numbers can be used to derive pleasing dimensions for any piece of furniture. For example, you have been commissioned to build a table for a client. You decide to use the Golden Rule to help determine construction dimensions that will be pleasing to the eye. The client requires the top to be 20 inches deep. To make the top into a Golden Rectangle, multiply 20 by 1.618 – the result is 32.36 inches. Rounding this to 32.5 yields a Golden rectangle measuring 20 inches x 32.5 inches. Interestingly, if you draw a square within your Golden Rectangle, the remaining rectangle will also be a Golden Rectangle. This principle can be used to scale all the other elements of the table. Ultimately, common sense and your eye should rule over the Golden Section. The Golden Section is a tool that you bring to the bench much like a finely tuned plane, razor sharp chisel or that special dovetail saw.

Construction of a Golden Rectangle
1. Construct a unit square.
2. Draw a line from the midpoint of one side to an opposite corner.
3. Use that line as the radius to draw an arc that defines the long dimension of the rectangle.

Some Interesting Online Fibonacci Resources

Fibonacci Gauge and How to Use It Woodworking Plan
Featured in the November 2006 issue

YouTube - WOOD Magazine Fibonacci Gauge Demo

The Golden Mean Gauge

The Golden Number Grid

Fibonacci Numbers and The Golden Section in Art, Architecture and Music

-- http://foldingrule.blogspot.com

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David

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View WayneC's profile

WayneC

5690 posts in 499 days


posted 350 days ago

Very informative post David. Thanks for taking the time to pull all this together. Glad to see you got some free time.

-- We must guard our enthusiasm as we would our life - James Krenov

View oscorner's profile

oscorner

4576 posts in 713 days


posted 350 days ago

That was a great article in WOOD.

-- Jesus is Lord!

View Lee A. Jesberger's profile

Lee A. Jesberger

2170 posts in 382 days


posted 350 days ago

David;

You did a big service to all woodworkers, by coming up with this, and publishind yor article.

Fibonacci series of numbers are consulted prior to us building anything.

Chippendale’s feelings on proportions were a man can’t be a cabinet maker without a complete understanding of proportions. Sheridan and Hepplewhite had similar convictions about it.

Many things in nature are directly related to the Fibonacci numbers, in addition to the example with the rabbits.

Your own arm is based on those same proportions: Part A: hand , Part B: hand and forearm (to elbow)
Part C: entire arm, from fingers to armpit

A is to B, what AB is to C.

Amazing stuff.

Lee

-- by Lee A. Jesberger http://www.prowoodworkingtips.com http://www.ezee-feed.com

View PanamaJack's profile

PanamaJack

4453 posts in 480 days


posted 350 days ago

Cool Tool David! Thanks!

-- Carpe Lignum - Seize The Wood,

View knothead's profile

knothead

29 posts in 350 days


posted 350 days ago

The Guy in the video is Jeff Mertz from WOOD Magazine – which happens to be right here where I live – he came to our woodworkers association meeting last fall and gave that very presentation – he is a wonderfull guy to know and was very informative Alot of the woodworking magazines that are out there originate right here so I have the luxury of attending the Woodsmith Seminars and the Shopnotes presentations ect ect.

So Much to learn…................

-- Chris --- So Much Wood - So Little Time!

View scottb's profile

scottb

2772 posts in 729 days


posted 350 days ago

It can be very hard to convey that information in a way that doesn’t quickly go over peoples heads. I understand the geometry of it, as well as how they discovered this ratio almost everywhere in nature… great set of resources and information you pulled together for us. Despite a fundamental understanding of the numbers, I can still get lost in the math of figuring out dimensions… this was very consice. Nice.

-- The opposite of war isn't peace. It's creation. -- Wood T's: http://www.printfection.com/snbcreative

View Jeff's profile

Jeff

943 posts in 496 days


posted 350 days ago

Thanks for this post, David.

-- Jeff, St. Paul, MN

View Thos. Angle's profile

Thos. Angle

3243 posts in 364 days


posted 350 days ago

Good work David. The more we learn about design it seems the more there is to learn. I started studying art in high school at the age of fifteen and it seems i still learn more every day. I was lucky to be taught the Golden Mean by an art teacher before the days of “do your own thing”.

-- Thos. Angle, Owyhee Design, Oregon

View dennis mitchell's profile

dennis mitchell

2822 posts in 717 days


posted 350 days ago

great info…Thanks

-- http://www.woodsongsfurniture.com

View furnitologist's profile

furnitologist

166 posts in 415 days


posted 350 days ago

He’s Baaaaack!!!!!..................and I’m glad.

Hey David:

Like Scottb above….........I seem to get lost in the mathematics during a total design, never fully use my “pisano”...Leonardo of Pisa, but he’s always there and shows up at the start.

Love the history…....thanks, and your wording of bringing it to the bench:

Ultimately, common sense and your eye should rule over the Golden Section. The Golden Section is a tool that you bring to the bench much like a finely tuned plane, razor sharp chisel or that special dovetail saw.

Thanks David very, very well done….........Neil


View Karson's profile

Karson

11924 posts in 803 days


posted 350 days ago

Lee:

You can go a little further back on the arm. The end of the finger to the first loint as to the second joint.

And the first – second joint to the end of the finger joint. Then that joint to the wrist.

David thanks for bringing up the wood article and showing it made.

-- Karson Southern Delaware karson_morrison@bigfoot.com

View Bill's profile

Bill

2508 posts in 563 days


posted 350 days ago

Nice job David. All the information in a single place. A nice history lesson, as well as a great application by creating the gauge.

Have you tried it out yet on any projects? How has it worked out for you?

-- Bill, Turlock California, http://www.brookswoodworks.com

View David's profile

David

1801 posts in 541 days


posted 349 days ago

Thanks for all the kind comments.

This has been on my “to do list” for a while so it was very satisfing to complete the Fibonacci Gauge. I am looking forward to using it in the design process for future projects. I have a fascination for the beauty and proportion found in nature and how this concept can be found at so many levels.

I have to give credit to Neil Lamens at Furnitology for simulating my interset in furniture design. Prior to exploring his website, subsequently other online resources and books on furniture design, I looked at each project as a project and did not fully appreciate the design elements and proportion.

-- http://foldingrule.blogspot.com

View Joel Tille's profile

Joel Tille

200 posts in 646 days


posted 349 days ago

Thanks David, I had read this article and set it aside, thinking of making it later. Then I tried to find it, problem was I thought I had read it in a Woodsmith magazine. Now I can go back and find the article and build it.

-- Joel Tille

View Sawdust2's profile

Sawdust2

802 posts in 490 days


posted 347 days ago

My Wednesday nite group decided to make these. We were going to end up making 3 each so I found a source to get all the screw posts for everyone for less than Wood was charging for 4 kits.
WSe had a great time making them. Only 2 were accurate.
YOu have to be very close on the holes to have it work correctly.

-- No piece is cut too short. It was meant for a smaller project.

View David's profile

David

1801 posts in 541 days


posted 347 days ago

Thanks everyone for the comments . . .

Xavier – you are absolutely correct that the holes and alignment need to be accurate for the gauge to work correctly. You can always do the math, however, I really like the idea of the gauge and the feel of the wood in my hands. The whole concept of the divine proportion is very intriguing.

Chris – I do sincerely hope that Jeff Mertz from WOOD Magazine will not mind the reference and inclusion of his video. The article really struck a chord with me and this is my way of paying homage.

-- http://foldingrule.blogspot.com

View mot's profile

mot

4830 posts in 439 days


posted 343 days ago

David,

Excellent writeup. Thanks for taking the time to provide the info for this. I think I have a place on my wall to hang one. I read that article in Wood with great interest and added it as #258 on my list of things to do.

Cheers!

-- You can discover more about a person in an hour of play than in a year of conversation. (Plato)

View Lee A. Jesberger's profile

Lee A. Jesberger

2170 posts in 382 days


posted 327 days ago

I failed to mention a mentor of mine, who has recently passed away. His name was Jefferson Clark, and he taught design at Drexel University in Philadelphia, PA, in addition to operating a design company.

It is largely at his doing that I became aware of and a student of proportion. As a general contractor, I was priviledged to work with Jeff for close to twenty years, and I was always amazed at his abilities. He could casually walk through a four story building, and after returning to his office, draw the building in remarkable detail, with surprising accuracy, including where the existing furniture was!

He had a way of teaching in a gentle fashion, which rather than raising the ire in someone, would inspire one to reach for a higher level of knowledge of their craft.

He and I spent many an hour researching proportions found in and around the Philadelphia area. This area is steeped in historic buildings, many still remaining form the 18th century. We visited buildings frequented by President Washington, and actually saw a bullet hole in a plaster wall, from a battle on Germantown Avenue, fired by the American army, lead by General Washinton, in the revolutionary war!

Even in his early seventies, with him carrying an oxygen tank, I would make it a point to take him on these outings, and he would insist I drive my corvette, even though he could barely get in and out of the car. I would have to push him aroung in a wheel chair, yet we had a great time. We would go to the Philadelphia Museum of Art and inspect the 18th century american furniture, for which I have an extreme amount of interest in. Their skills, attention to detail, methods of using the divine proportions to arrive at their designs, and conditions in which they worked, astounds me. I feel my abilities are childish in comparison to theirs.

Anyway, I just wanted to mention my friend Jeff, who was largely responsible for my apreciation and awareness of design. Without his guidence, my work would still be lacking in many ways.

Lee

-- by Lee A. Jesberger http://www.prowoodworkingtips.com http://www.ezee-feed.com

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MsDebbieP

11018 posts in 563 days


posted 325 days ago

sounds like a wonderful man and someone’s footsteps to follow in.

-- "Functional WoodArt" by Debbie, Canada (http://www.execulink.com/~yohan)

View David's profile

David

1801 posts in 541 days


posted 317 days ago

Lee -

Very busy summer so a bit late responding! Your friend Jeff sounds like a wonderful man. We have had a number of visits to Viginia and D.C. – my son is fascinated with history, The Revolutionary War and The Civil War. We both enjoyed all the mystery and rich history. I appreciate you sharing this story. Next time we are in the area we will call in advance and try to arrange a short visit.

-- http://foldingrule.blogspot.com

View Richard Williams's profile

Richard Williams

57 posts in 194 days


posted 91 days ago

This one has come up on me in my educational career a few times in my retirment years. You have spiked my interest in this intriguing formula sequence and I am forced now as curiosity has killed more cats, to partake in an investigation of it. I’ve even seen it done in class on the board and it was very interesting back then. There simply is not enough hours in my day. Great expose’ on this.

-- Rich, Nevada,

View David's profile

David

1801 posts in 541 days


posted 91 days ago

Rich -

Thanks for looking! I am fascinated with the Fibonacci Sequence and The Divine Proportion. I use this whenever I can in the shop.

David

-- http://foldingrule.blogspot.com

View Grumpy's profile

Grumpy

4025 posts in 253 days


posted 91 days ago

David, I just found your blog through Karsons blog http://lumberjocks.com/jocks/Karson/blog/4353. a most interesting appreciation of proportion. Thanks for sharing.

-- Grumpy - "Always look on the bright side of life"- Monty Python

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