The Mathematical Art Of M.C. Escher

Tessellations & Transformations Tessellations can be modified by using transformations. As you know, transformations are movements of geometric figures. One transformation, commonly used to create tessellations is a slide, or translation, of a figure.

Translation Tessellations For simple translation tessellations, polygons should have opposite sides that are parallel and congruent – squares, hexagons, parallelograms.

Example: Translation Tessellation You can create more complex designs starting with square tessellations and making changes on both pairs of sides.

Depending how you decide to color your tessellation, a very simple design can have a very creative result.

Glide Reflection Tessellation For glide reflection tessellations, polygons should have opposite sides that are parallel and congruent – squares, hexagons, parallelograms.

Example By reflecting and gliding over more than one side, you can create a more complex tessellation.

Adding coloring and features will enhance the artwork.

Tessellation created by Rotation Adjacent sides must be congruent – squares, equilateral triangles, regular hexagons, rhombi

Midpoint Rotations Triangles, Squares, and Quadrilaterals Note: More than one side may be altered for more challenging designs. Coloring one side of the pattern will help prevent accidental flipping during tracing.

Example: Rotational Tessellation

Rubric and Examples 1 – Does not meet expectations   1 – Does not meet expectations 2 – Approaching expectations 3 – Meet expectations 4 – Exceeds expectations SCORE Complexity of Template No effort was put into improving the tessellation template. A fair attempt was made to increase the complexity of the tessellation template. The tile design used a basic drawing. The tile design showed one form of transformation (Translation, Reflection or Rotation). A good attempt was made to increase the complexity of the tessellation template. The tile design used more creative drawing. An excellent attempt was made to create an appealing piece of art. The tile design used exceptional creative drawing. The tile design showed more than one form of transformation (Translation, Reflection or Rotation). Creativity of Tessellation design Plain no effort was made. Some effort was made to enhance the design. Good creativity on the design. Great creativity on the design. Neatness Messy, smudges. Design not moved correctly, major gaps or spaces throughout the design. Somewhat neat. Shape is not moved correctly, slight gaps or spaces throughout the design. Neat. Shape is moved correctly but pattern “shifts” or “tilts” throughout the design Neat. Shape is moved correctly and there are no gaps or spaces throughout the design. Colorfulness No colors used (pencil only) One or two colors used. Three colors used. More than 3 colors used.