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Sum the series
This article by Alex Goodwin, age 18 of Madras College, St Andrews
describes how to find the sum of 1 + 22 + 333 + 4444 + ... to n
terms.
Conjecturing and generalising
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articleWhy stop at three by one
Beautiful mathematics. Two 18 year old students gave eight different proofs of one result then generalised it from the 3 by 1 case to the n by 1 case and proved the general result.
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articleMagic squares
An account of some magic squares and their properties and and how to construct them for yourself. -
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articleFractional calculus I
You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.
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articleFractional calculus II
Here explore some ideas of how the definitions and methods of calculus change if you integrate or differentiate n times when n is not a whole number.
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articleFractional calculus III
Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.
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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. -
articleWinning lines
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games. -
articleGames related to Nim
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.