Investigate the family of graphs given by the equation x^3+y^3=3axy
for different values of the constant a.
Sketch the members of the family of graphs given by y =
a^3/(x^2+a^2) for a=1, 2 and 3.
What is the quickest route across a ploughed field when your speed
around the edge is greater?
Most people's first reaction to this
question is exactly the same as Ruth's: