I apologize for this being turned in so late. I was looking through my canvas the other day and I saw I didn't have a grade for this blog even though I remembered writing about it. I went to my blog and somehow I made the blog private and saved it in my drafts instead of publishing it. I apparently also forgot to email my link to you. I am so sorry for this being turned in so late! - Seth
For this blog I decided to explore
the topic of tessellations. The earliest
time I can remember seeing tessellations was in 6th grade. I remember seeing a poster of a sketch by MC
Escher. Here is a link to that piece of work: http://brettworks.files.wordpress.com/2012/04/escher_reptiles.jpeg
Anyway, I remember looking at the reptile tessellation in
that sketch nearly everyday during my first year at the Academy. Eventually I became fairly interested in
tessellations and did some research of my own into the subject. I found out
that there is only three tessellations that are composed of regular polygons
that symmetrically tile. These three
shapes are triangles, squares, and hexagons. This is because each of these
shapes has interior angles that are divisible by 360 (60, 90, and 120
respectively). Thus, only a shape with an interior angle that is a divisor of
360 can tessellate.
One
tessellation of this kind that is seen frequently in nature is the hexagonal
tessellation. This is more commonly recognized as the honeycomb. Bees
tessellate their hives for many reasons. One of the reasons is because it
allows for maximum storage within a small space.
However,
there are other types of tessellations. There are 8 tessellations that combine
two or more regular polygons in the same order each vertex are known as semi-regular
tessellations. I have also seen these referred to as Archimedean tessellations.
Here is an awesome picture of semi-regular tessellated tile: http://euler.slu.edu/escher/upload/3/30/Semi-regular-Seville.JPG
Finally,
there are 14 possible combinations for demi-regular tessellations. These are
composed of the eight semi-regular and three regular tessellations. One place
where this kind of tessellation is prevalent is in Islamic architecture and
art. I found this neat picture: https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzbsBH5pOmBatDgnq6MJrjCafYEgAs3NFCrG7OgVU8oVu3UGsjZc9z57uWoHvKtfXAkxX-QP7BmD_I_4d7Jv4ZkI9LCUGz9UZXm7RkGaCC2HIgFdQObgcqpGFh1a87Y6vczqajqAPpMyg/s1600/DSC00101.JPG
