Squares

  • Circle Box
    problem

    Circle Box

    Age
    14 to 16
    Challenge level

    It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?

  • Folding Fractions
    problem

    Folding Fractions

    Age
    14 to 16
    Challenge level

    What fractions can you divide the diagonal of a square into by simple folding?

  • Small pepper seedlings in turquoise pots.
    problem

    Unusual Polygon

    Age
    14 to 16
    Challenge level

    What is the perimeter of this unusually shaped polygon...

  • Similarly so
    problem

    Similarly So

    Age
    14 to 16
    Challenge level

    ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

  • A Tilted Square
    problem

    A Tilted Square

    Age
    14 to 16
    Challenge level

    The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

  • Trig Rules OK
    problem

    Trig Rules OK

    Age
    16 to 18
    Challenge level

    Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...

  • A Swiss sum
    problem

    A Swiss Sum

    Age
    16 to 18
    Challenge level

    Can you use the given image to say something about the sum of an infinite series?

  • 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.

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