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3.3 Podcast 7 Fun with Fibonacci

January 3, 2010

  

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A wonderfully simple, but visually pleasing mathematical topic is called the Fibonacci sequence.  

 What is the Fibonacci sequence?  

 Before you go running off to Wikipedia to find out (it’s somewhat scary – I’m warning you), let me explain Fibonacci here first.  

 The Fibonacci sequence is a series that can continue on forever (something to occupy your kids of school age for a period of time that can add multiple digits – challenge them to find the first 20 or 30 Fibonacci numbers and they’ll stay occupied for a while to give you sewing time).   

  1. You start with the number 1 and the other number 1. 
  2. Then you add the two numbers together: 1 + 1 = 2
  3. Then you add the last two numbers together: 1 + 2 = 3
  4. Then you add the last two numbers together: 2 + 3 = 5
  5. …   3 + 5 = 8
  6. …   5 + 8 = 13
  7. …   and so on … the numbers 1, 1, 2, 3, 5, 8, 13 …. are the first numbers in the Fibonacci sequence

Personal Fibonacci influences 

Where did I first learn about the Fibonacci sequence?  Square One Television 

 Square One was an educational television program in the late 80’s that helped kids learn math.  There were several other shows that held my interest at this time such as:  Mr Wizard, Where in the World is Carmen Sandiego, Braingames (on HBO), Encyclopedia (also on HBO), which focused on science, geography, brain puzzles, and vocabulary respectively.  

 On Square One, at the end of every episode there was a segment called ‘Mathnet’.  On Dragnet Mathnet, they were detectives that used math to solve crimes, and on one episode (series of episodes) there was a parrot that kept saying “1, 1, 2, 3, 5, eureka”.  It was the Fibonacci parrot.  Listen to the episode to hear my rendition of the parrot and some songs that I sing wonderfully that I embarrass myself for the sake of math.  

Fibonacci in Quilting  

The best example of a Fibonacci quilt that I found was on the blog Christina Creating  

Fibonacci quilt from Christina at Christina Creating

The colors, the contrast, the borders and the binding are just incredibly wonderful in this quilt!  Its informational, educational, visually appealing, square, AND well received by the recipients!  She talks about the process in her favorite quilt post.  No wonder it’s one of her favorite quilts!

Because I missed it the first time, here is a direct quote from Christina Creating about the inspiration for the quilt that she made:            

“I got the idea from the article “Pythagorean Tree” by Diana Venters in AQS’s American Quilter: Ultimate Projects (vol XIX, no 5, 2003).”  I have not been quilting all that long, so do not have access to that article (without going to the library I would guess they may have it).  If you’re into mathematical quilting, look up Diana Venters.            

Inspired by christina’s quilt, I played around in Photoshop a little bit and got a rough draft of a few quilts (or quilt block).  I turned on the grid to help with lining up in Photoshop (go to view / show / grid) 

 

Then I added several of these blocks together and changed some of the colors  

What an easy baby quilt idea this could be?  You could sew strips together of the different colors and just cut and sew them fairly easily. 

Here is the edges of the Fibonacci that shows the grid created by this quilt.  Maybe this would be good fabric pattern? (or not?) 

 

If instead of doing strips, you could do squares of each type.  This is (my) monochromatic version of the painting on the Square One / Mathnet parrot episode. 

You could also use the Fibonacci sequence to find visually pleasing border widths.  If you are stuck on several borders and knowing what widths to use for these, try Fibonacci numbers. 

For example, have a 1 inch border next to a 2 inch border next to a 3 inch border.  Or try a 2 inch border next a 5 inch border or a 1 inch border near an 8 inch border.  

I found a few other mathematical quilting sites along the road              

Including a challenge for mathematics quilts from 2006.         

 

Fibonacci in Nature 

Not all Fibonacci is straight lines and architecture.  Naturally you find Fibonacci in sunflowers.  I am NOT going to count them, but supposedly there are Fibonacci numbers of 34 and 55 on the following sunflower. 

 

 When you stop and look at things that you don’t normally pay attention to, you can find some unusual ideas, depending on how deep you actually look.  After mentioning Fibonacci and doing some Wikipedia research, and seeing tons of sunflower pictures, I stopped in my tracks when cleaning one of my dishes (by hand) and saw the same type of pattern – a Fibonacci pattern on my dish!  Amazing!  Did they purposefully make 13 little “dents” in each spiral?     

 

A natural spiral found in sea shells is shown here with this Wikipedia drawing.  

And if you divide the Fibonacci numbers in this way you get the Golden Ratio, which is also visually pleasing: 

  • 5/3 = 1.5
  • 8/5 = 1.66
  • 13/8 = 1.6
  • … on and on … until you get 1.61

The golden Ratio gives you a visually appealing relationship of 1 on the short side and 1.61 on the long side – many greek architecture follows this golden ratio rule of design. 

Additional Resources

A very comprehensive study of the fibonacci sequence with many pictures and ideas 

Go to Craftster and spread the word there on the quilting podcast posts        

Quilting & Crafting Podcasts mentioned in this podcast 

If you’re mathematically brave, head to the Wikipedia sites on Fibonacci and golden ratio

Thanks to my commenters this week!        

Keep Experimenting! 

13 comments

  1. Thanks for thanking me! Haha! I am so excited you found my blog, because I am amazed at items on YOUR blog! I figured this was a fitting quotation for inspiring people who read your super awesome ideas to start a project using Fibonacci sequences and the Golden Ratio:

    “Do not wait; the time will never be ‘just right.’ Start where you stand, and work with whatever tools you may have at your command, and better tools will be found as you go along.” – Napoleon Hill

    P.S. I was born in 1980 and LOVED Square One! I had completely forgotten about it. I can still hum the music to “Mathnet!”


  2. Thanks Darla! I was behind a couple podcasts, but when I saw this one, I had to jump ahead and listen to it. Great explanation and examples. I’ll have to check out your links

    Colleen


    • Thanks for the inspiration Colleen! Its a wonderful topic and I suppose I could have talked more about fibonacci borders, but I am gettting there slowly. Would need more time and research (and perhaps experience)


  3. Thanks for putting some of that math from High School and College to work. Those are great examples.


    • Thank you Rona for commenting. There are a lot more different things and types of things out there to do and try. There is a use for all this math that they told you about in high school – its quilting! And I found a way to put science in it too, which is really stretching my own brain creatively and thinking about it as well.


  4. love the fibonacci series, I made a fun rainbow quilt using the maths and it works perfect xx


    • Driftwood

      I’ll have to link back to your rainbow quilt & tutorial. It is a great example and a unique twist on the fibonacci series. I had seen it before about two months ago and lost the link in the meantime. I think more can be said about the fibonacci sequence in quilting, so maybe a second episode about it will be on the way sometime. Thanks for commenting & sharing!


  5. Darla, although I may not fully understand Fibonacci – I know what I like in a quilt and those quilts are beautiful. Thanks for reminding me that even at times when I’m not feeling very “artsy”, I can use MATH and create something beautiful.


    • Glenna,

      I need to actually make the quilts that I have the patterns for now, but I am thinking they would be pretty easy to do. I am drawn to the geometric side of the quilting, and using the mathematical principles to make them ‘artistically pleasing’ is always good. Now I need to relearn and remember the math that can get us there! Thanks for commenting!


  6. Hey Darla! I listened to your Fibonacci podcast (cool topic, btw) and it made me rummage around a bit in the educated part of my brain–err, what’s left of it–and I was wondering…what do you think of doing a podcast on fractals? I bet a quilt based on that would be awesome. Love the show!


    • Kelley,

      Thanks for your comments about liking the show. I think I could do another fibonacci quilt show with even more fibonacci patterns that didn’t make it into the show. I keep getting ideas about doing fractals – will have to brush up on it a little bit myself and maybe think about paper piecing them because depending on how many times you repeat, fractals can get pretty small pretty quickly!


    • That’s funnee – rummage a bit in the educated part of your brain – what’s left of it – since math and science tend to be LEFT-brained activities.


  7. Wonderful. Many thanks.



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