Shapely Tiling
Problem
Below is a pattern which can be created using a pair of compasses and a ruler, and a photograph of an Islamic Star.
Have a good look at this shape below.
What shapes can you see?
Find shapes that are the same.
Can you name the different shapes you find?
Can you produce the following tessellations:
regular octagons with two different types of triangle?
irregular hexagons with triangles and squares?
Getting Started
Experiment with colouring in different sections to make
particular shapes. How could you make a regular octagon?
Try finding as many different triangles as you can - this may help
you to see what can be done.
Student Solutions
Amanda from Wallace Hall Academy has sent us a solution to the first part of the question:
You make a regular octagon by making the outline of it with triangles. To do this, you make one quarter of the pattern (i.e. a quarter of the whole interactivity image) orange, so there is an orange square. Then you make the smaller triangles on the edges purple. Then you make the central octagon white, and you will have an octagon outlined by orange big triangles and purple small triangles.
Here is a picture of Amanda's octagon and triangles, using just one quarter of the pattern:
Ling from Beecroft Primary School, Australia has found a way of producing irregular hexagons with triangles and squares. Here is the image she sent:
Teachers' Resources
Shapely Tiling
Below is a pattern which can be created using a pair of compasses and a ruler, and a photograph of an Islamic Star.
Have a good look at this shape below.
What shapes can you see?
Find shapes that are the same.
Can you name the different shapes you find?
Can you produce the following tessellations:
regular octagons with two different types of triangle?
irregular hexagons with triangles and squares?