Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?
Can you make a square from these triangles?
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
Using the interactivity, 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 ?
Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.
Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
Tim Rowland introduces irrational numbers
An introduction to proof by contradiction, a powerful method of mathematical proof.
What fractions can you find between the square roots of 65 and 67?
Prove that if a is a natural number and the square root of a is rational, then it is a square number (an integer n^2 for some integer n.)
In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
Which of these triangular jigsaws are impossible to finish?
Can you work out where the blue-and-red brick roads end?
This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how. . . .
This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.
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.
Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.
Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
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?