## Golden Ratio Calipers (Fibonacci Gauge)

Written by Jim AdkinsThis easy-to-make gauge allows you to quickly check bowl "rough-outs" (or bowl drawings/sketches) for the **"Golden Ratio"** generally known as **1:1.6180**. This **"Golden Ratio"** has been in existence for many hundreds of years.

**Leonardo Fibonacci** (c. 1170-1250) was an Italian Mathematician, considered by some **"The Most Talented"** mathematician of the middle ages. He was best known to the then modern world for the spreading of the Hindu-Arabic numeral system to Europe. He is noted for a numbering sequence named the** "Fibonacci Numbers"**, although not discovered by him but used as an example in his book **"Liber Abaci"**.

In this book he posed, and solved, a problem involving the growth of a population of rabbits based on an idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as **"Fibonacci Numbers."**

In the** "Fibonacci"** sequence of numbers each number is the sum of the two previous numbers, starting with 0 and 1. This sequence as follows: **0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, 13+21=34, 21+34=55,34+55=89, 55+89=144, 89+144=233, 144+233=377, 233+377=610, 377+610=987**, on and on as far as one desires to go. The higher up the sequence, the closer two **"Fibonacci Numbers"** of the sequence **"divided-by-each-other"** will approach the **"Golden Ratio"** or approximately **1:1.6180**.

It is widely accepted that this ratio is most pleasing to our eyes and will reveal itself if we only check a few items around us (like our credit cards, driver license, etc.)

For those of us that turn "Southwestern-style", semi-closed forms, high-shouldered bowls, check-out the vertical ratios with this Caliper. Older Native-American pottery shapes are quite close to these ratios so the question arises. Did these early people know about this** "Golden Mean"** and use it in their pottery making?

This is a simple line drawing of the **"Plan View"** and a **"Component Layout”** of the calipers I fabricated.

The following is a description of the steps I used in fabricating my **"Golden Mean Caliper"**. I used a piece of Ebony that I had which was 3/4" thick x 2.5" wide x 18" long. Ebony being a very hard, dense wood I thought it to be a good choice.

I needed to fabricate a simple **"sled"** to ride against the fence of my table saw that would enable me to make repeated cuts of 1/8" wide strips.

I used an 80 tooth blade which gave me a reasonably clean cut and required minimal sanding. After sanding, I cut the four pieces to lengths as shown and then stacked the two longer pieces followed by the medium piece and lastly the shortest on top. I aligned the top evenly then taped the entire stack together in three places. I carefully marked the two hole locations with a pencil and using a very small drill I drilled both hole locations thru the stack. The actual diameter of the post screws will determine the finished size of the drill bit used. My posts were 3/16" dia., so I used a 13/64" dia. drill bit to enlarge the holes. After drilling, I removed the tape and lightly sanded the areas around the holes to remove any fuzz, etc.

The post screws I purchased at Lowes were 1/4" long, made of Aluminum. They were labeled as **"Aluminum Post w/screws”**. I penciled-in lines to indicate the pointy ends on pieces "A-D", "A-F" & "B-E". These cuts were made with a fine-toothed pull saw. Sanding off all sharp edged followed. I then re-taped all pieces together and using a ROS I sanded all rounded ends as required. The remaining end of piece "C-G" required sanding separately.

I applied a coat of Watco natural Danish Oil to all surfaces and allowed 5-6 days of ideal drying time. After allowing the finish time to dry, I buffed the pieces with the Beall White Diamond wheel followed with the Carnauba wheel for the finishing touches.

Prior to assembly, I cut-out thin acetate plastic **"washers"** for placement between all pivot points to provide a bearing/friction surface.

Assembly was easy, insert the female threaded post into a hole, place a **"washer"** onto the post and stack the mating piece in place and insert the screw. Once all the parts are assembled, I re-tightened/adjusted the screws for a slight drag when opening/closing the calipers. Once I was satisfied with the "action", I used a toothpick dipped into CA glue to place a very small amount on the screw threads.

The following is a drawing of **"Sample Calipers."** The dimensions for fabricating a caliper that is 23.5” are shown. Also, to the right, entitled **Math Formula**, provides the dimensions needed to fabricate any size calipers you may wish, just do the math by filling-in the underlined blanks.

I've included a photo of one of my Southwestern Basket forms with the Calipers in place for checking how close this form is to the** "Golden Ratio"**. I will leave the judging up to you viewers.

Good luck with this little project. As usual, **if I may be of any help** please contact me.