Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface of the water make around the cube?
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Imagine an infinitely large
sheet of square dotty paper on which you can draw triangles of any
size you wish (providing each vertex is on a dot). What areas is
it/is it not possible to draw?
Can you draw triangles of area 1, 2, 3, ... square
Can you draw a triangle with an area of 1.5 square units?
What is the area of the smallest triangle you can draw? Is this
How many triangles of of area 2 square units can you draw and
can you create "families" or "groups" of these triangles?