Locus/loci

  • How far does it move?
    problem
    Favourite

    How Far Does It Move?

    Age
    11 to 14
    Challenge level

    Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

  • Rolling Around
    problem
    Favourite

    Rolling Around

    Age
    11 to 14
    Challenge level

    A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

  • An Unusual Shape
    problem
    Favourite

    An Unusual Shape

    Age
    11 to 14
    Challenge level

    Can you maximise the area available to a grazing goat?

  • Speeding up, slowing down
    problem
    Favourite

    Speeding Up, Slowing Down

    Age
    11 to 14
    Challenge level

    Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

  • Up and across
    problem
    Favourite

    Up and Across

    Age
    11 to 14
    Challenge level

    Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

  • problem
    Favourite

    Triangles and Petals

    Age
    14 to 16
    Challenge level

    An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

  • Like a Circle in a Spiral
    problem

    Like a Circle in a Spiral

    Age
    7 to 16
    Challenge level
    A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
  • Construct the solar system
    problem

    Construct the Solar System

    Age
    14 to 18
    Challenge level
    Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
  • Symmetric Trace
    problem

    Symmetric Trace

    Age
    14 to 16
    Challenge level
    Points off a rolling wheel make traces. What makes those traces have symmetry?
  • Making Spirals
    problem

    Making Spirals

    Age
    7 to 11
    Challenge level

    Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

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