I have been modelling parallel curves to a parabola and realise if the parallel curve to a parabola is offset enough then the curve will overlap.
I came across this research paper to explain why a parallel curve to a parabola is not a parabola: http://apollonius.math.nthu.edu.tw/d1/disk5/js/geometry/osc/0.pdf However it does not give a mathematical explanation as to why the parabola invokes or evokes (in laymans terms overlaps itself)
Does it have anything to go with the focal length. ie If the focal length is less than the curve offset then it will invoke/evoke
Any I using the terms evoke and invoke correctly to state that a parallel curve overlaps itself.