  Padua points is a family of points on the square $[-1,1]^2$ given by explicit
formulas that admits unique Lagrange interpolation by bivariate polynomials.
The interpolation polynomials and cubature formulas based on the Padua points
are studied from an ideal theoretic point of view, which leads to the discovery
of a compact formula for the interpolation polynomials. The $L^p$ convergence
of the interpolation polynomials is also studied.
