the fibonacci sequence

Types of Spirals

• Archimedes-keeps the same distance as it spirals out
• Parabolic-starts big but becomes tighter, spiral ends
• Fibonacci-starts tight but increases distance as it spirals out

How to draw

spirals in nature

• fern fronds
• sunflowers
• pinecones
• others?

sequence of numbers

• 1+1=2
• 1+2=3
• 2+3=5
• 3+5=8
• so on...

pinecone example

• count the rows on the pinecone
• any similarities? patterns?

Leaf pattern of growth

• need an efficient way to absorb sunlight
• leaves should not fully overlap each other
• botanists realized plants are consistent in growing leaves 
• equal distance/angle degree
• follow one simple rule

phi

• most efficient irrational number
• cannot be expressed as a whole number
• 360/phi (golden ratio)
• =222.49 degrees -360= 137.5 degrees

phi...

• new leaves tend to pop up in open areas
• just enough space so it isn't completely filled
• always room for one more leaf

Fibonacci all around us

• plants follow one simple rule of 137.5 degrees
• rule so simple can create structures so complex

thank you