Squares

  • Zooming in on the Squares
    article

    Zooming in on the squares

    Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
  • Peg and Pin Boards
    article

    Peg and pin boards

    This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

  • Fitting In
    problem

    Fitting in

    Age
    14 to 16
    Challenge level
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    The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ
  • LOGO Challenge 5 - Patch
    problem

    LOGO challenge 5 - patch

    Age
    11 to 16
    Challenge level
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    Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

  • LOGO Challenge  - The humble square
    problem

    LOGO challenge - the humble square

    Age
    7 to 16
    Challenge level
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    Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.

  • Squares, Squares and More Squares
    problem

    Squares, squares and more squares

    Age
    11 to 14
    Challenge level
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    Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
  • Trig Rules OK
    problem

    Trig rules OK

    Age
    16 to 18
    Challenge level
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    Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...

  • Logo Challenge 3 - Star Square
    problem

    LOGO challenge 3 - star square

    Age
    7 to 16
    Challenge level
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    Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles