Golden Ratio Calipers (Fibonacci Gauge)Written by Jim Adkins
This 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.