Spirals and leaves... do leaves have spirals? It may seem very obvious to you why spirals are related to the Golden Mean, because we have already looked at some. But, why leaves? Lets look at spirals a little more closely and see what they have in common with leaves.

Ready:
Take a look at how the Golden Mean works in petals,leaves and spirals,
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#petals
http://www.cpm.informatics.bangor.ac.uk/rpamaths/rpampages/snail.html

Set:
Go outside and collect at least five different leaves or flowers. Make sure it is okay for you to gather them.

Go:
Think about how plants grow and how spirals are made. Do you see any patterns or relationships? What do we see in daily life that behaves as spirals and plant life?
http://www.cpm.informatics.bangor.ac.uk/rpamaths/rpampages/sunflower.html
In what kind of ways are the patterns used in architecture or design? Thinking about what you have learned about the Golden Mean and the Golden Section, why would people use these patterns? What is attractive about the patterns in the following link?
http://www.eskimo.com/~gluhm/wildlife/pattern.htm
Record your answers in your journal.

Create some of your own patterns in your journal using the leaves and flowers your found outside using drawing tools or the computer.

If you choose to use the computer:
1) Have your teacher instruct you on scanning.
2) Open your scanned image up in Photshop.
3) Increase the Canvas Size (the canvas is the area around your image) so you have a good work area for your pattern. Go to Images, Canvas Size, type in your desired size and hit return.
4) To create more images to add to your pattern, go to Layers in the menu, and choose Duplicate Layer. Hit return when the Duplicate Layer window comes up.
5) To rotate the layer, select the layer, go to Edit and choose Transform, and Rotate.
6) Use your Move Tools to move your layers around and develop your pattern.
6) Repeate steps 4 through 6 until you have the desired pattern.
7) Save your pattern as a JPEG, and insert it in an HTML page using Dreamweaver. Create a link on your main Golden Mean page for this new page.

When everyone is finished display the patterns, so that the they can all be viewed and dicussed.

Next step: The Golden Mean and Fibonacci's ratio...