Doing Math

Tessellations

The Islamic Empire has made significant contributions to the study of mathematics.  Islamic mathematics allowed math to be expressed in an art form.  There was an extensive use of geometric patterns that was used to help decorate buildings.  

Around 810 AD, the House of Wisdom was set up in Baghdad and the work done there to translate the major Greek and Indian mathematics and astronomy into Arabic began immediately.  An early director of the House of Wisdom, Muhammad Al-Khwarizmi, made an extremely important contribution to mathematics with his adaption of the Hindu numerical system (numbers 1-9 and 0).  Some 400 years later this was adopted by the entire Islamic world and Europe.

To make sense of Islamic mathematics, I obviously looked online for information.  I came across a website which I found to be extremely easy to follow and shows an example of how algebra and geometry are entwined in a tessellation.  Let a, b, and c each be the color represented in the second triangle.  When you add the color a+b, you are given this new color.  Each different triangle in the second BIG triangle is represented by some algebraic expression. 

Below is the tessellation that I worked on in class.  I had a lot of fun with this activity which is why I decided to research it further. 

Within this blog, I also touched a little bit on the history of the House of Wisdom, as well as the connection between geometry and algebra.  Tessellations are such an interesting subject.  A tessellation is known as pictures or tiles, which cover the surface of a plane in a symmetrical way without overlapping or leaving gaps.  Symmetry is a big mathematical idea in tessellations.  There are 17 possible ways for a pattern to tile a surface without overlapping or leaving gaps.  There are also four different ways of moving a motif to another position in the pattern: translation, reflection, rotation, and glide reflection.  I absolutely encourage anyone to visit this website (first website listed under source) which was used as a source for the information in this blog post.  It has some awesome examples of tessellations and is filled with even more information.  Below are some tessellations that really appealed to me.

                                                  

Source:

http://www.csun.edu/~lmp99402/Math_Art/Tesselations/tesselations.html

http://www.storyofmathematics.com/islamic.html