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An introduction to proof by contradiction
An introduction to proof by contradiction, a powerful method of mathematical proof.
Reasoning, convincing and proving
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articlePrimary proof?
Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level. -
articleThe golden ratio, Fibonacci numbers and continued fractions
An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.
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articleThe dangerous ratio
This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying. -
articleLogic
What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article. -
articleParadoxes
A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself. -
articleSome circuits in graph or network theory
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits. -
articleSprouts explained
This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with significant food for thought. -
articleGo forth and generalise
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important. -
articleEuclid's algorithm II
We continue the discussion given in Euclid's Algorithm I, and here we shall discover when an equation of the form ax+by=c has no solutions, and when it has infinitely many solutions.