Create Fibonacci Spiral Leather Earrings

 

Fun with Mathematics and Silhouette Cameo 4 

The golden ratio is defined as 

"The ratio between a larger number 'a' and a smaller number 'b' when a+b/a = a/b. 

It is also the positive solution to the equation x^2 - x - 1 = 0"

  as seen in this screenshot from the Compendium of Mathematical Symbols.

The symbol Phi (φ) represents the Golden Ratio. 

The Fibonacci spiral approximates the golden ratio using circular arcs connecting opposite corners of each successive square. Here is a rendering of the Fibonacci Sprial found on wikepedia:

This design is recognizable in the science world as a classic illustration of the golden ratio. So a properly geeky thing to do with it would be to create a pair of earrings - and if you're feeling up to it, a pendant - from pleather (fake leather) and some permanent vinyl. 

Challenge: Make a Fibonacci Spiral Cut File

Of course, the first challenge we are faced with is the drawing itself which consists of very fine lines. If you were to attempt to cut this as is, the pieces to keep (where the lines are) would be too narrow to handle. One option would be to use the pen attachment to have the Cameo draw the spiral on paper, but the drawing wouldn't be easily recognizable from a distance. 

The solution is to pull the image into Silhouette Studio and create a version of this with thick lines that could be cut out of vinyl and applied to a pleather backing. 

Download an image of the Fibonacci Spiral or scan a photo of one from your favorite geometry book. 

When I first imported this Fibonacci Spiral SVG, I discovered that the lines were not grouped together.

As you can see in the screenshot, when I grabbed the top line to move and resize the shape to fit my mat (it had opened at a size much greater than 12"x12" and wasn't centered on the mat) only that line moved. I hit undo to restore it to its original shape.

I then zoomed in and noticed the following at the top of the screen:

Cool geeky information on the construction of the spiral but not necessary for the earrings. Hitting delete with the words selected quickly removed the text.

Select everything - ctrl+a - then, right-click to pop up the context menu. Click on "Make Compound Path". 

The drawing will convert from a bunch of separate lines into a single drawing.

Next, we need to make the lines wider so the drawing is substantial enough to cut out in vinyl. Open the Offset Panel by clicking on the star shape icon on the right side menu bar.

Select the image and click on Offset. Adjust the distance to create an offset around all the sectors. I chose distance = 0.200 for my project.  

Click upon the original image and drag it off by one of its more prominent curves.

The original image may be deleted or simply dragged off of the mat to get it out of the way.

Next, select the new offset image. Open the color palette and click on a color tile to apply it to the drawing. This will make it easier to visualize as a completed item once it has been resized to earring proportions. I chose purple, but any color will work at this stage. If you have already chosen the vinyl for the spiral, you could choose a color matching the vinyl.

Sometimes it's nice being able to independently alter the width and height of a design, however since this design's definition depends upon its proportions, the aspect ratio should not change. Click on "Lock Aspect Ratio" in the upper menu bar to ensure that the image is not distorted when resizing. 

Click on one corner of the image and resize to about 2" wide.  

The size shown above is a reasonably good size for earrings. I usually like my leather earrings about 2" tall. The design will be rotated 90 degrees for the earrings, but cutting the designs this way will allow me to use a long and narrow scrap of vinyl to cut them.

While examining the design, I decided that the cut out pieces might be a bit narrow for the fake leather to properly maintain its shape. Therefore, I chose to have a solid rectangle of fake leather as the backing and to stick Orcal 651 to both the front and the back of the rectangle. 

In addition, having made several pairs of leather earrings previously, I have found that the wider the top of the design is, the more likely it is to show its back side. These earrings will be just over 1 1/4" wide when complete, so they will catch in my hair and show their back sides often.

This means that I will need to cut 4 copies of the design from the Orcal 651 vinyl - two for the fronts of each earring and two for the backs of the earrings. 

Copy, Paste Repeat

Select the design, Copy (ctrl-c) and Paste (ctrl-v) a second copy onto the design mat. Move the second copy next to the original. Select All (crtl-A) then Copy & Paste a second pair of designs. Move them below the first set.

 You now have 4 identical Fibonacci Spirals. 

I like to have earring designs that are mirrored. This isn't mandatory, so skip the mirroring if you wish. With the bottom pair still selected, right-click and select "Flip Vertically". 

This creates two pairs of opposing designs, which when held close to each other look a little bit like a stylized heart. That's a subtle "I love math" sign if I've ever seen one.

Load a sheet of Orcal 651 vinyl or other permanent vinyl of an appropriate color onto your mat. Click Send and cut out the vinyl. 

After the Cameo finishes cutting, remove the vinyl from the mat and carefully cut the design from the remaining vinyl. I usually cut about 1/4" away from the outermost cut line so that I am assured of clean edges all around. Cutting the extra vinyl off at this stage also helps preserve the rest of the vinyl sheet for a later project.

Leave the project image open on your computer screen to help you more easily locate the quarter circle wedges that need to be weeded from the design. Weed away everything that is not part of the Fibonacci Spiral. 

Take some transfer tape and pick up the Fibonacci Spirals one at a time. You may cut the backing between designs to make it easier. Line up the transfer tape backed design on the front of a piece of smooth fake leather. For this project, I selected a piece of metallic silver pleather.

Apply the vinyl to the front of the pleather. Burnish the design (rub it with your fingers or a scraper) to ensure all of the smaller pieces have stuck to the pleather. Remove the transfer tape. 

Repeat with a second copy of the Fibonacci Spiral, ensuring that you pick one that is a mirror opposite of the one recently placed. 

Place your pleather on a rotary cutting board and carefully cut around the outside of the design as close to the applied vinyl as you can. You may also cut with scissors, but a rotary cutter can cut a bit more accurately.

Flip over the earrings and using transfer tape, align each of the other spirals onto the back side of the vinyl rectangles and burnish until they have stuck firmly to the backing. 

Decide which end is the "top" and punch a hole through the pleather just below the vinyl lines. Attach a jump ring and an earring wire to each earring. Wear your geekiness with pride!

PS: you could also consider creating a larger version of this design as a necklace pendant. 

HAPPY CRAFTING!