Symmetry

  • Folium of Descartes
    problem

    Folium of Descartes

    Age
    16 to 18
    Challenge level
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    Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

  • Cocked Hat
    problem

    Cocked hat

    Age
    16 to 18
    Challenge level
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    Sketch the graphs for this implicitly defined family of functions.
  • LOGOSquares
    problem

    LOGOsquares

    Age
    16 to 18
    Challenge level
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    Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

  • Mean Geometrically
    problem

    Mean geometrically

    Age
    16 to 18
    Challenge level
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    A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?
  • Cut Cube
    problem

    Cut cube

    Age
    16 to 18
    Challenge level
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    Find the shape and symmetries of the two pieces of this cut cube.
  • Colouring Triangles
    problem

    Colouring triangles

    Age
    5 to 7
    Challenge level
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    Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

  • Topkapi Palace
    page

    Topkapi palace

    These images are taken from the Topkapi Palace in Istanbul, Turkey. Can you work out the basic unit that makes up each pattern? Can you continue the pattern? Can you see any similarities and differences in the designs?
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