Types of Tessellations
Date: 11/15/98 at 19:42:23 From: Kathy Siegel Subject: Tessellations Dear Dr. Math, I am writing a math report on tessellations, and I must explain the mathematics involved with tessellations. However I am not exactly sure what mathematics are involved. I understand that the node must equal 360 degrees and that there can be no more then 42 sides in a polygon if it is going to be tessellated, and there can be no less then three. I figured that in my report I would explain the reasons for why there are those rules on sides but I do not know what else to write about. Please explain to me the other mathematical issues involved with tessellations. Thank you. Sincerely, Kathy Siegel
Date: 11/16/98 at 19:23:43 From: Doctor Dianna Subject: Re: Tessellations Dear Kathy, Some things you may mention in your paper include discussing regular versus semiregular tessellations. A "regular" tessellation is made up of the same regular polygon. (Remember that a regular polygon means all angles have the same degree measure and all sides are the same length.) For example, a tessellation made with only squares is called regular. Contrast that with "semiregular" tessellations which are made up of at least two different polygons. Oftentimes you will see bathroom tile using octagons and squares. Since two shapes are used we call this tessellation "semiregular." An interesting fact is that there exist only 3 regular tessellations. Regular triangles, squares, and hexagons will form tessellations of the plane by themselves. Maybe in your paper you could discuss why this is so. (The answer has to do with the fact that these angle measures are perfect divisors of 360.) M.C. Escher is an artist who makes wonderful pictures with tessellations. Maybe you could check out his work and show examples in your paper. Finally, there are tessellations that may not cover the plane, but they cover other shapes. For example, the soccer ball is a tessellation that covers a sphere. Can you think of others? For more information, here is a good introductory source, by Suzanne Alejandre, on tessellations: http://mathforum.org/sum95/suzanne/tess.intro.html Good luck with your paper! - Doctor Dianna, The Math Forum http://mathforum.org/dr.math/
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