折纸是一门古老的艺术，广泛应用于建筑绘画等领域中.从1989年Huzita提出了折纸的公理系统开始，折纸与数学结合在一起成为了一门新的学科折纸几何（Origami）.本文分两个部分来讨论折纸公理系统，第一部分是将折纸公理系统数理化，将其与复数域结合起来，探究相关的性质.通过逐一添加公理完善折纸数理系统，同时与我们标准尺规作图所构造的数理系统做比较，得到相关的结论；第二部分是通过将折纸公理代数化来初步探讨折纸公理系统的完备性，并对黄燕平女士和李秉彝先生共同编著的《折纸与数学》中的公理系统进行完善和改进.

Paper folding is an ancient art, which is widely used in the field of architectural painting and so on. Since 1989, Huzita proposed the axiom system of origami, and then the combination of origami and mathematics has become a new subject of origami.This paper is divided into two parts to discuss the origami axiom system.In the first part, the paper makes a number systematic study of the axiom system of paper folding.An analysis of the hierarchy of fields which can be constructed using different axioms systems is detailed in this part.In the second part, we will discuss the completeness of the axiom system by using algebra of origami axioms and improve a the axiom system of "origami and mathematics" edited by Ms. Huang Yanping and Mr. Li Bingy.