Geometric solution of quintic equations

Question

There are many method of geometric solution of quadratic equations (for example Carlyle Circle).

Does there exist similar method for the quintic equation?

Answer 1

None that I am aware of, but you might find references in this overflow answer helpful and interesting.

Answer 2

If you mean geometric constructions with ruler and compass, then there can't be any such methods because $5$ is not a power of $2$. This is a weaker version of the fact that the general quintic is not solvable by radicals.

For other geometric methods, see the book Geometry of the Quintic by Shurman.