Protein is one of the most important macromolecules in structural biology. Its three-dimensional structure is uniquely determined by its amino-acid sequence. Due to large number of degrees of freedom and enormous diversity, it is important to seek universal geometric measures to describe the overall structure of proteins. Gauss Integral and its related quantities are shown to be capable of describing important features of protein structures on different levels. On the atomic level, the Gauss Integral provides a simple measure to illustrate the orientational relation between different atom groups. It can be viewed as a generalization of the Ramachandran map, and it also reveals several novel relations between backbone atoms. On the other hand, Gauss Integrals can be treated as a set of collective quantities that capture the overall shape of proteins. By comparing the values of Gauss Integrals, different types of proteins can be classified in accordance with the results of manually classified structure database.