Powerpoint display of a tessellation method

1. Tessellation is the covering of a flat surface with shapes so there is no space between. This is used in tiling and mosaics, and is a very ancient science. There are many different approaches to tessellating and I will only present one here.

2. If we start off with a random shape and then try to join it up, we find that no matter how hard we try, there are spaces between.

3. So now we make up a new shape, made up of the old one PLUS the space between. And we find that this new shape does tessellate!

4. But we could also have made up a new shape like this. And this tessellates as well!

5. Or this…………

6. Or this……

7. So we have made 4 shapes that tessellate with themselves. And, guess what, they also tessellate with each other!

8. Here’s a few tessellations I designed for using as pavers or tiles. In putting these together I have used an old piece of Mac software called Claris Draw - it’s ideal for this and imports directly into PowerPoint.

9. Two pavers - self tessellating or tessellating with each other Slide 1

10. Four pavers - Each can tessellate with itself or combine to produce a 4 shape tessellation Slide 2

11. Five sided paver - Tessellation achieved by progressive 180 degree rotations Slide 3

12. Two pavers - each Self- tessellating or combined to produce 3d tessellating effect Slide 4

13. Highly interlocked tessellation Five sided paver with tessellation achieved by progressive 180 degree rotations to produce an undulating effect Slide 5

14. Tessellation achieved by progressive 90 degree rotations Slide 6

15. Highly interlinked tessellation Slide 7

16. Two pavers each self tessellating by progressive 180 degree row rotations or tessellating in pairs using the same technique Slide 8

17. Tessellation achieved by progressive 180 degree rotations Slide 9

18. Tessellation achieved by progressive 180 degree rotations Slide 10

19. Circular pattern can be tessellated in several ways