
A rafter of fixed length L is moved in a coordinate system such, that begin and end are on the x,y axis.
The yellow colored area is covered as the the rafter changes position.
Question: calculate the equation of the curve that is the boundary between touched (yellow) and untouched (white) areas.
The rafter (or ladder) touches the ground at position x.
It touches the wall (vertical axis) at height y.
At horizontal position p the curve is touched at height h.
Because of similarity :
To find the maximum of h we calculate h'= dh/dx.
p is the place for maximal h if the ladder touches the ground at x.
Substitution in ...1) :
An amazing result.

