摘要:勾股定理在数学领域有着举足轻重的地位，是解决问题的很好工具。本文主要论述了勾股定理的历史并总结些其比较常见的证明方法和推广，另外通过分析勾股定理在二维、三维等空间上的推广，从而给出其与几何射影之间的关系。

关键词：勾股定理; 证明; 推广; 空间; 射影

Abstract:The Pythagorean Theorem in mathematics has a significant place; it is a good tool to solve the problem. This paper mainly discusses the history of the Pythagorean and summarizes some of the more common methods of proof method and promotion, the other by analyzing the Pythagorean theorem in two-dimensional, three-dimensional space, such as the promotion, which gives its geometric projective relationships.

Keywords: The Pythagorean; Proof; generalization; Space; Projective