本文从动态欧氏几何框架出发,论证法向移动操作不仅是欧氏空间内维度升级的唯一途径,更具跨几何体系的普遍适用性。进一步指出,经典几何学中"平行"的概念在不同操作起源的框架下呈现出截然不同的内涵:平行不是空间中的位置关系,而是不同起源操作的必然表现。本文还将动态几何的操作机制延伸至宇宙学领域,提出宇宙时空本身即由初始点的多重法向移动操作构建,球面膨胀即为球面自身的法向移动。 This paper starts from the framework of dynamic Euclidean geometry, demonstrating that normal-direction movement operation is not only the sole pathway for dimensional upgrade within Euclidean space, but also possesses universal applicability across geometric systems. Furthermore, it points out that the concept of "parallelism" in classical geometry takes on a completely different connotation under frameworks with different operational origins: parallelism is not a positional relationship in space, but an inevitable manifestation of different originating operations. This paper also extends the operational mechanism of dynamic geometry to the field of cosmology, proposing that cosmic spacetime itself is constructed by multiple normal-direction movement operations of an initial point, and that spherical expansion is the normal-direction movement of the spherical surface itself. ---Note: Some parts of this paper belong to the author's habitual personal reflections on the nature of the world, containing speculative and imaginative elements. They are not intended as rigorous academic communication, but rather as a display of personal thinking, offered for further discussion among like-minded enthusiasts. The core ideas, arguments, and all Chinese text of this paper are solely the author's original work. Due to the author's limited proficiency in English, particularly in mathematical English, the English translations throughout this paper were produced with the assistance of AI language tools. Any inaccuracies or infelicities in the English expression remain the author's responsibility.
zhigang zhang (Sun,) studied this question.