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Sums of squares and sums of cubes
An account of methods for finding whether or not a number can be written as the sum of two or more squares or as the sum of two or more cubes.
Explaining, convincing and proving
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articleTransitivity
Suppose A always beats B and B always beats C, then would you expect A to beat C? Not always! What seems obvious is not always true. Results always need to be proved in mathematics. -
articleModulus arithmetic and a solution to dirisibly yours
Peter Zimmerman from Mill Hill County High School in Barnet, London gives a neat proof that: 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n. -
articleThe frieze tree
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another? -
articleContinued fractions II
In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
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articleImpossible sandwiches
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot. -
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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articleSperner's lemma
An article about the strategy for playing The Triangle Game which appears on the NRICH site. It contains a simple lemma about labelling a grid of equilateral triangles within a triangular frame.