π-casso Pointers: learn about the ratio behind ‘golden’ works of art

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π-casso Pointers: learn about the ratio behind ‘golden’ works of art

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Welcome, artists and mathematicians!

This series will focus on how mathematical properties work to both create and improve art. Read on to learn about the beauty of the golden ratio, where artists have utilized it and how I drew up a piece of my own! 

The golden ratio, denoted by Greek letter phi, is approximately 1.618 and gets its name from Greek sculptor and mathematician Phidias. Just as pi represents the ratio of the circumference of a circle to its diameter, phi is the following ratio in a specially divided line segment:

 

Golden proportion, courtesy of Gary Meisner from goldennumber.net

A is to B as B is to C 

In other words, A is about 1.618 times B. 

 

 

This proportion constructs the ‘Golden’ rectangle and spiral, among other designs. Its use proliferates the works of famous artists: Leonardo Da Vinci, Michelangelo and Salvador Dali. Even nature follows the golden ratio: seed heads, spiral galaxies, hurricanes and more. I chose to make a ‘golden’ sunflower: 

First, use the Excel tutorial linked to graph a seed head employing the golden angle (i.e. when the ratio of the larger arc to the smaller arc is phi). The tutorial can be found here: timwolverson.wordpress.com/2014/02/08/plot-a-fibonacci-spiral-in-excel/. Then, print out the finished graph and gather a piece of parchment paper, canvas paper, yellow tissue paper and markers/colored pencils.

Place the parchment paper over the graph and trace it with a pencil (left). Next, press the parchment paper (pencil-side down) over the canvas paper and retrace the dots to imprint the pattern.

 

 

 

Go over the graph with a brown marker to create the seeds (yes, this is the third time). Cut out petals from the yellow tissue paper equal in length to the diameter of the seed head. Place each petal over the graph and cut off the overlap, then glue.

 

 

Final product! Be sure to use enough pressure with your pencil; my pattern was very faint in some spots and hard to trace. If I had to try it again, I would sketch out petals of exactly the same size and with more colors/shades. See you next time!

 

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