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Home School Life Journal ........... painting by Katie Bergenholtz
"Let us strive to make each moment beautiful."
Saint Francis DeSales

Escher and Tesselations: Art & Math Meet


Escher's lithographs really highlight his interest and proficiency in mathematics as well as art.
For there to be a true tessellation, three things are necessary: 1) there must be no gaps between the shapes, 2) there are no overlays, and 3) there is a pattern of shapes that repeats itself and can be extended.
A checkerboard or a honeycomb fit this criteria but Escher takes this idea one step further and makes his patterns interweave with other concepts. In Day and Night, the black and white birds not only tessellate but they also turn into the fields below. In Circle Limit III, he has two types of fish that link together through tessellation but introduces the concept of perspective as well, with the tessellation growing smaller until it fades around the edge. The boys wanted to get magnifying glasses to see if they could determine where the end was.

Build tessellations, bit by bit,
Repeating patterns, perfect fit,
Like checkerboards or bathroom tiles.
Make patterns stretch for miles and miles,
Remember: There can be no gap;
All shapes must fit, not overlap. -GEMS Build It!

To give them some hands-on experience with tessellations before attempting to make your own Escher-style art work, you can have your students fill in tessellation masters from the GEM's Build It! guide.
Your students may have a harder time with this project than most art projects, but hopefully it will then give them a greater appreciation for Escher's mastery.
Start with a square of cardstock. Cut a piece from one side of the square and taped it to the opposite side. Do the same procedure with the top and bottom. You now had a shape that you can tessellate as each bump will fit perfectly into each recess. Now trace the shape over and over onto white paper, making sure the edges touch. Color the shapes into patterns. Mount them on colored construction paper backgrounds. If you wish, you could also make a picture out of your shape, such as a bird, fish or frog, however, my students found it enough of a challenge just to have abstract tessellations.



4 comments:

  1. Awesome! Thank you for inviting me over! ;)

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  2. Just took some time to look around at more entries. I LOVE your blog! Can we come school with you??? ;) Thanks again for pointing it out.

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  3. One more thing... I was looking at the list of issues that you're dealing with in your family. I don't want to be annoying, but do you know about "neuro reorganization?" We did it for several years with one of our kiddos. You can learn more on the Yahoo group NEUROnetwork. Or you can email me through my email on the math forum. (I don't do this professionally...I just know of it from a parent's perspective.) You are doing some amazing work.

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  4. Thank you for your kind words. It does seem that we have a similar style of teaching. You are not annoying at all...thanks for the suggestion. I will look it up!
    -Phyllis

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Thank you so much for taking the time to comment. It means so much.