Share it! Science : Children's STEAM Festival: The Golden Ratio in the Garden

## Friday, June 26, 2015

### Children's STEAM Festival: The Golden Ratio in the Garden

It is Day 5 of the Children's STEAM Festival and today we are wrapping things up by examining how MATH fits into STEAM. For those of you who have been enjoying my "Glimpse of the Garden" posts, this will serve as the post for Week 13. We'll investigate some math principles that express themselves in some of the flowers blooming in my yard this week! Once you have learned all about the Golden Ratio in the garden, head over to Growing with Science where Roberta is focusing on three books in the "You Do the Math" series: "Solve a Crime", "Fly a Jet Fighter" and "Launch a Rocket into Space".

The Golden Ratio
What is the golden ratio? It has many names: golden ratio, golden section, golden mean, divine proportion, etc. It has been called many things by different groups of people as it has been discovered and rediscovered throughout our history. The golden ratio, or phi, can be found in nature and in human construction.

I think this concept is best understood visually, so this video will help those like me who need to see it to believe it! This is a clip from Donald in Mathmagic Land, an oldie but a goodie from Disney. This cartoon does a nice job of giving visuals for other math concepts as well as this one, so if you haven't seen it in its entirety, you might want to pick up a copy. (click on the image to find it at Amazon, affiliate link)

So how do we find the golden ratio mathematically? Two numbers are in the golden ratio if: their ratio is the same as the ratio of the numbers added together to the larger of the two numbers, or put more clearly: a/b = (a+b)/a. For example if our numbers are a= 8, b= 5 then we have 8/5 = (8+5)/8, or 1.6 = 1.625. The larger the numbers, the more closely they equal 1.618.
 By Ahecht (Original); Pbroks13 (Derivative work); Joo. (Editing) (Own work) [CC0], via Wikimedia Commons

Mathematicians generally use the number 1.618 to represent the golden ratio. Phi is similar to pi, 3.14, (the ratio of the circumference of a circle to its diameter) in the respect that the digits theoretically go on forever.

The Fibonacci sequence is a series of numbers that relate to the golden ratio in the respect that any two successive numbers' ratio is equal to the golden ratio. We see numbers in the Fibonacci sequence, and the Fibonacci spiral, or golden spiral all over nature.
 "Fibonacci spiral 34" by User:Dicklyon - self-drawn in Inkscape. Licensed under Public Domain via Wikimedia Commons
Here is another video to help us visualize the golden ratio and the Fibonacci sequence and spiral in nature.

The pentagram and pentagon shapes also hold the golden ratio.
 "Ptolemy Pentagon" by en:User:Dicklyon - Own work by en:User:Dicklyon. Licensed under Public Domain via Wikimedia Commons

 "Pentagram-phi" by Jamiemichelle at English Wikipedia - Transferred from en.wikipedia to Commons.. Licensed under Public Domain via Wikimedia Commons

Let's go on a garden scavenger hunt to find these shapes in the garden!

 I've found it on this laurel! ©SBF 2015
 Not one, but 2 pentagons! ©SBF 2015
Now you try it!

These proportions can also be found in seashells, pine cones, stems of plants, trees, etc. Where else can you find them?

 "Aeonium tabuliforme" by Max Ronnersjö - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons