A tessellation is basically a way to tile a floor (that goes on forever) with shapes (called tiles) so that there is no overlapping and no gaps. We typically look at using a tile of the same shape repeatedly (think of a floor of square tiles or a walkway of rectangular bricks). Sometimes we use two shapes or more in a tessellation. We often use polygons (a polygon is a closed plane figure made by joining line segments, like a rectangle, a triangle, a stop sign shape) to tessellate (or tile) surfaces. You can find out most of what you might want about using polygons to tesselate at this link.
One of the most famous creator of tessellations was MC Escher, who created a large number of tessellations featuring recognizable figures as the tiles. He performed explorations to catalog all of these kinds of tessellations — see some of his sketches here. You can find lots of instructions about creating different kind of tessellations online, here are a few examples:
- Video: https://www.youtube.com/watch?v=ZNVyrxdlrGQ (this is based on a square tessellation)
- Video: https://www.youtube.com/watch?v=212XC1zfxXY (this is based on a tessellation by equilateral triangles)
- Directions for several kinds of tessellations can be found here: http://euler.slu.edu/escher/index.php/Tessellations_by_Recognizable_Figures
- This will automatically create tessellation as you edit a triangle, square, or hexagon: http://www.shodor.org/interactivate/activities/Tessellate/
Practice with tessellations, seeing what you can do by hand and on computers. Look around at the work of MC Escher and other work for inspiration. For your response this week, focus on either creating tessellations or finding tessellations and wallpaper patterns in the outside world — they really are everywhere. Send along some images and we will discuss them in my next class. Also think about what kinds of symmetry all of these images have — rotation, reflection, translation, and glide reflection.
Oh, and for thos of you interested in frieze patterns, paper dolls that you cut in strips form a frieze pattern, check this out: http://www.origami-resource-center.com/kirigami-for-kids.html