The golden Mean or Golden Ratio is a number that people use when making items, buildings and furniture, They are determined a couple of different ways.

The number is used to determine proportions between pieces of the item being constructed.

One of the easiest to remember is to take 1 and 1 and then to add two consecutive numbers to get the next. The numbers in sequence are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc. This might work if you were making something 89” tall and the width would be 55” wide.

A different way of calculating the number is take a calculator that has a square root function. Your computer has one. Enter any number 89, 22222, -45, .24876 etc. Take the square root of that number, add 1, take the square root again, add 1 take the square root again. Keep this up until the square root number never changes. You will get a number like this 1.6180339887498948482045868343656. If I add 1 to this number and do the square root again I get the same number.

You can take this number and multiply or divide it by a measurement and calculate the other one.

For example a box with a height of 4” the width on the side would be 4 X 1.618 = 6.472 your width of the end should be 6.472 or 6.5 inches. The top would then be 6.5 X 1.618 = 10.517. So the box dimensions would be 10.5” wide, 6.5” deep and 4” high.

For the bookcase that I was designing for the Challenge04, I estimated the height to be 54” high and 40” wide. Lets see how this would calculate out 54” divided by 1.618 = 33.37 or 33 3/8” But I was planning to put legs on it and I estimated them to be 10” for an overall case size 64”. Lets determine the width now.

64 / 1.618 = 39.555. That is within the range that I was wanting to build.

The base was estimated at 10” high. What then should be the width of the base at the side. 10 X 1.618 = 16.18” In my rough estimates I guessed at 15” for the case sides and about 16” for the top and probably the case bottom. All of these measurements are within the pleasing range for the eyes.

The shelves would be about 17.5” wide across the front. 40” – (1.75” X 2) – 1” = 35.5” Each shelf would be 17.75” wide. The spacing between the shelves then should be 17.75 / 1.618 = 10.98”. Since a lot of books are 11” high, the spacing should be at least 11.5”

This is a way of determining measurements for items that you plan to build.

See Davids blog Furniture Design #1: Fibonacci gauge

You can search of other pages on LumberJocks that reference Golden Mean.

## 12 comments so far

rikkor

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11295 posts in 3628 days

#1 posted 04-19-2008 09:12 PM

Whew! Way too much arithmetic for me in that one. Great explanation Karson.

jockmike2

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10635 posts in 4000 days

#2 posted 04-19-2008 11:06 PM

Karson you must have taught college trig or something, you lost me back at the 1and 1 thingy. And I got straght 4 points in college allgebra. LOL I love you anyway. mike

-- (You just have to please the man in the Mirror) Mike from Michigan -

David

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#3 posted 04-19-2008 11:25 PM

Karson -

One of my favorite subjects! Great write up and application of the Fibonacci Sequence and Divine Proportion . . . I added this to my favorites list.

David

-- http://foldingrule.blogspot.com

Karson

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35077 posts in 4154 days

#4 posted 04-19-2008 11:37 PM

Sorry Mike. It’s more something. I took a 3 hour class in furniture design taught by Graham Blackburn, I made a statement and he cut me to pieces. So I figured out that I needed to figure it out. So this was my trials at making something that looked proportionally good. Making something that looks good in construction came about by making some firewood first.

-- 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 †

Lee A. Jesberger

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6836 posts in 3733 days

#5 posted 04-20-2008 12:34 AM

Hi Karson;

One of my favorite subjects.

We design nothing without these formulas. A lesson learned long ago was it takes the same amount of time to build something clunky, as it does to build something graceful.

My favorite designer I’ve had the opportunity to work with taught me most of what I know about design.

One thing he brought to my attention is the fact that these same numbers work together in many combinations.

Great topic.

Lee

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

GaryK

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10262 posts in 3741 days

#6 posted 04-20-2008 01:32 AM

One of my favorite subjects!

-- Gary - Never pass up the opportunity to make a mistake look like you planned it that way - Tyler, TX

Betsy

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3391 posts in 3649 days

#7 posted 04-20-2008 02:47 AM

Whew – my head is spinning—- that’s a lot of numbers and figuring. Thanks for lesson.

-- "Our past judges our present." JFK - 1962; American Heritage Magazine

Karson

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35077 posts in 4154 days

#8 posted 04-20-2008 03:34 AM

The thing I like about the calculator version of the formula is it works with all numbers not just 5:8 and 8:13. You can use it for size even the Lincoln Memorial in Washington DC.

And you only need to remember the 1.618. If you forget just use the calculator and figure it out again.

-- 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 †

Grumpy

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22788 posts in 3604 days

#9 posted 04-20-2008 03:48 AM

With you all the way Karson, thanks for sharing. the 1.618 is close to the ratio of kilometres to miles (1.609), so easy for me to remember.

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

bbqking

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328 posts in 3477 days

#10 posted 04-20-2008 04:01 AM

This is a fundamental ratio in all furniture design. I use it all the time when doing takeoffs from old catalogs and photos. It renders proportions pleasing to the human eye (for who knows what reason) and can be first seen in the Greek Parthenon.

-- bbqKing, Lawrenceville

itsme_timd

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689 posts in 3584 days

#11 posted 04-21-2008 03:43 PM

Thanks for a great explanation of this, I’ve added this to my favorites.

-- Tim D. - Woodstock, GA

Karson

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35077 posts in 4154 days

#12 posted 04-21-2008 05:07 PM

Thanks for the comments, I appreciate it.

-- 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 †

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