Monday, November 25, 2013

Fun with Fibonacci, Phi, and the Golden Ratio

I think the Fibonacci sequence is spectacularly amazing and mind blowing.  Even though I have taught about it for six years now, every year I am just so amazed at the intricacies of our life and how the Golden Ratio relates to so many things.

We learn about Fibonacci in my Math Analysis class when we briefly (i.e. one day) look at recursive sequences.  I could have students just do a bunch of mindless work with a bunch of recursive sequences, but instead I introduce general recursive sequences and we jump into studying Fibonacci's sequence in great detail.

See pages 7-8 of the Unit K SSS packet to see some awesome information about Fibonacci's sequence, Phi, and the Golden Ratio!

Here is a playlist of some videos and websites I have found about the "Golden Ratio" (also known as the Beauty Ratio, Phi, Golden Number, and other names) that I have students look at before class so we can jump right into the activity during class time.

  • The first step goes over the "Fibonacci Assignments" that they can do.  Some are required, some they can earn bonus points for.  
  • The second step is the required "introduction" video to the Golden Ratio.
  • The third step is the instructional video for the in class activity they do.
  • The rest of the steps are just awesome videos and websites I have found that I wanted to share.


So, what do my students think about all of this?  Here is what they said after doing their Concept 4 WSQ (BEFORE doing the in class activity)

  • It's between the body and nature because those two are radically just woah. The body is already pretty cool but then you throw in plants and well plants are already beautiful, makes sense that the Golden Ratio is in it. 
  • The information about how we find people attractive based on the proportion and symmetry of someone's face because I would just imagine ourselves thinking someone was cute by just our first sight, not by examining the facial structures.
  • That buildings can be considered beautiful, I mean the pyramids have a the number that is considered beautiful. What were the possibilities of that?!!!!
  • I found how the Golden Ratio is incorporated into music interesting because of the 13 notes in an octave (8) and so on. It's creepy... I can never sing the same again... just kidding, you can't stop me. 
  • The part I found most interesting was the part where physical attraction depends on ratio because I was thinking the other day that why do we all feel that someone is more beautiful like we all have an image of beauty.
  • The most interesting is the music. When thinking about the golden ratio, I thought it was mainly focused on appearance of something, but the golden ratio is also in music! 
  • The golden ratio and how it is used in buildings, that they saw this mathematical beauty in their early time periods.
  • I found the information about music the most interesting because I am so involved in music in my life; it is a major part of my life and it is interesting to see that the Golden Ratio exists in such a place. I am very excited about this. 
  • I find the part of PHI being an ideal type of physical attraction because of all the people I was and am attracted to, I never stopped and thought "nice ratio, girl ;)"
  • I found the part about buildings to be very interesting because I never knew that the Golden Ratio was used even in earlier times, such as in the building of the Parthenon or the Egyptian pyramids.
  • That the number is seen in nature, apparently the universe likes Italians. 
  • -snails and fingers have the beauty ratio as well
    -there are various ways to find the beauty ratio in your body such as your arms, legs, face etc. EVEN YOUR TEETH HOLY MOLY AND NOSTRILS WHAT
    -it's even in your DNA and lungs, like how cool is that?!  

Here are some pictures from our in class activity (Haiku-writing and Beauty-ratio measuring)










Here are some of the resulting blog posts turned in already

Haiku (I have many more links if you are interested in more samples)

Beauty Ratio

Reflective Essay (hoping to get more this week!)

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