## Exact and Intuitive Geometry Explanation: Why Does a Half-angle-rotation in Spin or Quaternion Space Correspond to the Whole-angle-rotation in Normal 3D Space?

**Authors:** Hongbing Zhang

Why does a half-angle-rotation in quaternion space or spin space correspond to a whole-angle-rotation in normal 3D space? The question is equivalent to why a half angle in the representation of SU(2) corresponds to a whole angle in the representation of SO(3). Usually we use the computation of the abstract mathematics to answer the question. But now I will give an exact and intuitive geometry-explanation on it in this paper.

**Comments:** 18 Pages. Please Indicate This Source From Hongbing Zhang When Cite the Contents in Works of Sience or Popular Sience

**Download:** **PDF**

### Submission history

[v1] 2018-10-21 03:08:17

[v2] 2018-10-22 05:26:02

[v3] 2018-10-23 10:40:48

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