Fibonacci, what a notion of the motion of the world. . .

*Fibonacci, What a Notion!* was originally commissioned by the Children’s Festival Chorus of Pittsburgh. Written for children’s choir and jazz ensemble Catch 22, the piece is about the Fibonacci number series and also uses Fibonacci numbers in its construction. I’ve been writing and recording for the past few weeks and am in the process of reworking this piece for myself as well as for my ensemble. Here’s the first verse of the original piece.

Fibonacci, what a notion of the motion of the world! One, one, two, three, five, and eight, Add each one accumulate the number called the Golden Section. How to measure such perfection? One, one, two, three, five, and eight, Fibonacci, what a notion of the motion of the world! (lyrics ©2006 Lynn Emberg Purse, All Rights Reserved

If you haven’t heard of the Fibonacci number series, perhaps you are familiar with Fib Poetry – a variation of Haiku that uses the Fibonacci number series (1,1, 2, 3, 5, 8 etc.) for its syllable per line construction. If you add each number to the previous number, you get the next number in the series. 1+1=2, 2+1=3, 3+2=5, 5+3=8, and so on.

The numbers of the Fibonacci series, codified by Leonardo of Pisa, a 12th century Italian mathematician, were based on his observations of the proliferation of rabbits. What science continues to discover is that the number series is prevalent throughout nature, possibly the result of how the earth rotates around its light source, the sun. The leaves and branches of plants grow in spiral formations. Many flowers bloom in groups of 3, 5, 8, or 13 petals; daisies and other composite flowers often produce 21 or 34 petals. It is thought that plant seed production is best dispersed through the double spiral of seed heads, most easily seen in sunflowers and other similar plants. A young boy recently got The Young Naturalist Award for exploring the hypothesis that solar power based on the Fibonacci pattern in tree formation makes an efficient solar collection design.

It shapes our fingers and our face, the rings of Saturn hung in space, the petals of a rose, the wings of a moth, the leaves of a tree, the hives of a bee, the shells from the sea!

The Fibonacci numbers occur over and over again in music and the physics of sound. In Western music, the first, third, fifth and eigth notes of the scale form a complete harmonic chord. Although there are 12 notes in the chromatic scale, the 13th note completes the octave. It is easy to see this laid out on the piano keyboard. I had fun with my Fibonacci piece, using the numbers to determine part of the melody as well as form the lyrics and influence the rhythm; the middle section features Catch 22 jamming on a 13 bar blues in 5/8 meter, instead of the usual 12 bar blues in 4/4.

When the numbers are plotted graphically, they form a spiral pattern. One well known example of the pattern is the nautilus shell that I picked up in a shop in San Francisco to photograph; other common examples from your own backyard are pine cones and the seed head of a coneflower (*Echinacea*). My mother, a mathematician and basket maker, designed a basket based on the over-under woven patterns of 1,1, 2, and 3. You can see the spiral design in the completed basket.

When the numbers are used proportionally, they form the Golden Section or phi. The pattern of proportions, it is sometimes called the Golden Section, which the Greeks used in the design of the Parthenon and which is the foundation of architecture and garden design as well. The goal is to achieve *balance, beauty and harmony* and we unconsciously use it when we perceive something as beautiful. (See “The Math Behind the Beauty”) The arbor I designed for my garden is 5 feet wide and 8 feet high, a proportion that I find pleasing.

Balance, beauty, harmony, harmony. Fibonacci, what a notion of the motion of the world!

Plant studies done in outer space and zero gravity suggest that plants don’t grow in the Fibonacci pattern when not on earth. So perhaps it really is about the way we spin through space on planet earth – *Fibonacci, what a notion of the motion of the world!*

For a great post on Fibonacci in nature with more examples, photos, and links, visit Frank at A Frank Angle.

All music and lyrics ©2006 by Lynn Emberg Purse, All Rights Reserved

Text and images (except Spiral Galaxy) of post “Fibonacci, What A Notion” ©2012 Lynn Emberg Purse, All Rights Reserved

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I’m always happy to see someone promoting the Fibonacci numbers (and math in general). You’re aware that the Golden Section or Golden Mean or phi is a ratio equal to approximately 1.618, but you may not be aware that

anyadditive sequence leads to that number, not just the Fibonacci sequence. For example, starting with the arbitrary numbers 7 and 4, we get the additive sequence:7, 4, 11, 15, 26, 41, 67, 108, 175, 283, etc.

As you go farther and farther out in that sequence, the quotient of each term divided by the previous term gets closer and closer to phi. At the point where I stopped, with only ten terms, 283 divided by 175 already gives approximately 1.617. It’s magic!

Steve Schwartzman

http://portraitsofwildflowers.wordpress.com

Hi Steve! I did realize that other number patterns lead to phi but I did not know that any additive sequence does so. That is so fascinating; now I will be playing around with number sequences for the next few days! Thanks for contributing this – maybe I can write another math/music piece with this in mind – hmmmm…. I love this sort of thing!

Me too. That’s why I taught math on and off for four decades. There’s no end to the patterns to be found in mathematics. Fibonacci-related things are a particularly rich playground.

How interesting!

Thanks for visiting, Paula!

When I researched and wrote about Fractals in relation to my dill flowers, I didn’t stumble over the term fibonacci. Thanks for expanding my understanding!

Hi Margie, thanks for visiting. Every time I do more research, I am more astounded by these connections. Here’s a link to a great video that makes the Fibonacci – Fractal connection. http://www.youtube.com/watch?v=bE2EiI-UfsE

I think someone recently did

a song about the mandelbrock

set. That’s a famous fractil

though –

I’ve heard of this secquence,

makes you wonder that if the

sun can have such an impact

on life – maybe the other stars

can as well – and there could

be something to astrology.

Hi Rastelly! There are a few songs around on all of that – I love fractals too. They make great graphics for image manipulation.

fabulous! I always think ‘what was in his (fibonacci) mind at the time his number born…’

Thank you for visiting, Fibonaccist, I thought you would enjoy this post!

What a fabulous post. The short musical interludes were wonderful and set the music tone … so when I heard the blues piece, I went WOW!

Also thanks for the referral, and I hope you readers visit. By the way, here’s something similar … our paths may not have crossed when I did this, but you (and others here) will enjoy this post about the Tau.

http://afrankangle.wordpress.com/2011/10/04/on-a-hot-tau/

Well done!

Frank, thanks so much – I thought you might enjoy this and I have already seen some traffic to your site from here. I remember the Tau post – I encourage EVERYONE to follow it and watch the video – I posted a response.

Math and music – what a beautiful thing!

Ah, yes! spirals and fractals…I think a loving relationship, too, is invited to unfold/multiply with similar elegance and progression…thank you for the wonderful inspiration!

What a great connect, Catherine. Yes, I think you are right, everything, seen and unseen, follows a larger pattern that unfolds . . . which is really the adventure of living here and now.