Farther than before

I walked farther today than the previous days: three miles. I crossed Napa River on an elevated  bridge and connected to the river trail, to the downtown then returned home on another street.

It was 65 degrees, sunny with a cool breeze. I met along the way other walkers and cyclists.  We all practiced the safe distancing. There colorful flowers and plants and art.

I stopped a lot to take photos.

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Fibonacci

 

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Fibonacci numbers by itself and in nature fascinates me.Image 

Who is Fibonacci and what is Fibonacci numbers?

from Wikipedia:

Leonardo Pisano Bigollo (c. 1170 – c. 1250)[1] – known as Fibonacci, and also Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci – was an Italian mathematician, considered by some “the most talented western mathematician of the Middle Ages.”[2]

Fibonacci is best known to the modern world for[3] the spreading of the Hindu–Arabic numeral system in Europe, primarily through his composition in 1202 of Liber Abaci (Book of Calculation), and for a number sequence named the Fibonacci numbers after him, which he did not discover but used as an example in the Liber Abaci.[4]

 

http://jwilson.coe.uga.edu/emat6680/parveen/fib_nature.htm

gives examples of Fibonacci number in nature:

The Fibonacci numbers are Nature’s numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.

Fibonacci in Plants

 Phyllotaxis is the study of the ordered position of leaves on a stem. The leaves on this plant are staggered in a spiral pattern to permit optimum exposure to sunlight. If we apply the Golden Ratio to a circle we can see how it is that this plant exhibits Fibonacci qualities.

photos: plants in my daughter’s backyard