Visualising and representing

  • Kite in a Square
    problem

    Kite in a square

    Age
    14 to 18
    Challenge level
    filled star filled star empty star

    Can you make sense of the three methods to work out what fraction of the total area is shaded?

  • Vanishing point
    problem

    Vanishing point

    Age
    14 to 18
    Challenge level
    filled star filled star empty star
    How can visual patterns be used to prove sums of series?
  • Always Perfect
    problem

    Always perfect

    Age
    14 to 18
    Challenge level
    filled star filled star empty star

    Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

  • Between
    problem

    Between

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

    If you know some points on a line, can you work out other points in between?

  • Parabella
    problem

    Parabella

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

    This is a beautiful result involving a parabola and parallels.

  • Three by One
    problem

    Three by one

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

    There are many different methods to solve this geometrical problem - how many can you find?

  • Fitting flat shapes
    problem

    Fitting flat shapes

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    How efficiently can various flat shapes be fitted together?
  • Curve match
    problem

    Curve match

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

    Which curve is which, and how would you plan a route to pass between them?

  • Coordinated crystals
    problem

    Coordinated crystals

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    Explore the lattice and vector structure of this crystal.