Lessons

TESSELLATIONS

How To..

 

 

 

Translation Tessellation

Rotation Tessellation

Reflection Tessellation

 

Tessellations in Appleworks

 

 

 

TESSELLATION

Patterns of geometric design are all around us. We see them every day, woven into the fabric of the clothes we wear, laid in the hallways of buildings and printed on the wallpaper of our homes. These patterns are intriguing to the eye.

There is a special class of geometric patterns called tessellation. The word tessellation comes from the Latin word tessella, which was the small, square stone or tile used in ancient Roman mosaics. Tessellations are also known as tilings or mosaics. A tessellation is a pattern made up of one or more shapes, completely covering a surface without any gaps or overlaps.

In the twentieth century, a number of artists have applied the concept of tessellating patterns in their work. The best known of these is Dutch artist M. C. Escher. He altered geometric tessellating shapes into such forms as birds, reptiles, fish, and people. Leading artists in the Op Art movement of the 1960s used tiling patterns or modifications of tiling patterns in their art works. Victor Vasarely, a Hungarian-born painter working in France, created striking designs in stark black and white as well as in vibrant colors. Another Op artist is the English painter and designer Bridget Riley, whose work shows a mastery of the characteristic visual effects of Op art, with geometrically precise patterns that vibrate and flicker before our eyes.

To better understand tessellations, let's review a few basic geometric terms and concepts.
A Plane is a two-dimensional, flat surface that is infinite.

Polygon is the general classification for plane shapes. A polygon is a simple closed shape, bounded by line segments. Polygons are named according to the number of sides and angles they contain. ie. - a triangle is 3 sided; a quadrilateral is 4 sided; a pentagon 5 sided; a hexagon is 6 sided; a heptagon is 7 sided; a octagon is 8 sided; a nonagon is 9 sided; a decagon is 10 sided

Tessellation - a covering of an infinite plane, without any gaps or overlaps, by a pattern of one or more congruent shapes.

Transformation - a movement of a figure to a new location, leaving the figure unchanged in size and shape.
Four types of transformations (movements)
1. Translation (or slide) - A transformation/movement involving a slide of a rigid figure without changing their size or shape
2. Rotation - A transformation/movement that turns a figure about a point in a plane.
3. Reflection (or a flip) - A transformation that mirrors a figure in a plane
4. Glide Reflection - A transformation that moves a figure in a slide and also mirrors it.

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