Regular polygons and circles

  • Cube Paths
    problem

    Cube Paths

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

    Given a 2 by 2 by 2 skeletal cube with one route 'down' the cube. How many routes are there from A to B?

  • LOGO Challenge 10 - Circles
    problem

    Logo Challenge 10 - Circles

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

    In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.

  • LOGO Challenge 6 - Triangles and Stars
    problem

    Logo Challenge 6 - Triangles and Stars

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

    Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

  • LOGO Challenge 11 - More on Circles
    problem

    Logo Challenge 11 - More on Circles

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

    Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates this relationship.

  • LOGO Challenge 12 - Concentric Circles
    problem

    Logo Challenge 12 - Concentric Circles

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

    Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.

  • LOGO Challenge - Following on
    problem

    Logo Challenge - Following On

    Age
    11 to 18
    Challenge level
    filled star filled star filled star

    Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

  • Star Gazing
    problem

    Star Gazing

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

    Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

  • Dodecawhat
    problem

    Dodecawhat

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

    Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

  • Efficient packing
    problem

    Efficient Packing

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    How efficiently can you pack together disks?