Escher's Tessellation
This course will cover two types of Escher's Tessellations
- based on altering opposite parallel sides
- based on rotations
Exploration 1: Altering Opposite Parallel Sides (Translation)
Challenge:
Cut a shape out of one side of your square. Slide (translate) that piece directly across to the exact opposite side and tape it down.
cut and slide another shape for the other pair of parallel sides if you wish.
Alternatively, you may use the grid below to construct the shape.
Evaluation Focus:
Does the modification on the left side 'cancel out' the modification on the right?
What translation vector (x, y) did you use to move your cut-out?
*Note: The vector must be equal to the side length of the polygon
Exploration 2: Rotational Tessellations
Challenge:
Choose a vertex (corner) of your shape (equilateral triangle / square). Cut a piece out of one side connected to that vertex.
Instead of sliding it, rotate the piece around that vertex until it ends up on the adjacent side.
Alternatively, you may use the grid above to construct the shape.
Evaluation Focus:
Which isometric transformation is used?
Compare the rotation angle with the interior angle of the initial polygonal shape used.
*Note: The rotation angle should match the interior angle of the polygon
Example: Evaluating an Escher's Tessellation motif
Original shape:
Cut out the green shape on the left side of the square and translate across the opposite parallel side:
Cut out a yellow triangle on the bottom side and translate across the opposite parallel side of the square:
The new shape looks like this now:
Based on the patterns below, evaluate the motif and type of isometric transformation that occur.
