# Phi and the golden rectangle. Make a Fibonacci gauge

You may recall back in December when Ian sent me a photo of his Fibonacci Gauge. I was completely intrigued by the whole concept of Phi, the golden ratio. It only took me three months to finally get around to making one of my own.

I have learned that this ratio is everywhere! Logos, for example:

It’s really quite amazing and can come in very useful when designing woodworking projects. If you would like to make one, Mark Whitsitt designed one you can download, with all the correct dimensions. Here’s a PDF version and a Sketchup version.

Thanks Mark and Ian!

Great Video Steve.. FYI The Golden Ratio is 1 to 1.6 So in a design pick one deminsion for example if you have a cabinet you are making. that is 18 inches wide so then how tall do you make the cabinet?? well take 18 X 1.6 = 28.8 or 28 3/4 which is how tall to make the cabinet. now you can round down to make a 18 X 28 cabinet and still be within the golden ration , and create a “Golden Rectangle”…. I use the Golden ratio in a lot of my cabinet building as well as jewelry boxes etc….

Esthetically I find the Golden Ratio a bit on the fat side myself.

Thanks for your videos, Steve.

Just wanted to let you know of an iTunes U free podcast series on the math of design. That is the title, “Math of Design”, presented by Prof. Jay Kappraff from the NJIT. I thought you could let your other readers/watchers know so this comment doesn’t just languish here. After watching the series you’ll know that phi is one plus the square root of five divided by two.

I made a Fibonacci gauge after your first post on the subject a few weeks ago. I made mine from sheoak and it looks very similar to yours – but mine is a metric version. I like those rivets. I think they are cutlery rivets for fixing a handle to a knife blade.

All the best from Oz,

Paul

Golden ratio is traditionally used in drum shells sizes as well. Some people build drum shells that deviate from that, but often make it a point that they are deviating from it.

cheers,

wm_crash, the friendly hooligan

Great Video,

thanks for the credit.

Paul from Oz, is correct about the rivets. A knife making supplier should have the rivets if leevalley.com is not available to you.

cheers, IanW

I loved the video! My woodturning teacher is always on about the fibonacci ratio, I think I might have to ake one of these to show him.

Thanks again

Alviti

Thanks, I just read today that many blogs are set up with the phi ratio. I think mine needs adjusting!

where is the template?

In the last paragraph. There’s a PDF and a SketchUp version.

impressive tool

thanks Steve.

The phi ratio is the number of 1.618033988 with approximation to 10 significant digits. It is calculated as (sqrt(5)+1)/2. This phi number has some prety features like:

1+phi = phi*phi

1/phi = phi-1

You can make a 3D construction, say a box having volume of 1 if the three lengths of x, y and z are 1, 0.618 and 1.618 respectively (x=1, y=phi-1, z=phi.

Fibonacci seems to made work a lot with this number and so the called Fibonacci series numbers.

BUT is you look at history the Pythagorians in Athens, Ancient Greece had done extreme work with this kind of numbers, eg the pentagon lengths are crossed exactly with phi ratio. All the beatiful buildings have been and still build using this ratio. Acropolis is just one of them.

It is nice to give this video and the pdf file for the phi-diabete tool construction.

I was interested in making a Fibonacci gauge, our the planes still available? I clicked on both the sketch up and the PDF and neither link was viewable. Are the links MAC os compatible?

Countries That Don’t Use the Metric System

http://www.joeydevilla.com/wordpress/wp-content/uploads/2008/08/map_of_countries_that_dont_use_metric_system.jpg

thanks for measurements! made a pair a long time ago and have lost the numbers but want a bigger set. Golden section is a pretty good starting point for design – if you follow it too rigidly

though, your stuff starts looking contrived or mechanical. just like with any ‘rule’ of design i guess.

Great video. Very helpful in the construction of a golden mean gauge. That may be a more accurate name than a Fibonacci gauge, as the Fibonacci sequence only approximates the golden ratio as you continue through the sequence. The logos above showing the golden ratios in their design were created using PhiMatrix Golden Ratio Design and Analysis software. This is available at http://www.phimatrix.com, along with many other illustrations of applications of the golden ratio.