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 1.168.
By Ahecht (Original); Pbroks13
(Derivative work); Joo. (Editing) (Own work) [CC0], via Wikimedia
Commons
Mathematicians generally use the number
1.168 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!
What other shapes can you find in nature? Triangles, hearts, circles? Next time you are out for a walk or hike play the shape scavenger hunt game. You'll be surprised at what you find!
Thanks for exploring math in the garden
with me today and for joining us for our Children's STEAM Festival! I'd love to hear how you use these ideas. Be sure to post a
comment below! To review our schedule and find links to all of the
festival posts, click the Children's STEAM Festival button below.
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