Rational structure in two dimension means that not only there exists an orthogonal net of curves in the plane but also, for each curve, the stellar density on one side of the curve is in constant ratio to the density on the other side of the curve. Such a curve is called a proportion curve or a Darwin curve. Such a distribution of matter is called a rational structure. Spiral galaxies are blended with dust and gas. Their longer wavelength (e.g. infrared) images present mainly the stellar distribution, which is called the naked galaxies. Jin He found many evidences that galaxies are rational stellar distribution. We list a few examples. Firstly, galaxy components (disks and bars) can be fitted with rational structure. Secondly, spiral arms can be fitted with Darwin curves. Thirdly, rational structure dictates New Universal Gravity which explains constant rotation curves simply and elegantly. This article presents the systematic theory of rational structure, its general solution and geometric meaning. A preliminary application to spiral galaxies is also discussed.