are patterns of shapes that fit together without any gaps way to tile a floor that goes on forever ...

Tessellations

Regular, Semi regular and irregular

Tessellations

Are patterns of shapes that fit together without any gaps

Way to tile a floor that goes on forever

Puzzles are irregular tessellations

Artists

Regular Tessellations

Made from regular polygons with equal sides and angles

Triangles, squares, hexagons

The Three Rules

RULE #1:   The tessellation must tile a floor (that goes on forever) with no overlapping or gaps.

RULE #2:  The tiles must be regular polygons - and all the same.

RULE #3:   Each vertex must look the same.

Not a regular tessellation

Heptagon

Pentagon

More than 6 sides WILL OVERLAP

Semi-regular Tessellations

These tessellations are made by using two or more different regular polygons.

The rules are still the same. Every vertex must have the exact

same configuration.

M. C. Escher

Lived from 1898 to 1972. He was a Dutch artist who came to specialize in

patterns that tessellated He took the boring square and looked at it

mathematically. If you took some off of one side, and added it to

the opposite side, even if what you took was a funny piece, you created a pattern.

He experimented in rearranging space in very creative ways! His tessellations are the most famous in the world!

Irregular Tessellations