Bow tie
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.
Age
11 to 14
Challenge level
Problem
Image
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling. The lengths AE and ED are 1 unit and the length CD is 2 units. The angles B and E are right angles and the angles A, C and D are 120 °.
Here is a printable copy for you to download, print and try yourself.
Here is an interactive that may help you.
Click on the grey shapes to create new tiles. You can rotate the pieces using the corner points.
Printable NRICH Roadshow resource.
Getting Started
You may find it helpful to cut out some accurately drawn tiles and
experiment fitting them together or to cut out one tile to use as a
template and to draw the tiling by drawing the outline of your
template over and over again.
It may help to use the relationships: 2A+D=360 ° and 2C+D=360 °.
Student Solutions
Thanks to Hannah, Sophie Rebecca of the Roos C.E Primary School, who sent in the beginnings of a solution but there is still much to do. I have added some comments below.
Firstly, we decided that we should use the rightangles on the shape
to create a 360 degree pattern. We found that the pattern made a
shape of a butterfly. We also found out that the butterfly pattern
could be joined together.
Image
