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Continued 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/...)).
Explaining, convincing and proving
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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? -
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. -
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. -
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articleSums 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. -
articleModulus arithmetic and a solution to differences
Peter Zimmerman, a Year 13 student at Mill Hill County High School in Barnet, London wrote this account of modulus arithmetic. -
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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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articlePicturing Pythagorean triples
This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.