The Fibonacci Sequence and The Golden Ratio By Reed Cogliano

Leonardo Pisano Bigollo  Lived  Born in Italy and traveled excessively  Arabic Numeral enthusiast  Liber Abaci  Lived  Born in Italy and traveled excessively  Arabic Numeral enthusiast  Liber Abaci

What is the Fibonacci sequence?  How do we get these numbers?  1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,9 87,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040, , , , , , , ,  Add the first number to the number before it (0+1=1, 1+1=2, 2+1=3…) nowadays we use computer programs to generate large Fibonacci numbers  How do we get these numbers?  1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,9 87,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040, , , , , , , ,  Add the first number to the number before it (0+1=1, 1+1=2, 2+1=3…) nowadays we use computer programs to generate large Fibonacci numbers

What is the Golden Ratio?  1,1,2,3,5,8,13,21,34,55…  F1 = 1, F2 = 1, F3 = 2…  To find the Golden Ratio we divide Fn/Fn+1 =   5/8 = 1.5, 8/13 =  1,1,2,3,5,8,13,21,34,55…  F1 = 1, F2 = 1, F3 = 2…  To find the Golden Ratio we divide Fn/Fn+1 =   5/8 = 1.5, 8/13 = 1.625

Fibonacci Sequence in Nature  Spirals let leaves have maximum sunlight

Golden Ratio  Angles of leaves

The Lucas Numbers  When a plant grows differently it tries to copy the Fibonacci sequence  Some plants like corn grow opposite each leaf  When a plant grows differently it tries to copy the Fibonacci sequence  Some plants like corn grow opposite each leaf

How we use it  Architecture  Painting  Crytography  Architecture  Painting  Crytography

The End