TESSELLATIONS
The tessellations are patterns made of identical shapes:
• the shapes must fit together without any gaps
• the shapes should not overlap
REGULAR TESSELLATIONS
A regular tessellation is a pattern made by repeating a regular polygon. It is a regular division of the plane.
There are only 3 regular tessellations:
Squares Triangles Hexagons
SEMI-REGULAR TESSELLATIONSA semi-regular tessellation is made of two or more regular polygons. The pattern at each vertex must be the same!
There are only 8 semi-regular tessellations:
MODULE
A module is a regular or irregular form that makes a uniform surface by repeating itself a specific number of times and in a certain order.
In this image the module is the octopus |
The Nazari tessellations are created by the transformation of a basic geometric shape. The final figure has the same surface as the original but the shape is different.
TRANSFORMATIONS
To modify the modules we can use three concepts:
-Translation
- Reflection
- Rotation
1. Translation
To translate means to move a figure to a new location with no other changes.
-Translation
- Reflection
- Rotation
1. Translation
To translate means to move a figure to a new location with no other changes.
2. Reflection
The reflection is a transformation where each point in a shape appears at an equal
distance on the opposite side of a given line - the line of reflection.
3. Rotation
A transformation where a figure is turned about a given point.
HOW TO CONSTRUCT TESSELLATIONS
To draw your own tessellation you can start with a square (or other basic geometrical shape) and make the transformations.
1. Translation
Click on the picture to practise this method.
2. Reflection
2. Reflection
M.C. Escher
Maurits Cornelis Escher (1898-1972) was a great artist who studied deeply this technique.
He became fascinated by the regular Division of the Plane,
when he first visited the Alhambra in 1922. He made 137
Regular Division Drawings in his lifetime.
You can find more artworks here
http://www.mcescher.com/gallery/symmetry/
And now you can visit an exhibition in Madrid:
http://www.rtve.es/noticias/20170201/mundos-imposibles-escher-llegan-madrid/1482166.shtml
1. Start with a square
2. Draw a design on of side of the square
3. Cut the design piece out and make one of the three types of transformations (or the three)
4. Tape it tho the square
5. Trace the design on your white paper until it is covered completely
Marking criteria:
- Pattern tessellates the plane
- Module or template with modifications (at least 1 type)
- Neatness
- Creatitivity
- Effort
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