Rational and irrational numbers
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problemImpossible Triangles?
Age16 to 18Challenge level
Which of these triangular jigsaws are impossible to finish?
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problemThe Clue Is in the Question
Age16 to 18Challenge level
Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?
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problemIrrational Arithmagons
Age16 to 18Challenge level
Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?
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problemRational Roots
Age16 to 18Challenge level
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.
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problemRational Round
Age16 to 18Challenge level
Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
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problemRoad Maker 2
Age16 to 18Challenge level
Can you work out where the blue-and-red brick roads end?
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articleAll Is Number
Read all about Pythagoras' mathematical discoveries in this article written for students.
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articleWhat Are Numbers?
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. -
articleThe Dangerous Ratio
This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.