An isoperimetric type problem for primitive Pythagorean hodograph curves

An isoperimetric type problem for primitive Pythagorean hodograph curves is studied. We show how to compute, for each possible degree, the Pythagorean hodograph curve of a given perimeter enclosing the greatest area. We also discuss the existence and construction of smooth solutions, obtaining a relationship with an interesting sequence of Appell polynomials.

► An isoperimetric type problem for primitive Pythagorean hodograph curves is studied.
► We show how to compute, for each possible degree, the Pythagorean hodograph curve of a given perimeter enclosing the greatest area.
► The existence and construction of smooth solutions is discussed, obtaining a relationship with an interesting sequence of Appell polynomials.