论文标题
在角度及其单位的维度上
On the dimension of angles and their units
论文作者
论文摘要
我们研究了具有自身尺寸的角度的含义，就像长度，质量，{\ it等相同的意义，}涉及角度角度或指数函数的科学应用中的常规实践是假设该论点是弧度单位表示角度的数值部分。还假定函数是相应的基于Radian的版本。这些（通常不明显的）假设通常允许一个人对待角度，就像它们没有尺寸和没有单位一样，这种方法有时会带来严重的困难。在这里，我们考虑了角度的任意单元以及三角和指数函数的相应概括。这样的概括使功能完成，即与任何特定的角度选择无关。它们还为在计算机代数程序中包含角度单位提供了一个一致的框架。
We examine implications of angles having their own dimension, in the same sense as do lengths, masses, {\it etc.} The conventional practice in scientific applications involving trigonometric or exponential functions of angles is to assume that the argument is the numerical part of the angle when expressed in units of radians. It is also assumed that the functions are the corresponding radian-based versions. These (usually unstated) assumptions generally allow one to treat angles as if they had no dimension and no units, an approach that sometimes leads to serious difficulties. Here we consider arbitrary units for angles and the corresponding generalizations of the trigonometric and exponential functions. Such generalizations make the functions complete, that is, independent of any particular choice of unit for angles. They also provide a consistent framework for including angle units in computer algebra programs.
