Explaining, convincing and proving

  • Pythagorean Triples I
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    Pythagorean triples I

    The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!

  • Pythagorean Triples II
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    Pythagorean triples II

    This is the second article on right-angled triangles whose edge lengths are whole numbers.

  • Geometry and Gravity 2
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    Geometry and gravity 2

    This is the second of two articles and discusses problems relating to the curvature of space, shortest distances on surfaces, triangulations of surfaces and representation by graphs.
  • A Knight's Journey
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    A knight's journey

    This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
  • Telescoping Functions
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    Telescoping functions

    Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.
  • Where do we get our feet wet?
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    Where do we get our feet wet?

    Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.
  • Picturing Pythagorean Triples
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    Picturing 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.

  • Why stop at Three by One
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    Why 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.

  • Magic Squares II
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    Magic squares II

    An article which gives an account of some properties of magic squares.