A tessellation is the
name given to a pattern of repeating, interlocking shapes. The
shapes are repeated indefinitely without gaps or overlaps. If the
shape is a polygon, the tessellation may be referred to as a tiling.
STUDENT CREATED TESSELLATIONS:
Geometric figures tessellate: equilateral
triangles, parallelograms, rhombuses, rectangles, squares, hexagons.
Ask students to create their own personal tessellation using a geometric
shape. Students must be ready to describe what transformations
occurred in their creations. Tessellations can be hand-drawn or
produced with dynamic software. If the diagram is hand-drawn, have
students create a template of the shape being used, so that the
repetitions are congruent shapes.
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What geometric transformation(s)
occurs in this tessellation? |
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What geometric transformation(s)
occurs in this tessellation? |
To create a more exciting tessellation, start with a geometric
shape and cut out any shape. Translate the cut-out shape
vertically to the
top of the geometric shape to form a new shape that will tessellate.
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Start with a geometric shape.
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Cut out and translate vertically. |
THE WORK OF M. C. ESCHER:
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Some
of the most famous tessellations were created by artist M.
C. Escher. Escher's works are wonderful examples of
transformations. Reflections, translations, dilations and
rotations are abundant in Escher's art work.
Escher's works appear in countless mathematical textbooks,
while posters of the famous prints adorn classrooms.
To see the works of M. C. Escher, visit these sites:
http://gauss.technion.ac.il/~rl/M.C.Escher/
http://www.worldofescher.com
Show
students several of M. C. Escher's works. Ask
students to describe what transformations are occurring in
the pictures.
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