Rational and irrational numbers

Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

Can you work out where the blue-and-red brick roads end?

Which of these triangular jigsaws are impossible to finish?

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

Can you make a square from these triangles?

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.