2D shapes and their properties

  • Hex
    problem

    Hex

    Age
    11 to 14
    Challenge level
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    Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
  • LOGO Challenge 10 - Circles
    problem

    LOGO challenge 10 - circles

    Age
    11 to 16
    Challenge level
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    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
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    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 2 - Diamonds are forever
    problem

    LOGO challenge 2 - diamonds are forever

    Age
    7 to 16
    Challenge level
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    The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

  • LOGO Challenge 8  - Rhombi
    problem

    LOGO challenge 8 - rhombi

    Age
    7 to 16
    Challenge level
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    Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

  • Circles in Circles
    problem

    Circles in circles

    Age
    16 to 18
    Challenge level
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    This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.
  • Overlapping Circles
    problem

    Overlapping circles

    Age
    7 to 11
    Challenge level
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    What shaped overlaps can you make with two circles which are the same size?

  • Pentagonal
    problem

    Pentagonal

    Age
    14 to 16
    Challenge level
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    Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?
  • Central Distance
    problem

    Central distance

    Age
    11 to 14
    Challenge level
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    Weekly Problem 1 - 2006
    The diagram shows two circles enclosed in a rectangle. What is the distance between the centres of the circles?
  • First Forward into Logo 4: Circles
    problem

    First forward into Logo 4: circles

    Age
    7 to 16
    Challenge level
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    Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?