地球曲率對水平距離影響

The Influence of Earth Curvature to Horizontal Distance

圓之「弧長」與「弦長」的差異，是數學教學中的基本項目。「水平直線距離」與「地球參考面投影距離」的化算，也是測量教學基本內涵中一項。但是在計算面，「距離」的部分可以有不同的定義場景，由而產生混淆。本文嘗試分辨，並探討異同，除了希望提供初學者參考，亦期望能夠提醒教學者，差異與誤解可能生成之處。為期數學演算之簡化，本文探討之地球參考體為「圓球」。

The difference between arc length and chord length of a circle is a fundamental concept. Likewise, the distinction between straight horizontal distance and the distance on a reference globe is also basic knowledge. But, there are different definitions on the reduction for the distance. Consequently, confusion could arise. This note clarifies variations in formulating the reduction, not just for those who are new to surveying, but also remind teachers of this confusion. For the simplicity in mathematical formulation and computation, a sphere is used as the reference globe.