Problem

Source: Iranian National Olympiad (3rd Round) 2008

Tags: algebra, polynomial, geometry, perimeter, analytic geometry, function, parameterization



=A subset $ S$ of $ \mathbb R^2$ is called an algebraic set if and only if there is a polynomial $ p(x,y)\in\mathbb R[x,y]$ such that \[ S = \{(x,y)\in\mathbb R^2|p(x,y) = 0\} \] Are the following subsets of plane an algebraic sets? 1. A square 2. A closed half-circle