On May 4th, 2020

Weekly STEM Exploration: Golden Spirals

Welcome to this week’s STEM exploration!

  • In case you missed it: Check out last week’s exploration of Coding, where you can learn what it is and where to find it your everyday lives to solve complex problems and questions! 
  • This week’s STEM topic: Math: Golden Spiral & the Fibonacci Sequence 

Have you ever noticed the symmetry in nature? Did you even know that the world around you could be so mathematical?! Take a look at any of these photos. What do you see? 

The Golden Spiral is a pattern that can be found in nature, art, engineering, and even human construction. It has several names: Golden Ratio, Golden mean, the divine proportion, and Phi (similar to Pi, in the respect that the digits theoretically go on forever). Phi is the infinite number of 1.618 used to represent this so-called Golden Spiral. Is your head spinning yet? Let’s take a look at this visually:

You start with the main rectangle, which is drawn to that Phi number, in ratio form: 1:1.618. If you draw a line inside the rectangle to form a perfect square, the remaining rectangle will have the same ratio as the main rectangle. You can keep doing this over and over forever! Look at the spiral shape found within the drawing. See how the line starts at the bottom left corner, and the spiral forms by following the opposite corner of each square as it goes clockwise?

How does the Fibonacci Sequence fit into this? An Italian mathematician, named Leonardo Fibonacci, discovered this idea of finding the Golden Spiral within the design of our universe. Think of it as the recipe for how to make that Golden Spiral! His “recipe” is a simple pattern of numbers made by adding the previous two together to get the next number in the sequence, which looks like: 0,1,1,2,3,5,8,13, 2, 34, 55, etc. The math looks like this: 0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8 and so on. 

Why is it important? Lots of geometric shapes found in nature and art are related to the Golden Spiral and Fibonacci Sequence, from sunflowers to hurricanes to galaxies to the Mona Lisa painting! For example, sunflower seeds are arranged in a Fibonacci Sequence, keeping the seeds uniformly distributed no matter how large the seed head may be, which helps harness the sun more efficiently! While this series of numbers from this simple brain teaser may seem silly, the Golden Spiral and the Fibonacci Sequence have been rediscovered in an astonishing variety of forms, from computer science to engineering new buildings, the stock market, and even Picasso’s art!

Where else can you find them? Next time you go on a walk, play a scavenger hunt game for Golden Spirals in nature! You’ll be surprised at what you find! 

In today’s playlist(s), you will see videos that answer the following questions:

  1. What is the Fibonacci Sequence and the Golden Spiral?
  2. Where can I see the Golden Spiral in my everyday life?

Check out our YouTube playlist HERE

Have an art-obsessed member in the family? Check out “Doodling in Math: Spirals and the Fibonacci Sequence”:

Part 1

Part 2

Part 3

*disclaimer: These videos were not created by the Discovery Center of Idaho and have only been shared as suggestions for quality sources of fun and accessible STEM education regarding this week’s STEM topic. 

Try this activity at home!


Golden Spirals in Nature


  • Large Paper or printer paper taped together (need a large drawing space)
  • Pencil
  • Ruler
  • Colored Pencils
  • Items from nature (leaves, pine cones, pebbles, sticks, flowers, weeds)

Set up:

  1. Lace-up your boots and go on a nature walk as a family! Look for the Golden Spiral all around you! Collect pine cones, leaves, small pebbles, flowers, weeds, or whatever other small items that attract your eye. This will be for the art portion of this activity!


  1. Discuss the golden ratio and Fibonacci sequence together by looking at a pine cone. Think of this: where else have you seen this pattern?!
  2. Grab your large paper, ruler, and pencil. Write out first few numbers of Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13. You’ll need this through the activity!
  3. Measure out a 1x1 centimeter square in the middle of the paper. Color this red. 
  4. Add another 1x1 square to the right of that first square. Color this one blue. 
  5. Add a 2x2 square underneath those two squares. Color these yellow.
  6. Add a 3x3 square to the right of the existing squares. Color these green. 
  7. Add a 5x5 square above the existing squares. Color this one purple.
  8. Add an 8x8 square to the left of the existing squares. Color this orange. 
  9. If you have room, add a 13x13 square underneath the existing squares. Color this pink. 
  10. Once all the squares are drawn and color-coded, use your artist eye to now make your best spiral from your Fibonacci square, using your goodies from your nature walk! Your spiral will be bigger than your squares drawn. 

It’s okay to fail a few times before you get it!

Remember to tag us in your curiosity and creations on Facebook, Instagram or Twitter! We’d love to see them!
@dcidaho #dcidaho #STEMatHome #DCIatHome

Have a topic that you want us to explore? Are you curious about a STEM topic that we haven’t thought of yet? Make suggestions HERE!  We fixed our form!

Photo Sources:

  1. https://thefibonaccisequence.weebly.com/ 

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