Rational and irrational numbers

problem
Favourite

Repetitiously

Age

14 to 16

Challenge level

Can you express every recurring decimal as a fraction?
problem
Favourite

The Root of the Problem

Age

14 to 18

Challenge level

Find the sum of this series of surds.
problem

Good Approximations

Age

16 to 18

Challenge level

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
problem

Spirostars

Age

16 to 18

Challenge level

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?
problem

Making Rectangles, Making Squares

Age

11 to 14

Challenge level

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
problem

Equal Equilateral Triangles

Age

14 to 16

Challenge level

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

Rationals Between...

Age

14 to 16

Challenge level

What fractions can you find between the square roots of 65 and 67?
problem

The Square Hole

Age

14 to 16

Challenge level

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

Proof Sorter - The Square Root of 2 Is Irrational

Age

16 to 18

Challenge level

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.
problem

Be Reasonable

Age

16 to 18

Challenge level

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.