By Julia Heinly, Reagan Roeber, and Paige Haskins Tessellation Project A tessellation is a pattern made of identical shapes.

The shapes must fit together without gaps and the shapes should not overlap and each vertex should look the same.

A polygonal tessellation is a pattern consisting of polygons that fit together to form a plane.

A non-polygonal tessellation is a pattern of non-polygonal shapes consisting of at least one curved side, that fit together to form a plane. What are tessellations? Non-Polygonal Tessellation: Not all polygons tessellate a plane. These are some that do:

-Equiangular Triangle

-Square

-Hexagon

Others can't because a full 360 degrees will not divide evenly among the interior angles of some polygons. In fact, all polygons with more than six sides won't tessellate because they'll overlap! http://psd.tutsplus.com/articles/web/31-icon-design-tutorials/

http://www.mathisfun.com/definitions/tessellation.html

http://answers.yahoo.com/question/index?qid=200904281012AAZ2kgr

http://www.beva.org/math323/asgn5/tess/regpoly.htm

http://mathworld.wolfram.com/Tessellation.html

http://www.exploratorium.edu/geometryplayground/Activities/GP_Activities_3-5/MakingATranslastionTessellation_3-5_v5.pdf

http://www.coolmath4kids.com/tesspag1.html

http://mathworld.wolfram.com/Tessellation.html

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

http://cstl-csm.semo.edu/tansil/123/Geometry/tessellation.pdf Credits Polygonal Polygonal Non-Polygonal Non-Polygonal These polygons all tessellate a plane because the measures of their interior angles divide evenly into 360 degrees. 360/6 = 60 360/4 = 90 360/3 = 120 An 11-gon does not tessellate a plane because it has eight interior angles and 360/11 = 32.727272... Step 1: Step 2: Step 3: Irregular Polygon: Step 1: Step 2: Step 3: Polygonal Tessellation Polygonal Tessellation Personal Inputs There are many ways that you can repeat a shape so that it tessellates.

Translation/Slide:

Sliding the figure without rotating, flipping, or changing the actual shape.

Rotation/Turn:

Spinning the figure around a certain point. You can't change the point as you tessellate and you have to keep the rotation constant.

Rotation at midpoints:

Chose a side of a figure and draw a line from one vertex to the midpoint along that side. Cut out the segment, and rotate the segment 180 degrees around the midpoint. Attach that segment to the original line and repeat the technique using rotation. Paige

For this project, we all worked together to create our tessellations. In class, we worked together to define polygonal and non-polygonal tessellations and some of the other questions that we could answer. Separately, we all created one of the three tessellations. Personally, I created the irregular tessellation. Rotation/Turn Example Translation/Slide Example Rotation at Midpoint Reagan

We completed the project by each of us doing specific things here and there. We all worked together as a group for the most part. I contributed to this group project by helping with all of the definitions and I specifically created the non-polygonal tessellation as my personal part. I also helped with defining the ways to tessellate shapes. Julia

For our project we each did little random parts and put them together to create the final product. On our ICP day, we worked without the computer and looked at our assignment sheet and we all came up with the definitions for tessellations and answered all of the questions required. Then I came home and started the SMART Notebook file. I made the regular polygonal tessellation and also provided the examples for the questions and methods we had to explain through visual representation. After finding out SMART Notebook was not going to work, I transferred everything to PowerPoint. Then I realized I would have to bring my computer in to school if I kept it on PowerPoint so I transferred everything once again, on to Prezi.

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# Tessellation Project

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