THE SPIRAL

SPIRALS IN THE WORLD AROUND US

PLANTS

SPIRAL PATTERN IN AN ARTICHOKE

SPIRAL PATTERN IN
THE UNFOLDING PETALS OF AN IRIS

SPIRAL PATTERNS IN DAISIES AND SUNFLOWERS

Spiral pattern in the
structure of a pine cone

SPIRAL PATTERN IN THE WAY LEAVES GROW AROUND A STEM

THE FIBONACCI SPIRAL APPEARS
IN THE PETALS OF A ROSE

BROMELIAD FLOWERS


Why do so many plants form a spiral pattern as they grow? Scientists and mathematicians have been asking this question for hundreds of years.  The mathematics department at Smith College created  a very informative online exhibit on plant spirals to help people understand this phenomenon.
 CLICK HERE TO TAKE THE SMITH COLLEGE
PLANT SPIRAL VIRTUAL TOUR



SPIRALS IN THE WORLD OF MATHEMATICS

THE FIBONACCI SPIRAL


In mathematics, the Fibonacci numbers are the numbers in the following sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144,…

The first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.

If you trace the squares of a piece of graph paper using the Fibonacci sequence you will create a pattern like this one:

The side of each square equal the sum of the previous two squares. The squares become progressively larger following the Fibonacci sequence.
Copy this pattern on to a piece of graph paper and continue to add squares, following this sequence until you run out of room.
Next draw a spiral starting at the first number one and getting progressively larger as it arcs through each square. It should grow smoothly and touch two diagonally opposite corners on each square in the sequence.
Congratulations! You have created your very own Fibonacci spiral.
The rectangle that is formed by your Fibonacci sequence is known to mathematicians and artists as the golden rectangle. click here to learn more about the golden rectangle.

CLICK HERE TO LEARN MORE ABOUT THE FIBONACCI SPIRAL

WHAT IS THE CONNECTION BETWEEN THE SPIRALS IN PLANTS AND THE FIBONACCI SPIRAL IN MATHEMATICS?

WATCH THESE VIDEOS TO FIND OUT

Still confused? Click here to visit a website that does a pretty good job of explaining the math behind the videos you just saw.

Warning: There is a great deal of misinformation about the Fibonacci spiral on the Internet. The Fibonacci spiral is not found in nautilus shells, ram's horns, spiral galaxies or spider webs.

Occasionally, you might find a few numbers from the Fibonacci sequence in a ram's horn or a sea shell but no known animal consistently forms spirals in this manner the way plants do. Click here to visit an excellent website that debunks the most common myths about the Fibonacci spiral.

Spirals are beautiful and amazing in their own right but they do not hold the key to all the secrets of the universe as some would have you believe. Enjoy them for their beauty and mystery and let them inspire you to create magnificent art.

        

                       

   

Watch this video of an artist drawing a rose:

Click here for the first in a series of art assignments based on the spiral                                      by the Helpful Art Teacher

Would you like step by step directions for how to draw a rose? Click here.

Would you like a simpler worksheet with step by step directions for how to draw a rose? Click here

Printable Worksheets
Art activities based on the Fibonacci Spiral by Rachel Wintemberg,The Helpful Art Teacher

PRINT OUT THIS HELPFUL POSTER

Incorporate the different types of rhythmic line designs into your spiral drawings to make your artwork more interesting to look at. The more detail you use, the more engaging your pictures will be.

Click on the link below to see a diverse collection of spirals in art, architecture, computer generated design, sculpture and jewelry by many different artists. 
http://www.flickr.com/groups/spiral/
How will you use spirals in your art?

Fibonacci Zoetrope Sculptures from Pier 9 on Vimeo.