Many designers, artists, architects, woodworkers, and mathematicians are familiar with the Golden Ratio. Not to be confused with the Golden Rule (also very important). This eye pleasing shape is also known as the Golden Mean, Golden Section, Divine Proportion, and phi (the 21st letter in the Greek alphabet) which has a ratio of 1:1.618. This ratio was developed by the ancient Greeks and has been in use for thousands of years. The architects who designed the Parthenon even used the dimensions.

The Golden Ratio can be found all around you! I'm only going to give you the basics here, but if you want to do more research, feel free to start with the links below. If you want to skip the links, you can get to the file in step 2.

Teachers, I've also included a few activities you can do with students in the final step in case you need some fun lesson plans.

Wikipedia: https://en.wikipedia.org/wiki/Golden_ratio

Harvard University: http://www.math.harvard.edu/~ctm/gallery/gold/

There is also this Instructable by matthewtmead that is very well done and shows how to make a gauge if you can't get access to a laser cutter.

YouTube - SciShow:

YouTube - Vi Hart

## Step 1: Materials

Laser Cutter

Luan or Acrylic

Nylon bolts (x4)

Nylon nuts (x4)

Cutters

Computer with Adobe Illustrator

The Fibonacci Gauge computer file

## Step 2: Cut Your Gauge

Load the files. These documents were created using Adobe illustrator. One file has four gauges ready to be cut in case you wanted extras or needed to make a class set.

Send the document to be cut by the laser cutter.

## Step 3: Assemble Your Gauge

- Lay out your parts as shown in the picture.
- Line up the holes and insert the nylon bolts.
- Tighten the nylon nuts and cut off the excess length of bolt.

Don't tighten them too much because it might be hard to open and close your gauge. It's easy to tighten them by hand. I'm sure you could use metal nuts and bolts from the hardware store to make your gauge look super sharp.

## Step 4: Extension for Teachers

Here are a few lessons that can be used to help explain the golden ratio and give students a chance to use their Fibonacci gauge.

**Day 1 Objectives: **

- I will explain the Fibonacci Sequence.
- I will build a golden section tool (Fibonacci Gauge).
- I will understand how the ratio of 1:1.618 was achieved.

Warm Up: What inventions did we get from ancient Greece that we still use today?

http://classroom.synonym.com/10-things-invented-gr...

http://www.inventions-handbook.com/ancient-greek-...

Review Warm Up

Activities: Watch youtube clip on Golden Section and Fibonacci. (SciShow Video) https://www.youtube.com/watch?v=wTlw7fNcO-0

The parts of the gauge should already be cut out and organized into gallon sized plastic bags with the nylon nuts and bolts. Have students assemble the Fibonacci Gauge. Use the tool to look at the divine proportion in our own bodies. Some examples they might find include the distance between finger joints... hand length : forearm length... head width : head height... It's best to work with a partner.

Closure: What is the Fibonacci Sequence? How did the Ancient Greeks use the golden section? Make sure you bring your Fibonacci Gauge home tonight AND back to school tomorrow!

Home Learning: Use your Fibonacci Gauge to find three examples of the golden ratio in your own homes.

**Day 2 Objectives:**

- I will discover examples of the golden section in and around school.
- I will record photographic evidence of examples found in Architecture and in Nature.
- I will share my examples with my classmates.

Warm Up: What examples of the golden ratio did you find in your homes last night? Where do you think you might find examples around campus?

Activities: Students will need a way to take pictures so they should either bring a camera from home or have one provided for them. Explore campus for examples of the golden section using the Fibonacci Gauge. Try to get the Fibonacci Gauge in the foreground with the photographed example in the background. Look for examples in architecture, furniture, and in nature.

Closure: Share examples with one another as a class. It's best if they can email the teacher their best examples so the teacher can project them onto a larger screen for the entire class to see. Were there any examples that surprised you?

**Day 3 and 4 Objectives: **

- I will design a building, a piece of furniture, or a work of art using my Fibonacci Gauge.
- I will imagine my design from multiple perspectives.
- I will share my artwork with my classmates

Warm Up: Watch the youtube clip

https://www.youtube.com/watch?v=fwYfuJfIgaw

https://www.youtube.com/watch?v=fwYfuJfIgaw

Activities:

- On graph paper, draw a pentangle using only your Fibonacci gauge and a ruler.
- On graph paper, draw a draw a Fibonacci spiral. (What is the biggest spiral you can fit onto your graph paper? Students will need to plan out where they are going to start!)
- Draw a picture of a building or piece of furniture utilizing the golden section and your Fibonacci Gauge (make sure you use a ruler). Be able to explain how the golden section was used. Showing multiple views of the object (birds eye, side view, and front view) are strongly encouraged.

Closure: Trade artwork so you can try to uncover how the golden section was used within someone else’s drawing.

## 10 Discussions

10 months ago on Introduction

Great project! Nice job

2 years ago

Hello, may I ask what the power of you'r" laser is? I have a cnc router, but for some tasks i'd like to be able to switch to laser. Now I am investigating what power I need to cut wood and plastics.

Reply 2 years ago

It really depends on the thickness of the wood you're using. A 40 watt hobby laser will cut 1/8" thick Baltic birch ply with ease. It might even do 1/4" if you tweak it just right.

2 years ago

Nice :)

2 years ago

Cool

2 years ago

Do you have the design in a .DXF or an .IGS format? I have access to CNC mills but not laser tech.

2 years ago

IIRC the famous man drawn by the other Leonardo (namely DaVinci) placed in a square and a circle demonstrates the Golden Ratio.

http://www.goldennumber.net/leonardo-da-vinci-golden-ratio-art/ shows some more facts (the man can also be found in the middle of the article)

Reply 2 years ago

That's a great link. I also like some of the comments at the bottom of the page. Thanks for sharing!

2 years ago

I actually didn't know about this. Most interesting.

Reply 2 years ago

Thanks for taking a look. It's incredible when you start to see all of the examples around us.