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07 September 2010

Homage to Fibonacci










Size:           34” wide x  55” tall
Medium:     Oil on Canvas
Date:          2010

   
 No Longer Available


I am fascinated by the proportions and natural growth patterns of nature.  The physical structure and proportions of plants correlate to those of humans, animals and insects.   The rhythms and patterns in nature resonate with a frequency that, like a tuning fork, sets the tone for all living creatures.

    This painting honors Fibonacci, the greatest mathematician of the middle ages.  Leonardo of Pisa (1170-1240), known as Fibonacci (son of Bonaccio), wrote Liber Abaci (literally, Book of  Calculation) which introduced Western Europeans to the ten-digit Hindi -Arabic numerals, the concept of zero as a number, and the ‘place-value’ method of calculating that we use today, as well as a fascinating sequence of numbers that we now call the Fibonacci Series. 

    The Fibonacci Series, closely related to the Divine Proportion (aka Golden Section), is observed in phylotaxis, the study of the ordered position of leaves on a stem.  This phenomenon occurs from the dynamics of plant growth which creates the spirals that can be seen in sunflowers, pine cones, and twining vines.  It is referred to as a ‘law of nature’.

    The number of petals found on a flower is quite often one of the Fibonacci numbers, especially 3-5-8-13-21-34-55 and 89-petaled flowers.  Daisies commonly have either 21 or 34 petals.  The arrangement of the florets (which turn into seeds) of Sunflowers is a spiral, with 55 spiraling out in one direction and 89 spiraling out in the other direction (or 21/34 or 34/55).  These are logarithmic or equiangular spirals. 

    Starting with the number 1, add it to the number before it.  Continue adding each number to the one before it:    1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610…    When you divide each successive pair of Fibonacci Numbers (3:2, 5:3, 8:5), you get a ratio.

   The farther along the series you calculate the ratio, the closer and closer you get to a very specific irrational number, 1.618…, called phi, which is prevalent in the natural world.  Phi is also known as the Divine Proportion or the Golden Section.  

    The number sequence and the Hindu-Arabic place-value method of calculating were well known to ancient Indian mathematicians who applied it to the metrical sciences (prosody, the study of rhythm in music and poetry).  To give them credit, their names can be found in the upper portion of the painting (Pingala, 200 BC; Virahanka, 6th Century; Gopala and Hemachandra 12th Century).

    This painting is on a board that has Golden Section proportions (Fibonacci Numbers 34 & 55).  Zinnias, Devil’s Walking Stick in foreground

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