**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**

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

-- http://foldingrule.blogspot.com

## 32 comments so far

WayneC

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12642 posts in 3564 days

#1 posted 08-05-2007 02:24 AM

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

oscorner

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4564 posts in 3777 days

#2 posted 08-05-2007 04:44 AM

That was a great article in WOOD.

-- Jesus is Lord!

Lee A. Jesberger

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6821 posts in 3446 days

#3 posted 08-05-2007 05:08 AM

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

PanamaJack

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4474 posts in 3544 days

#4 posted 08-05-2007 05:33 AM

Cool Tool David! Thanks!

-- Carpe Lignum; Tornare Lignum (Seize the wood, to Turn the wood)

knothead

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162 posts in 3415 days

#5 posted 08-05-2007 05:37 AM

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…................

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

scottb

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3648 posts in 3794 days

#6 posted 08-05-2007 06:00 AM

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.

-- I am always doing what I cannot do yet, in order to learn how to do it. - Van Gogh -- http://blanchardcreative.etsy.com -- http://snbcreative.wordpress.com/

Jeff

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1011 posts in 3560 days

#7 posted 08-05-2007 02:55 PM

Thanks for this post, David.

-- Jeff, St. Paul, MN

Thos. Angle

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4445 posts in 3429 days

#8 posted 08-05-2007 03:03 PM

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, Jordan Valley, Oregon

dennis mitchell

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3994 posts in 3781 days

#9 posted 08-05-2007 03:30 PM

great info…Thanks

furnitologist

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198 posts in 3480 days

#10 posted 08-05-2007 04:22 PM

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

Karson

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35035 posts in 3867 days

#11 posted 08-05-2007 06:04 PM

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.

-- I've been blessed with a father who liked to tinker in wood, and a wife who lets me tinker in wood. Southern Delaware soon moving to Virginia karsonwm@gmail.com †

Bill

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2579 posts in 3628 days

#12 posted 08-05-2007 06:26 PM

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

David

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1970 posts in 3605 days

#13 posted 08-05-2007 11:42 PM

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 LamensatFurnitologyfor 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

Joel Tille

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213 posts in 3711 days

#14 posted 08-06-2007 01:22 PM

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

Sawdust2

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1467 posts in 3554 days

#15 posted 08-08-2007 02:28 AM

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.

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