Introduction: Build a Fibonacci Golden Section Gauge for $1

About: I'm a maker and love building things using 3D printer, wood, metal, software, microcontrollers, fabric and other materials. I love to use creativity to build things with attention toward usability and aestheti…
Throughout the years I've read a lot about the golden ratio from a design perspective. The Greeks noticed there was a common ratio in nature that was pleasing to the eye. This ratio is 1:1.618 (i.e. 1 to 1.618) and is referred to as the golden section. Today, you will find this golden section reflected in design of buildings, logos, products, artwork, etc.

I wanted to create a durable measuring gauge that would allow me to refer to this ratio when designing things that I build with wood, metal, software and other materials. The gauge in this instructable allows you to measure drawings or on screen items and keep the scale and proportion of elements in a design. And, because the golden section is about things that are visually appealing, I wanted the gauge to be visual appealing as well.

The gauge has 3  points, which always retains the ratio of 1 to 1.618, even as you expand and collapse the gauge. In the picture, the distance from the center and right point is always 1.618 times the distance of the left to center points.

WOOD magazine has great video regarding the golden section with examples of the golden section in nature (your body),  greek architecture and an example of how to use it to design furniture.

And you can read about it in Wikipedia as well.

I was able to build this instructable for $1 and your results should be similar. 

SIMPLIFICATION OPTION: If you don't want to hassle with cutting plastic on a bandsaw and torching it to get a nicer edge, there is an alternate approach (that I do not currently explain) that will reduce the effort and tools required for this instructable. I will create a followup instructable showing a simplified approach using wood.

Step 1: Gather Materials and Tools

Wood would be nice for the material to build this measuring device, but I decide that plastic would be more durable and last longer. I wanted to find plastic that would be the desired thickness (1/8") to provide the right rigidity, but not be too bulky. So I walked around the local Dollar Store and wandered until I found what I thought was the most suitable plastic piece for reuse...a Betty Crocker cutting board. And at $1, the price was right.

I also assumed I would use 1/4" aluminum rivets to hold the pieces together. However, as you will read later in this instructable, I found through experimentation, that rivets did not provide the best mechanical joint and, possibly worse, looked horrible. For this device, that measures what is pleasing to the eye, it is a requirement that the device itself is pleasing to the eye. I decided using machine screws provided the best option to holding the tool together. But I'm getting ahead of myself...let's about the parts and tools you'll need.

- Band saw or some other saw to cut the plastic
- Printed PDF of parts template (
- Phillips screwdriver
- Propane torch or lighter
- Straight edge
- Tape
- Scissors
- Sharpie marker
- Safety glasses
- Wood or metal file
- Center punch
- Hammer
- Drill
- Drill bits (1/8", 9/64", 1/4" and 7/8")

- Plastic for gauge pieces. I used a Betty Crocker cutting board I bought at the Dollar store for $1. I'd recommend material that is about 1/8" thick, although you could vary depending on the material you choose. For example, some people might use cardboard or wood rather than plastic. Bring your template (see step 2) with you to the Dollar store to find the appropriate dimensional material. The cutting board (without the handle) is about 5.5" x 8" and just barely fits the template pieces.
- 4 6/32 - 1/4" machine screws

Step 2: Prepare Gauge Template

In this step you download and print your template from the Internet.

First, download the template as a PDF. The template, that provides an outline of every part and location for holes to make joints, is NOT something that I created. There are many templates on the public Internet. I liked the shape of the following template:

Next, print the template to your printer. I printed to an 8.5 x 11 sheet of regular printer paper.

Finally, tape the pieces to the board or material from which you are going to cut the parts. Try to use only one piece of tape for each template piece as it will interfere with the outlining in the next step.

As you position the templates, make sure you leave enough room for the kerf (width of your cut) for the blade on your saw. Don't, for example, tape the pieces so they need to leave some room for the saw blade to pass between the pieces. 

Step 3: Mark Material Using Templates

In this step we outline each part onto our plastic cutting board material so we know where to cut in a future step.

Start by using a marker (I used a Sharpie) to mark the border of each piece. Note that you need to be careful to mark because the paper can easily be moved by your marker. I used one hand to hold down the paper (even though it is also taped) and marked the shape with the other hand. 

Specifically, I found it easiest to hold the template with one finger and flick the sharpie tip from the template off to the plastic. This resulted in a very jagged and sloppy outside shape to each piece, but the inside of the outline was perfect (see pictures below). It is important to have a good edge to your markings so you can cut it neatly in a future step.

Keep the cut out templates pieces after marking the board because they are required in a later step.

Step 4: Cut Gauge Pieces

In this step we cut out the pieces using a band saw.

With your safety glasses on, start by slowly rough cutting all pieces from the large cutting board. This is to ensure you don't accidentally cut into an adjacent piece as you are every so carefully cutting another piece. Go slow.

Once all the pieces are rough cut, slowly keeping an eye on your line, cut each piece. The secret of the bandsaw is to cut close to the line, but not on or beyond the line. You can easily use sandpaper, a sander or file to clean up the pieces once they are cut. Because I was taking my time, I spent about 20 minutes making all my cuts.

Cut your pieces slowly. If necessary, you might not be able to make all turns with your blade, so you might have to make multiple cuts and end up having smaller pieces being cut out.

If you have any small pieces of plastic get stuck in the mouth of the saw table, turn off the saw, wait for it to stop, and remove it before continuing. As you are cutting your pieces, you will notice that plastic is cut away and partially melted and is left hanging from the bottom of the cut piece. You should remove these pieces with a metal file.

Finally, using a file or sandpaper, make sure all pieces are smooth and that any irregular bumps are removed. 

Step 5: Lightly Torch Plastic Cutouts

In this step we play with fire because it is fun. Actually, we use some sort of flame (I used a propane torch) to ever so slightly melt the areas that were cut to make them smooth and melt any material left hanging on the edge. This step is purely cosmetic and if deadly plastic fumes make you nervous, you should skip this step! 

NOTE: I'm sure the fumes from this step are very bad for you to breath, so do this step outside where there is plenty of ventilation. Do not breath the fumes!

Turn your torch to its lowest setting and practice on a piece of scrap material!

Wearing gloves and safety glasses, you want to bring your cut edge close to the flame and let it warm up so it quickly acquires a glossy finish. The material should NOT melt to the point where your piece is malformed or anything drips from the heat. In fact, the flame should not touch your piece, just the heat from the flame. You can see in a picture below that the flame should be pointed parallel to the piece that is being heated. 

When you heat your piece, any loose material should be burned away and any surface that is white from the saw blade should regain its original color (red for me) and also get a gloss finish.

Step 6: Mark and Drill Holes

In this step we will mark the hole location and drill them. 

Keep in mind that your cut pieces will likely not be perfect like your printed template, but what is critical is that the points on each piece and the hole position is maintained. The exact shape of the handles and ends away from the points do not matter as long as the distance from each hole matches the template. 

Place the paper template on top of each cut out part so we can see where the holes need to be drilled.

Using a center punch or something with a sharp point, mark the center of each hole in the template. Once the center punch is poking into the paper template, using a small hammer, put a dent in the plastic piece through the center of the hole in the paper template. Repeat marking all holes using the paper templates.

Before you drill, mark the holes for the appropriate bit (1/8", 9/64", 1/4" and 7/8") using the image below as your guide. The 9/64" hole allows the screws to fit without any friction whereas the screws are threaded into the 1/8" plastic hole. The 1/4" hole is simply a way to hang your gauge and the 7/8" hole is for your fingers while using the gauge.

Make sure you have wood underneath your plastic as you are drilling to control tear out and make sure the plastic does not crack. Drill slowly and take your time. Test each drill bit on scrap plastic prior to drilling the actual gauge pieces. 

Step 7: Again Lightly Torch Plastic Pieces

In this step we use a flame (I used a propane torch) to ever so slightly melt the areas where we just drilled holes to make them smooth and melt any material left hanging on the edge. This step is purely cosmetic and if deadly plastic fumes make you nervous, you should skip this step!

(See step 5 for additional details)

Step 8: Screw Together Gauge Pieces

In this step, you will screw together your plastic pieces.

For this instructable, I assumed I would use rivets, but through experimentation using scrap pieces of the plastic material, I found it difficult to rivet the pieces and allow the pieces to still rotate easily. I tried experimenting with various objects temporarily jammed between the plastic boards to create a temporary gap while inserting the rivets. Eventually, I was able to get the rivets to pop and allow the joints to rotate, but ultimately, what drove me to find another option was that the rivet backs looks awful, even after I used a grinder to "knock them down". (See the pictures for details on this experimentation.)

So, through experimentation, I decided to use screws that would thread directly into the plastic.

Screw your pieces together as specified in the template PDF. Remember to start your screw through a 9/64" hole (which is wide enough to allow the piece to easily rotate) and then continue the screw into the second 1/8" hole. I found that the 1/8" hole does not need to have threads tapped (although you could tap the plastic depending on the softness or brittleness of your plastic). If you simply apply moderate pressure on the screw as you drive the screw (by hand using a screwdriver) into the 1/8" hole, the screw will carve threads in the plastic. Do not tighten the screw too much as you do not want to strip the plastic threads you are creating and also want the parts to be able to move with just a bit of friction.

See the incremental process of putting the pieces together in the pictures.

Step 9: Test Gauge

In this step we measure the opening of the gauge to make sure it maintains the 1:1.6 ratio. And we verify the gauge against known golden section architectures.

As you can see in the picture below, I've opened the gauge to a somewhat arbitrary width of 2" and measure the width on the other side of the gauge. The other side is about 3.2", which is what we expect (2" * 1.6 = 3.2").

Additionally, from the picture of the Parthenon in Greece, it is clear that the gauge accurately measures two aspects that follow the golden section.