Three examples of particular tilings of the plane, namely those
where - NOT all corners of the tile are vertices of the tiling. You
might like to produce an elegant program to replicate one or all of
Stage: 4 and 5 Challenge Level:
You might like to make a tessellation with copies of $\Delta ABC$
and three triangles drawn on the sides of $\Delta ABC$ and prove
your conjecture from the tessellation. This uses only elementary
geometry. An alternative method is to use the Cosine Rule.
Alternatively you can use vectors or complex numbers.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.