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Because many teachers are aware of the mathematical relationships involved in creating Escher-type tessellations, they are able to use his drawings to illustrate geometric concepts such as reflections, glide reflections, translations, and rotations. Additionally, it is also possible to discuss the mathematics that allowed Escher to create images that are paradoxical and figures that are impossible.
Therefore, I have created an activity that involves two challenges. The first requires students to answer a question from an Escher tribute poem by use of appropriate coordinates for certain balls located inside a 3D grid. The second challenge to students is to illustrate that a certain point can appear to be in different locations in space depending upon the path taken to arrive at those positions.
The "Tribute to M.C. Escher" poster can be used as an individual challenge for an in-class activity or as a take-home activity for students who are familiar with three-dimensional coordinate geometry. Although the challenge of this activity is to identify what has caused such dissension in Escher’s work, it is hoped that students will also examine some of Escher’s drawings to see how he intertwined mathematics with art.
The “Three Dimensional Challenge” can be used in conjunction with the first activity or as a separate challenge. It to can be used as either an in-class or take-home activity. It requires students to be able to visualize different rectangular prisms with three-dimensional coordinate geometry.