Reflections

  • Simplifying Transformations
    problem

    Simplifying transformations

    Age
    11 to 14
    Challenge level
    filled star filled star filled star
    How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?
  • Combining Transformations
    problem

    Combining transformations

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Does changing the order of transformations always/sometimes/never produce the same transformation?
  • Decoding Transformations
    problem

    Decoding transformations

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?
  • Rotations Are Not Single Round Here
    problem

    Rotations are not single round here

    Age
    14 to 16
    Challenge level
    filled star filled star filled star
    I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only one centre of rotation ? Or if you thought that was impossible, could you say why ?
  • One Reflection Implies Another
    problem

    One reflection implies another

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that was impossible, could you explain why ?
  • A Roll Of Patterned Paper
    problem

    A roll of patterned paper

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection
  • Footprints
    problem

    Footprints

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    Make a footprint pattern using only reflections.
  • Orbiting Billiard Balls
    problem

    Orbiting billiard balls

    Age
    14 to 16
    Challenge level
    filled star filled star filled star
    What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
  • Patchwork Quilt
    problem

    Patchwork quilt

    Age
    7 to 14
    Challenge level
    filled star empty star empty star
    Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?
  • Screen Shot
    problem

    Screen shot

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees before being reflected across to the opposite wall and so on until it hits the screen.