等角螺线的光路几何
The Geometry of Light Paths for Equiangular Spirals
摘要：
首先简要介绍了几何微积分及其对等角螺旋线、反射和旋转的描述。然后，单，双反射在这样的螺旋调查。它证明适合于区分相对于径向方向的\textit{right}和\textit{left}的入射。讨论了等角螺线中光的几何传播特性，以及逃逸条件和逃逸特性。最后，从源位置的右和左入射的依赖性进行检查，揭示了一个定义良好的内部\textit{critical}曲线，它划定了纯右入射传播的区域。这条临界曲线与原来的等角螺线是自相似的。
英文摘要：
First geometric calculus alongside its description of equiangular spirals, reflections and rotations is introduced briefly. Then single and double reflections at such a spiral are investigated. It proves suitable to distinguish incidence from the \textit{right} and \textit{left} relative to the radial direction. The properties of geometric light propagation inside the equiangular spiral are discussed, as well as escape conditions and characteristics. Finally the dependence of right and left incidence from the source locations are examined, revealing a well defined inner \textit{critical} curve, which delimits the area of purely right incident propagation. This critical curve is self similar to the original equiangular spiral.
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