Hide Ads About Ads. Tessellation A pattern of shapes that fit perfectly together! Examples: Rectangles. Octagons and Squares. Different Pentagons. Triangles 3. Squares 4. Another place in art to see tessellations is in the work of M. Escher was actually inspired by the geometric figures covering the walls and floors of the Alhambra. He created mathematical woodcuts, sketches, and lithographs that utilized tessellations and symmetry.
Today, M. Thin cardboard like from a cereal box cut into a rectangle. Colored pencils, crayons, markers or other coloring material of your choice. Draw a design on either the top or bottom and either the left or right of the rectangle. Cut out the designs and move them to the opposite side of the rectangle. Tape together. Trace your stencil on the piece of paper to tessellate your design.
Maybe the shapes remind you of your favorite animal—we thought ours looked like chickens—make your tessellation look like that! McAuliffe Shepard Discovery Center. Activities that explore astronomy, aviation, earth and space science. View fullsize. Colored pencils or crayons optional. Regular Polygons Print-Out. All regular tessellations:. There are three regular shapes that make up regular tessellations: the equilateral triangle, the square and the regular hexagon.
For example, a regular hexagon is used in the pattern of a honeycomb, the nesting structure of the honeybee. Semi-regular tessellations are made of more than one kind of regular polygon. Within the limit of the same shapes surrounding each vertex the points where the corners meet , there are eight such tessellations.
Each semi-regular tessellation is named for the number of sides of the shapes surrounding each vertex. For example, for the first tiling below, each vertex is composed of the point of a triangle 3 sides , a hexagon 6 , another triangle 3 and another hexagon 6 , so it is called 3.
Sometimes these tessellations are described as "Archimedean" in honor of the third-century B. Greek mathematician. In the language of mathematics, the shapes in such a pattern are described as congruent. Every triangle three-sided shape and every quadrilateral four-sided shape is capable of tessellation in at least one way, though a select few can tessellate in more than one way. A few examples are shown below:.
According to mathematician Eric W. Weisstein of Wolfram Research's MathWorld , for pentagons, there are currently 14 known classes of shapes that will tessellate, and only three for hexagons.
Whether there are more classes remains an unsolved problem of mathematics. As for shapes with seven or more sides, no such polygons tessellate unless they have an angle greater than degrees. Such a polygon is described as concave because it has an indentation. A few examples of pentagonal tessellations are shown below.
The 14 classes of pentagonal tessellation can all be generated at the Wolfram Demonstration Project.
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