# Pythagoras Tessellation Project

### All About Tessellations

## What is a tessellation?

**A tessellation is created when a shape is repeated over and over again, showing nothing on the page but the shape, except the shapes must not overlap.****Dictionary's meaning:**

** **A

**tessellation**of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics,

**tessellations**can be generalized to higher dimensions. A periodic tiling has a repeat pattern.

## The properties of a tessellation.

**The properties of tessellations are:**

**1. The shapes don't over lap**

**2. It fits together**

**3. Each of the vertex's have the same pattern **

**4. It doesn't have any gaps. **

## Translation Tessellation A translation tessellation is a shape that is simply translated, or slid, across the paper and drawn again in another place. The translation does not turn or flip. | ## Reflection Tessellation A reflection tessellation is a shape that has been flipped. Most commonly flipped directly to the left or right (over a "y" axis) or flipped to the top or bottom (over an "x" axis), reflections can also be done at an angle. If a reflection has been done correctly, you can draw an imaginary line right through the middle, and the two parts will be symmetrical "mirror" images. To reflect a shape across an axis is to plot a special corresponding point for every point in the original shape. | ## Rotation Tessellation Rotation is spinning the pattern around a point, rotating it. A rotation, or turn, occurs when an object is moved in a circular fashion around a central point which does not move. |

## Translation Tessellation

The translation does not turn or flip.

## Reflection Tessellation

If a reflection has been done correctly, you can draw an imaginary line right through the middle, and the two parts will be symmetrical "mirror" images. To reflect a shape across an axis is to plot a special corresponding point for every point in the original shape.

## Escher's Tesselations

Many people have tried to re-create his work because how good it looks, Escher mostly uses black and white in his tessellations to add more of an effect except, if Escher does use colour in his tessellations the tessellation will turn out very colourful.