Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
Can you explain why it is impossible to construct this triangle?
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
What do these two triangles have in common? How are they related?
Investigate these hexagons drawn from different sized equilateral
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
This interactivity allows you to sort logic blocks by dragging their images.
Recreating the designs in this challenge requires you to break a
problem down into manageable chunks and use the relationships
between triangles and hexagons. An exercise in detail and elegance.
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Using LOGO, can you construct elegant procedures that will draw
this family of 'floor coverings'?