Rational and irrational numbers

Find the sum of this series of surds.

Can you express every recurring decimal as a fraction?

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?

Can you make a square from these triangles?

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

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

Which of these triangular jigsaws are impossible to finish?

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

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

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?