This document provides an overview of tessellation through animated demonstrations and examples. Tessellation is defined as using shapes to cover a flat surface without gaps or overlaps. Only some shapes like triangles, hexagons, and rectangles can tessellate. Regular tessellations use one shape with equal vertex angles, while irregular tessellations mix shapes. Tessellation is used in areas like tiling, packaging, and M.C. Escher artwork which transform shapes through translations, rotations, and reflections.

1. Tessellation – Demonstration
This resource provides animated demonstrations of the mathematical method.
Check animations and delete slides not needed for your class.

2. Denise wants to tile her bathroom.
Which shape tiles could she use?
To stop water leaking, the tiles must join together with no gaps.

3. Rectangles
Tessellation
Only some shapes can fill a plane (flat surface) without any gaps.
For example…
Triangles
Hexagons

4. Many shapes don’t tessellate.
There will always be gaps.
How could we fill the gaps?

5. Tessellation
Roman mosaic
(2000 years old)
‘Using shapes to cover a flat surface,
with no gaps and no overlaps’
tessella:
small cubes used to
make mosaics.
Hexagonal shower tiles
Modern Moroccan mosaic
tessellate:
to create a tessellation

6. Regular tessellations
One type of shape &
vertices (corners) with equal angles.
Only 3 shapes can do this.
Irregular tessellations
Any mix of shape or shapes.

7. As well as on a plane (flat surface),
we can also tessellate in 3D space!
When we package goods
(like food & drinks),
why do we want the shapes to tessellate?
Rhombic
dodecahedrons

8. At each vertex,
what is the total of the angles?
Why is this important?
120° × 3
60° × 6
90° × 4
Where tiles meet,
the interior angles must total 360°
so there are no gaps.

9. Which shapes do you think will tesselate?
Do we need do change the orientation of the shape to make it tessellate?
reflect, or rotate?

10. We can tesselate shapes using 3 transformations.
Translate
move the shape
Rotate
spin the shape
Reflect
mirror the shape

11. Maurits Cornelis Escher
1898 –1972
M. C. Escher was a Dutch graphic artist who
used maths in lots of his artwork.
He was interested in transforming shapes.
‘Day and Night’
1938

12. How can you describe this tessellation?
translation

13. How can you describe this tessellation?
reflection

14. How can you describe this tessellation?
rotation

15. How can you describe this tessellation?
reflection

16. How can you describe this tessellation?
translation

17. How can you describe this tessellation?
reflection

18. How can you describe this tessellation?
rotation

19. How can you describe this tessellation?
2 different shapes, translated

20. Questions?
Comments?
Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to email:
tom@goteachmaths.co.uk