Galaxies are the basic components of the universe. A massive Hubble Space Telescope photos survey reveals that the diversity of galaxies in the early universe was as varied as the many galaxy types seen today. Therefore, understanding galaxies is the great challenge to humans. This paper deals with the disk-typed galaxies which is called spirals. In longer wavelength image, galaxy arms are mostly gone, and spiral galaxies fall to two types: ordinary and barred. The ordinary ones are basically an axi-symmetric disk whose stellar density decreases exponentially outwards. It is called the exponential disk. It is straightforward to show that any exponential disk has infinite nets of orthogonal curves such that the stellar density on one side of each curve is in constant ratio to the density on the other side of the curve. These curves are call proportion curves or Darwin curves. It happens that the Darwin curves of exponential disk are all golden spirals. Amazingly, astronomers found out that the arms of ordinary spiral galaxies are all golden spirals. Therefore, I had a proposition in 2004 that a two dimensional structure is called a rational one if there exists at least one orthogonal net of Darwin curves in the structure plane. Now in this paper, the mathematical solution to rational structure is completely obtained. We prove that rational structure is unique.