# Difference between revisions of "Tessellation Exploration: The Basics"

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{{Exploration}} | {{Exploration}} | ||

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− | {{Objective| Find a method to tessellates the plane with any triangle. Introduce regular and semi-regular tessellations.}} | + | {{Objective|Find a method to tessellates the plane with any triangle. Introduce regular and semi-regular tessellations.}} |

==Tessellations by Triangles and Quadrilaterals== | ==Tessellations by Triangles and Quadrilaterals== | ||

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<li> Convince yourself that the parallelogram below will tessellate the plane. Draw your tessellation on a separate piece of paper. It should cover 1/4 of your page. | <li> Convince yourself that the parallelogram below will tessellate the plane. Draw your tessellation on a separate piece of paper. It should cover 1/4 of your page. | ||

− | [[Image:Parallelogram.png|center]] | + | [[Image:Parallelogram.png|center|300px]] |

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+ | <li> Show that a square tessellates the plane and show that a rectangle tessellates the plane. Your tessellations should cover 1/4 of your page. | ||

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+ | <li> Draw an acute, an obtuse and a right triangle. Now convince yourself of the fact that two congruent copies of the same triangle fit together to form a parallelogram or a rectangle. | ||

+ | |||

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+ | <li> Why does this imply that all triangles will tessellate the plane? | ||

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+ | ==Tessellations of the Plane by Regular Polygons== | ||

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+ | A {{define|regular tessellation}} is a tessellation made of regular, congruent, convex polygons. | ||

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+ | |||

+ | A {{define|semi-regular tessellation}} is a tessellation made of regular polygons of two or more types so that the arrangement of polygons at each vertex is the same. | ||

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+ | <li> What is the common name for a regular 3-gon? | ||

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+ | <li> What is the common name for a regular 4-gon? |

## Revision as of 12:34, 18 May 2007

**Objective:**
Find a method to tessellates the plane with any triangle. Introduce regular and semi-regular tessellations.

## Tessellations by Triangles and Quadrilaterals

- Convince yourself that the parallelogram below will tessellate the plane. Draw your tessellation on a separate piece of paper. It should cover 1/4 of your page.
- Show that a square tessellates the plane and show that a rectangle tessellates the plane. Your tessellations should cover 1/4 of your page.
- Draw an acute, an obtuse and a right triangle. Now convince yourself of the fact that two congruent copies of the same triangle fit together to form a parallelogram or a rectangle.
- Why does this imply that all triangles will tessellate the plane?
## Tessellations of the Plane by Regular Polygons

A

**regular tessellation**is a tessellation made of regular, congruent, convex polygons.

A**semi-regular tessellation**is a tessellation made of regular polygons of two or more types so that the arrangement of polygons at each vertex is the same.

- What is the common name for a regular 3-gon?
- What is the common name for a regular 4-gon?