Iteration

  • Peaches in General
    problem

    Peaches in General

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.
  • Triangle Incircle Iteration
    problem

    Triangle Incircle Iteration

    Age
    14 to 16
    Challenge level
    filled star filled star filled star
    Keep constructing triangles in the incircle of the previous triangle. What happens?
  • Dalmatians
    problem

    Dalmatians

    Age
    14 to 18
    Challenge level
    filled star empty star empty star
    Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.
  • Difference Dynamics
    problem

    Difference Dynamics

    Age
    14 to 18
    Challenge level
    filled star empty star empty star
    Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
  • Archimedes Numerical Roots
    problem

    Archimedes Numerical Roots

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

    How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

  • A Very Shiny Nose?
    problem

    A Very Shiny Nose?

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

    This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.

  • V-P Cycles
    problem

    V-P Cycles

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

    Form a sequence of vectors by multiplying each vector (using vector products) by a constant vector to get the next one in the seuence(like a GP). What happens?

  • Ford Circles
    problem

    Ford Circles

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

    Can you find the link between these beautiful circle patterns and Farey Sequences?