Because da Vinci was obsessed with finding order in the universe, mathematics was a huge part of his life.  He said, "the point is the first principle of geometry and no other thing can exist in nature or in the human mind from which the point can originate."  He said other principles of geometry are the line, the body, and the body clothed by these surfaces.  

The golden ratio, or golden spiral, has been used in art for centuries to aid in establishing composition.  The shape is also frequently seen in nature and various other places.  Here is an example above.

Art forgeries are often detected using mathematical techniques.  Various equations were created based on time, age, decay, color retention, etc.  This became a popular way to detect forgery with the issue between van Meegeren and Vermeer.

The entire article can be found here.

Angle Calculator

I found this cool angle calculator online that negotiates focal lengths of lenses and film formats.  Click

Math and Painting

I found this interesting article about the relationship between mathematics and painting.  There are a lot of great relationships made.  The article discusses van gogh, kandinsky and fractals.

CLICK

Holiday Fractals

Get 4 large shiny Christmas balls, some coloured wrapping paper, some lights from the Christmas tree, and you have you own fractal laboratory to amuse yourself with over the festive season.

The basic setup is four identical, highly reflective balls sitting is a pyramid formation so that each ball touches every other ball. You can look into the gaps between three balls and either shines light into all or one of the other gaps or places colored paper over the gaps and shines light into the same gap one is looking into (or variations of the above). The resulting of reflections, fractal, has what is known as the Wada property after the Japanese mathematician who studied these spatial divisions in 1917. The Wada property refers to cases when there are three basins of attractions so convoluted that every point on a basin boundary is also on the boundary of all other basins.

More Fun Self-Similar Shapes.

http://www.youtube.com/watch?v=A4MZubCt87s



I found this video looking for more cool patterns created by self-similar shapes. Some of the patterns in here we have discussed like snowflakes, and other we haven't touched upon, like planets, leaves, and shells.