Friday, March 08, 2013

Math and Art... huh???

Here's what an artist does to make a connection to "examples of real world math" for a college math assignment... Hope you enjoy it...

Art since the early Renaissance times has included mathematics, especially geometry, in creating the most pleasing compositions for drawings, paintings, and architecture. As an artist, I still use these methods today to create interesting compositions that hold a viewer’s interest and put emphasis on the focal point of the work. Two main examples are the use of the “Rule of Thirds” and the “Golden Mean.”

The “Rule of Thirds” simply divides the canvas into thirds with a “Tic, Tac, Toe” type grid. The four points where the lines intersect naturally create the points of the most interest on the canvas. The artist situates his or her focal point on or near one of these points to create a pleasing composition.

Example from one of my paintings…

The “Golden Mean” or “Golden Ratio” is another mathematical way artists use to set up engaging compositions. The “Golden Mean” is based on the mathematical sequence discovered by mathematician, Leonardo Pisano Bogollo, who lived between 1170 and 1250 in Italy. "Fibonacci" was his nickname, which roughly means "Son of Bonacci".

As well as being famous for the Fibonacci Sequence, he helped spread through Europe the use of Hindu-Arabic Numeral (like our present number system 0,1,2,3,4,5,6,7,8,9) to replace Roman Numerals (I, II, III, IV, V, etc).

By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation and can be written as a rule mathematically:

xn = xn-1 + xn-2
or

The “Golden Mean” highlights a spot very close to the “Rule of Thirds” method determined to be the point of interest.

Examples of the “Golden Mean” in art and architecture…

The Fibonacci sequence is a consistent and infinite sequence that is found in nature. Here is a surprise. If you take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio "
φ" which is approximately 1.618034...

Recent studies have linked the Fibonacci sequence follows the patterns in nature, uniting math, science, and nature design. For example, sunflowers often have precisely 55, 89, or 144 petals, numbers that figure in the famous Fibonacci sequence. Nature, it seems, has certain mathematical underpinnings.

Researchers have even dubbed the sequence as the fingerprint of God. Read more on this at http://www.pbs.org/wgbh/nova/physics/describing-nature-math.html .

This all proves that math can be COOL!

Thanks for dropping by...
In Art (and Math),
Bernie

Sources and resources:

http://www.mathsisfun.com/numbers/fibonacci-sequence.html

http://www.pbs.org/wgbh/nova/physics/describing-nature-math.html

http://www.homeschoolmath.net/teaching/fibonacci_golden_section.php

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html