Statistics of Nature

Go to
http://www.cs.appstate.edu/~sjg/class/1010/wc/goldenmean/

Definitions

First some definitions, so that we all work with the same lingo. We will define this to be a counterclockwise spiral - ie from the center of the spiral you go counterclockwise to form it. The terminology is confusing since you can also think of this as going from the outside spiraling in clockwise to form it.
counterclockwise hurricane spiral

counterclockwise hurricane spiral
clockwise hurricane spiral

clockwise hurricane spiral

 
 


STATISTICS How many clockwise and counterclockwise spirals do each of these have?

Pineapple and Pinecone


 
 

Pinecone spirals


8 clockwise spirals

13 counterclockwise spirals

 
 

Sunflowers


34 counterclockwise spirals


21 clockwise spirals


34 counterclockwise spirals
 
 

Coneflower


The picture here is T. Stone's photograph of a Coneflower, The part of the flower in the picture is about 2 cm across. It is a plant of the daisy family with a scientific name pf Echinacea purpurea and native to the Illinois prairie where he lives. The picture below is the coneflower center/head taken from a "head-on" view.
 
 

Coneflower


34 counterclockwise spirals


55 clockwise spirals

  • Explore ideas systematically








  • Look for a pattern








  • Create abstract ideas by modeling nature








  • Unexpected patterns are often a sign of hidden, underlying structure. (Open Microsoft Excel)











    1+sqrt(5))/2=1.6180339887498948482045868343656381177203091798058
    Golden mean or golden ratio
  • Explore the consequences of new ideas.





    arm,
    body,
    leaf,
    river,
    lightning. The golden ratio can be found in many places!


    Creative Inquiry and Effective Thinking Techniques we used today
  • Explore ideas systematically
  • Look for a pattern
  • Create abstract ideas by modeling nature
  • Unexpected patterns are often a sign of hidden, underlying structure.
  • Explore the consequences of new ideas.
  • Understand simple things deeply.

    Where else can you find the golden ratio? If time remains, you should try to find out by using your web searching techniques.