Visualising and representing

problem
Folium of Descartes

Age

16 to 18

Challenge level

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
problem
Ford circles

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

Can you make a curve to match my friend's requirements?
problem
Sheep in wolf's clothing

Age

16 to 18

Challenge level

Can you work out what simple structures have been dressed up in these advanced mathematical representations?